commit 86675018a868bbaf614652f422819c21a62d3319 Author: Nicolas MASSE Date: Wed Sep 11 11:36:25 2019 +0200 migration from svn diff --git a/doc/Makefile b/doc/Makefile new file mode 100755 index 0000000..08f941a --- /dev/null +++ b/doc/Makefile @@ -0,0 +1,22 @@ +SUBDIRS := $(wildcard doc-*) + +help: + @echo "Usages: make " + @echo " all : build all documentations" + @echo " new-doc : create a new documentation from a template" + @echo " clean : clean all documentations" + +all: $(SUBDIRS) + +$(SUBDIRS): + make -C $@ all + +clean: + @for i in $(SUBDIRS); do make -C "$$i" clean || exit 1; done + +new-doc: template + @echo "Enter the name of your documentation (no space, special chars, etc.): " + @echo -n "name> " ; read name ; echo "Creating doc-$$name..." ; cp -r template "doc-$$name" + +.PHONY: $(SUBDIRS) new-doc all help clean + diff --git a/doc/doc-dpa-ensi/Makefile b/doc/doc-dpa-ensi/Makefile new file mode 120000 index 0000000..3a269a0 --- /dev/null +++ b/doc/doc-dpa-ensi/Makefile @@ 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+ nicolas27.masse@laposte.net + + + + + + Thomas + LIMIN + ENSICAEN + + thomas.limin@laposte.net + + + + + + Les fabricants de matériels "sensibles" ont + besoin d'outils à même d'évaluer les performances des + contre-mesures face aux attaques par canaux secondaires. Ce + rapport de projet détaille notre travail autour d'un + laboratoire d'attaques par analyse de courant pour la société + Ingenico. + + + Mots clés : Analyse de courant, DPA, Side Channel, Laboratoire d'attaques. + + + + + + "Sensitive" hardware's manufacturers need a tool + to evaluate the achievement of the countermesures against side channel + attacks. This project report details our work about an attack laboratory + based on power analysis for the company Ingenico. + + + + + + + + Remerciements + + Nous avons bénéficié du soutien et des conseils de nombreuses + personnes tout au long de ce projet. Qu'elles en soient ici + remerciées. + + + + + + M. NACCACHE, Chief scientist chez Ingénico, notre tuteur + entreprise, pour nous avoir confié ce projet passionnant et + pour avoir orienté nos recherches. + + + + + + M. OTMANI, professeur à l'ENSICAEN, notre tuteur + école, pour ses conseils et le temps qu'il a consacré au + suivi du projet. + + + + + + M. CUOZZO et M. PASQUET, professeurs à l'ENSICAEN, + pour leur aide précieuse. + + + + + + M. PAILLIER, chercheur chez Gemalto, pour nous avoir + fourni des informations et un ensemble de données pour + appliquer la DPA et la CPA. + + + + + + M. EL HAIDACHE et M. QEBIBO, élève ingénieurs ENSICAEN, + spécialité électronique, pour avoir pris en charge la partie + acquisition du laboratoire d'attaques. + + + + + + + + + + Introduction + + La troisième année de cycle ingénieur à l'ENSICAEN nous + a offert la possibilité de nous impliquer dans un projet de fin + d'étude en lien avec le monde professionnel. Issus de la + spécialité monétique et sécurité des systèmes, nous avons travaillé + avec la société Ingénico, spécialiste mondial des terminaux de + paiement et des transactions sécurisées. + + Les systèmes dont la sécurité revêt un caractère critique, + comme c'est le cas pour les terminaux de paiement électronique + doivent, depuis peu, faire face à des attaques qui dépassent le + cadre de la cryptanalyse classique. En effet, l'aspect + matériel et électronique est pris en compte par les cryptanalystes, + par le biais de la mesure du temps d'exécution, de + l'électricité consommée ou des émanations électro-magnétiques + (voir ). Ces informations issues des + "canaux secondaires" divulguent, une fois analysées, une + part souvent non négligeable des secrets. + + Face à cette menace, des contre mesures efficaces doivent + être intégrées aux matériels. Ingénico est impliqué dans ce + processus, et doit à tout moment s'assurer de + l'efficacité de leur parades. Un outil adapté leur étant + nécessaire, Ingenico a proposé le développement d'un + laboratoire d'attaques par analyse de courant + + Ce projet a donc pour objectif la réalisation d'un outil + permettant d'appliquer des attaques par + DPADifferential Power Analysis, attaque par analyse + différentielle de courant. Nous approfondirons + dans une première partie le sujet, le contexte et + l'organisation du projet. La seconde partie sera consacrée aux + détails des attaques par canaux secondaires. Elle explicitera les + fondements et les principes de base de ces attaques, puis + quantifiera leur efficacité. La troisième partie s'appliquera + à présenter le travail réalisé et les difficultés surmontées, puis + concluera en dressant l'état d'avancement du + laboratoire. + + + + + + Présentation du projet + + + + + + Contexte + + La sécurité des télécommunications repose sur la fiabilité + des cryptosystèmes employés et sur la non divulgation des clefs + de chiffrement/déchiffrement. Principalement axée sur la + recherche des faiblesses intrinsèques des algorithmes utilisés, + la cryptanalyse s'intéresse depuis peu au matériel + supportant les applications cryptographiques. En effet, bien que + souvent considérés comme des environnements clos et dignes de + confiance, les composants électroniques peuvent eux aussi laisser + échapper des informations concernant les secrets manipulés. Les + attaques basées sur ce constat, regroupées sous la dénomination + "attaque par canal secondaire" (Side Channel Attack) + peuvent mettre à bas des cryptosystèmes pourtant réputés + surs. + + + + + + Origine de la proposition + + Le sujet émane de la société Ingenico, spécialiste mondial + des solutions de transactions sécurisées. + + Créé en France en 1980, le groupe est maintenant implanté + dans toute l'Europe de l'ouest, mais aussi aux + États-Unis,en Amérique latine, en Chine, au Japon, en Australie + et dans de nombreux autres pays d'Europe de l'Est, + d'Asie et d'Afrique. + + Ingenico détient la base installée de terminaux de paiement + (plus de 350.000 appareils) la plus importante de France. La + fusion-absorption de MoneyLine par Ingenico intervenue le 31 + octobre 2006 a fait en outre d'Ingenico le leader des + solutions monétiques pour la grande distribution et le commerce + organisé. + + + + + + Intérêt du projet + + Impliqué dans le développement et la fabrication de + terminaux de paiement, Ingenico se trouve confronté, en tant que + fournisseur de matériels effectuant des opérations + cryptographiques sensibles (transactions bancaires), aux + éventuelles fuites d'information engendrées par des attaques + par canaux secondaires. La mise en place de contremesures est + indispensable, tout comme la mesure de leur efficacité en vue + d'obtenir les certifications nécessaires. + +
+ + Place du laboratoire d'attaques dans la chaîne de + certification + + +
+ + L'attaque par canal secondaire la plus efficace à ce + jour reposant sur une analyse de la consommation électrique des + composants, Ingénico doit se doter d'un laboratoire + d'attaques par analyse de courant. Ce laboratoire doit être + capable d'appliquer les attaques en vue d'apprécier la + résistances des contres-mesures, logicielles ou matérielles + intégrées aux composants. + + Disposer en interne d'un tel outil permettra à + Ingenico d'effectuer des tests poussés de ses produits avant + soumission aux organismes de certification, et ainsi de + s'assurer d'obtenir rapidement les autorisations de + mise sur le marché. En effet, le processus de certification est + un processus qui peut être long et coûteux, d'autant plus en + cas de non conformité du produit. Il est donc impératif pour + Ingenico de proposer à la certification des produits fortement + testés pour réduire le "time to market". + + + + + + Objectifs du projet + + Il s'agit de mettre au point un laboratoire de test + permettant l'évaluation de la sécurité des composants de + terminaux face aux attaques par analyse de courant. La résistance + sera évaluée en fonction du nombre de couples données + manipulées/traces de consommations nécessaires pour obtenir le + secret. Lorsque ce nombre surpasse ce qu'il est possible + d'obtenir (cette quantité peut, par exemple, excéder la + durée de vie de la carte à puce), alors il est possible de + conclure que les contres mesures sont efficaces. + + Le laboratoire d'attaque peut se décomposer en deux modules distincts + + Le premier module, appelé "chaîne d'acquisition" devra permettre + la capture des consommations électriques d'une maquette équippée d'un + microprocesseur ARM. ARM est le type de microprocesseur retenu par Ingenico car + c'est la principale architecture embarquée dans les terminaux de paiement + électronique. La chaîne d'acquisition se compose: + + + + + + D'un point de mesure de la consommation de courant sur la maquette. + Une version simple peut se résumer à une résistance de faible impédance + placée entre l'alimentation et la broche Vcc du microprocesseur. La tension + mesurée aux bornes de cette résistance permet d'obtenir la consommation. + + + + + + + D'un oscilloscope numérique permettant un échantillonnage haute fréquence + (de l'ordre de 500 Mhz) et capable de stocker temporairement tous les échantillons + + + + + + + D'un ordinateur relié à l'oscilloscope pour récupérer en quasi temps réel les + mesures, et programmé pour stocker ces résultats pour exploitation ultérieure + (lot de fichiers, type trace001, trace002 etc...) + + + + + + D'une méthode de synchronisation entre l'algorithme de + chiffrement s'exécutant sur la maquette et l'oscilloscope, afin d'obtenir des + traces de consommation correspondant toutes à la même phase de l'algorithme. + + + + + + + + + Le second module correspond aux attaques cryptanalytiques. Il repose sur + l'implémentation d'algorithmes d'attaque. Ces programmes seront exécutés sur une + machine distincte et s'appuieront sur les données récoltées par la chaîne + d'acquisition pour extraire les secrets de la simple consommation de courant. + Les attaques qui seront implémentées s'articuleront autour de: + + + + + + + Attaque par analyse différentielle de courant, dite DPA (Differential + Power Analysis) + + + + + + + + Attaque par analyse de la corrélation du courant, dite CPA (Correlation + Power Analysis) + + + + + La réalisation de ce second module est le point central de notre projet. + + + + + + + Moyens + + Étant en filière informatique, nous disposons d'une journée et demi par + semaine pour travailler le projet : le lundi et le jeudi matin. Mais + suivant par ailleurs les cours de Master Recherche Algorithmes et + Modèles de l'Information le lundi, nous sommes obligés de + répartir l'équivalent d'une journée de travail sur la + semaine. Au total, nous représentons 3 jours-homme par semaine. + Le projet s'étalant de la semaine 4 (9 octobre, calendrier + ensicaen) à la semaine 17 (5 février, calendrier ensicaen), il + est réparti sur 13 semaines. De plus, 5 jours entiers sont dédiés + au projet : 8 au 12 janvier 2007 (10 jours-homme). Nous disposons + donc, théoriquement pour ce projet de 49 jours hommes. Des + modifications d'emploi du temps ont toutefois réduit ce + capital. + + Afin de nous prêter main forte, deux élèves de la filière + électronique nous ont rejoint et contribuent au projet à + hauteur de 34 jours-homme. Les moyens humains alloués au projet + totalisent donc 83 jours-homme. + + + + + + Répartition du travail + + L'objectif global du projet est de mettre en place un + outil qui permet de tester la résistance d'un dispositif + cryptographique aux attaques par DPA. Il est divisé en deux + sous-objectifs : acquérir les traces de courant (acquisition) et + les traiter (traitement). L'aquisition est réalisée par M. + EL HAIDACHE et M. QEBIBO, élèves ingénieurs issus de la filière électronique. La + réalisation du traitement nous incombe. + + Afin de permettre un travail délocalisé dans le temps et + dans l'espace, nous avons défini en collaboration avec nos + collègues les pré-requis et les objectifs de + chacun des sous-objectifs. + +
+ + Répartition du travail + + +
+ + + + Pré-requis de l'acquisition + + Pendant la phase d'acquisition, + l'expérimentateur a à sa disposition un oscilloscope + numérique avec une connexion PC, une sonde et les logiciels + adéquats (Matlab / Labview / Mathematica). De plus, on émet + l'hypothèse que le calcul cryptographique peut être + délimité facilement (utilisation des + GPIOGeneral Purpose Input + Output. Il est possible de programmer l'algorithme de chiffrement de sorte qu'il + envoie une information via ce port de communication au début et à la fin du + chiffrement. Cette information peut alors être utilisée pour synchroniser la chaîne + d'acquisition. par exemple). + + + + + + Objectif de l'acquisition / pré-requis du + traitement + + Le but de l'acquisition est de fournir des traces de + courant associées à leur chiffré (la trace doit être délimitée + et utilisable informatiquement). Ces données seront utilisées + par la partie traitement. + + + + + + Objectif du traitement + + La phase de traitement a pour but de déterminer le nombre + de traces de courant nécessaires pour trouver la clé d'une + opération cryptographique. + + + + + + + + + + Travail effectué + + + + Organisation + + Le projet étant divisé en deux grandes parties (acquisition + et traitement), chacune traitée par un groupe de personnes + différent, il était primordial de trouver un outil de + communication simple et efficace. Nous avons décidé, après étude, + d'utiliser le logiciel Trac. C'est une application web + de gestion des sources (SCM) et de gestion de projet intégré. Il + est très adapté pour les petits projets (quelques dizaines de + personnes) et est utilisé par beaucoup de projets Open Source. Il + nous permet de travailler de manière désynchronisée dans le temps + et dans l'espace avec nos collègues, via + l'url + . + + + + + + Diagramme de Gantt + + + + La + + présente les différentes tâches de notre projet. La + signification des couleurs est la suivante: + + + + + Le vert correspond aux tâches communes de + documentation + + + + + + Le jaune définit les tâches propres à la partie + acquisition + + + + + + En bleu sont regroupées les tâches de traitement, + c'est le corps de notre travail + + + + + + + + La barre noire au centre de chaque tâche représente son + état d'avancement. + +
+ + Diagramme de Gantt + + +
+ + Durant l'étape "recherche documentaire" nous + avons réalisé une étude approfondie des techniques d'attaque + par canaux secondaires, qui comprend les attaques par analyse de + courant (SPA, DPA, CPA). Elle fait l'objet du + + + + + Élaboration du diagramme de Gantt + + Suite à la spécification des besoins de ce projet, nous + nous sommes appliqués à définir une liste précise de tâches + finement délimitées et à les échelonner dans le temps en + fonction de leurs liens de précédence. + + Cette approche nous a permis, d'une part, + d'évaluer plus précisément le temps nécessaire pour mener à + bien le projet. D'autre part, nous avons pu mesurer au fur + et à mesure l'avancée du projet, et ainsi éviter + l'effet tunnel. + + Un dernier avantage de ce découpage est qu'il nous a + été possible de recetter individuellement les tâches, des tests + ayant été écrits pour valider le bon fonctionnement de chaque + nouvelle tâche. + + + + + + Suivi des prévisions + + L'importance que nous avons accordé à la + plannification du projet nous a permis de bien démarrer le + projet et de pouvoir accorder un temps suffisant à chaque + partie, sans craindre la prise de retard. + + Dans un premier temps, nous avons pu réaliser nos tâches + dans le temps imparti, mais les problèmes que nous avons + rencontrés, en particulier les soucis autour de la fourniture de + la maquette et des algorithmes ont finalement eu raison de + notre ponctualité. + + + + + + + + Problèmes rencontrés + + Au fur et à mesure de l'avancement du projet nous + avons rencontré un certain nombre de difficultés. + + + + Traitement dépendant de l'acquisition + + Le premier problème auquel nous avons dû faire face est + la dépendance des parties acquisition et traitement. En effet, + afin de vérifier la validité de nos algorithmes nous avions + besoin des données (traces de courant et messages chiffrés) + produites par l'équipe travaillant sur la partie acquisition. Il est + clair que nous ne pouvions attendre que nos collègues aient + fini leur partie pour commencer à travailler. Nous avons alors + décidé d'utiliser un modèle mathématique pour générer des + traces de courant. Ce modèle étant assez éloigné de la réalité, + un second problème s'est alors posé : l'algorithme ne + se comportait pas comme prévu, nous obligeant alors à appliquer + du traitement de signal à certains moments de + l'algorithme. + + + + + + Implémentation sous Mathematica + + Initialement, le descriptif du projet prévoyait une + implémentation des algorithmes sous Mathematica, un langage de + calcul formel. L'obtention de ce logiciel nous aurait très + certainement posé problème, c'est pouquoi nous lui avons + préféré le logiciel de calcul matriciel Matlab, dont une + version est fournie par l'école. De plus, ayant déjà + utilisé Matlab auparavant, nous n'avions pas à apprendre + un nouveau langage. Nous avons mentionné ce point dans le + cahier des charges et cela a été validé. + + + + + + Absence de la maquette ARM + + Dès le début du projet, il a été convenu que nous aurions + accès à une maquette de test afin de recueillir les données + nécessaires à la validation de notre travail. Cette maquette + comporte un microprocesseur de type ARM sur lequel nos + collègues auraient pu brancher un oscilloscope numérique et + acquérir les traces de courant. Malheureusement, malgré nos + demandes répétées et l'intervention de M. CUOZZO auprès + d'Ingénico nous n'avons toujours pas reçu cette + maquette. Son absence fût fort dommageable pour + l'avancement du projet. En effet, sans elle la validation + des algorithmes fût lente et difficile. + + Ne pouvant obtenir la maquette auprès d'Ingénico, nous nous + sommes alors tournés vers Pascal PAILLIER, chercheur chez Gemalto, lors de + son intervention à l'université de CAEN. Il nous a aimablement fourni + des informations et un ensemble de données permettant de tester nos + implémentations. Ces données comprennent : + + + 40 traces d'émanation radio-fréquence (100 µs échantillonnées + à 500 MHz) d'une carte à puce exécutant un DES, + + 5000 traces de courant d'une carte à puce exécutant une + exponentiation modulaire RSA. + + + + + + + + + + État d'avancement + + Comme convenu dans le cahier des charges, nous avons + implémenté les algorithmes nécessaires à la mise en place du + laboratoire d'attaques. Néanmoins les tâches nécessitant la + maquette ARM n'ont pu être menées à terme (benchmarking + d'algorithmes, prise en main de la plateforme ARM, tests et + validation). Au vu de l'avancement du projet et du temps + restant, nous avons choisi de ne pas débuter la phase + d'implémentation. De plus, les algorithmes n'ayant pas + pu être validés rigoureusement, il serait futile de vouloir les + transcrire dans un langage bas niveau, toute correction ou + amélioration impliquant de très lourdes modifications dans le + code transcrit. + + Afin de palier à l'absence de validation rigoureuse (due à + l'absence de la maquette) et + d'implémentation dans un langage bas niveau, nous proposons + à Ingénico de procéder à la validation des algorithmes au sein de + leur laboratoire, d'y appliquer les éventuelles + modifications et enfin d'utiliser l'outil + Matlab CompilerMatlab + Compiler permet de traduire automatiquement du code Matlab en + C/C++, Java ou .Net afin de transcrire + automatiquement le code Matlab dans un langage bas niveau. Le + code résultant peut ensuite être intégré à une application + métier. + + + + + + Descriptif du produit livré + + Le produit que nous livrons à Ingénico est composé de deux + ensembles : les algorithmes du laboratoire d'attaques et une + documentation. Les algorithmes sont implémentés à l'aide de + Matlab. Ils comprennent une implémentation du DES, de la DPA, de + la CPA et un modèle de consommation de courant. La documentation + détaillée des attaques par analyse de courant est présentée + . Elle est aussi disponible en ligne + La documentation est accessible via , + ce présent rapport et une soutenance orale la complètant. + + + + + + Résultats obtenus + + + L'objectif du laboratoire d'attaque est de tester l'efficacité des + contremesures. Ainsi il doit être en mesure de trouver le secret (en totalité ou + en partie) utilisé lors d'une opération cryptographique. + + + + Cet objectif est atteint. En effet, notre implémentation de l'algorithme + de la DPA a, avec succès, retrouvé une sous-clé DES (48 bits) en + utilisant environ 200 traces de courant, et ce en 10 minutes sur un PC personnel. + + + + Notre implémentation de l'algorithme de la CPA a quant à elle + retrouvé une sous-clé DES en utilisant 40 traces d'émanations + radio-fréquence, et ce en 20 minutes sur un PC personnel. + + + + + + + + Analyse de courant + + Traditionnellement, les cryptanalystes se basent sur les + propriétés mathématiques des algorithmes cryptographiques pour en + trouver les faiblesses, mais depuis peu sont apparues de nouvelles + méthodes de cryptanalyse, visant non plus les propriétés + mathématiques mais leur implémentation. Cette nouvelle approche + rassemble les attaques par canal secondaire. On dit qu'une + telle attaque est possible lorsqu'un attaquant a accès à de + l'informations fournie à son insu par l'implémentation + d'un algorithme cryptographique. Ces informations ne sont ni + le texte clair ni le texte chiffré, c'est pour cette raison + que l'on parle de canal secondaire. (cf. + et ) + +
+ + Principe des canaux secondaires + + +
+ + + + Il existe plusieurs canaux secondaires : + + + + + la consommation de courant + + + + + + les radiations électromagnétiques + + + + + + les sons (pour les systèmes mécaniques) + + + + + + les informations temporelles (cf. + ) + + + + + + + + En 1998 Paul Kocher a annoncé une nouvelle méthode de + cryptanalyse : l'attaque par analyse de courant. Cette attaque + repose sur le fait que les circuits intégrés sont composés de + portes logiques qui, lorsqu'elles changent d'état, + consomment une certaine quantité de courant. En mesurant cette + consommation et en la mettant en rapport avec certains bits des + données de la clé secrète, on peut retrouver cette dernière. Par + exemple, il peut arriver que lors de l'exécution d'un + algorithme, la condition d'un branchement s'appuie sur la + valeur d'un bit d'une information secrète, comme la clef + par exemple. Les sauts engendrant des différences importantes dans + la consommation de courant, il est relativement trivial de détecter + si le saut a eu lieu, et donc d'obtenir de l'information + sur la valeur utilisée dans la condition du branchement. Il existe + différents types d'attaques, que l'on peut classer en + deux catégories : les attaques simples et les attaques + différentielles. + + + + Modèle de fuite + + La est un modèle simplifié + d'une carte à puce qui permet de mieux comprendre + l'origine des fuites d'information. La carte est + normalement alimentée en 5V entre Vdd et Vss mais si l'on + place une faible résistance (quelques Ohms) entre Vdd et la + masse, on peut mesurer la consommation de courant à l'aide + d'un oscilloscope. + + Dans un circuit CMOS la consommation de courant a + majoritairement lieu lors des changements d'état. Lorsque + Vgate change de voltage, les transistors Q1 et Q2 sont tous les + deux conducteurs pendant un très court instant, créant ainsi une + légère surconsommation de courant. Pendant ce temps, le + condensateur Cload est déchargé (ou chargé) diminuant (ou + augmentant) la consommation de courant. Il y a ainsi deux types + de fuite d'information : celles liées au poids de Hamming + (état de Cload) et celles liées au nombre de transitions + (changement d'état de Vgate). + +
+ + Mesure de la consommation de courant + + +
+ + Une grande partie des fuites d'information est due + aux bus de communication du microprocesseur. Il est intéressant + de noter que les bus préchargés (cf. + ) sont très intéressants lors des attaques par analyse de + courant. En effet, avec ce type de bus on connait toujours la + valeur présente sur ce dernier avant une transition. Ainsi, le + nombre de zéros chargés sur le bus détermine la quantité de + courant déchargée (l'état de Cload est la source de courant + prédominante). + + Lorsque le système analysé n'utilise pas les bus + préchargés, il est fort probable que la valeur précédente du bus + soit une constante (une adresse mémoire par exemple). On peut + alors déterminer par mesure du courant le nombre de changements + d'état sur le bus (le changement d'état de Vgate est la + source de courant prédominante). Pour de plus amples détails, + voir . + + + + + + Attaques par analyse simple de courant + + Dans les attaques par SPA, on mesure le courant consommé de + manière très précise dans le temps (haute fréquence + d'échantillonnage) puis, visuellement, on identifie les + différentes parties de l'algorithme et enfin on analyse les + différentes opérations effectuées afin d'en déduire des + informations sur le secret. + + Par exemple, la forme de la courbe de courant sur la + permet de retrouver tous les bits de la + clé secrète d utilisée lors d'une + signature RSA. En effet, l'exponentiation modulaire + s = md mod + e est souvent implémentée à l'aide de + l'algorithme Carré-Multiplier ("Square and + Multiply" en anglais). Ce dernier consiste, pour chacun des + bits de l'exposant d (la clé secrète), + à mettre la variable s au carré et si et + seulement si ce bit vaut 1, la multiplier par + m. Ainsi, il suffit d'observer la trace + de courant pour différencier les carrés (ils sont identiques) des + multiplications (elles ne se ressemblent pas et sont toujours + suivies d'un carré). Il également intéressant de noter que le + premier bit valant toujours 1, les deux premières opérations sont + toujours un carré puis une multiplication. + +
+ + Attaque par SPA sur une exponentiation modulaire + RSA + + +
+ + Cette attaque a l'avantage d'être simple, mais + elle a de nombreux inconvénients : elle nécessite une haute + fréquence d'échantillonnage, elle est difficilement + automatisables et ses contremesures sont simples. + + + + + + Attaques par analyse différentielle de courant + + Cette attaque s'appuie sur des relevés de + consommation, tout comme la SPA, mais un traitement statistique + approprié permet de glaner de l'information à partir de + relevés moins précis. + +
+ + Extraction de la clé + + +
+ + Le traitement statistique s'appuie sur le maximum de + vraisemblance d'une hypothèse pour obtenir le secret. Dans + un premier temps, une analyse de l'algorithme attaqué est + nécessaire pour découper le problème en sous problèmes plus + petits, problèmes dont on connait soit l'entrée, soit la + sortie, et qui utilise un secret (méthode "diviser pour + regner"). Pour chaque sous problème, une hypothèse est faite + quand au secret qu'il manipule, puis les données connues + (entrée ou sortie) sont fournies à un oracle qui sépare en deux + groupes les relevés de consommation associés. Considérant que le + secret manipulé influe sur la consommation de courant, il est + possible de constater le bien fondé de l'hypothèse en + mesurant l'écart entre les 2 groupes de traces formés. En + effet, si l'hypothèse est correcte, l'oracle a séparé + les traces en fonction de la valeur des données inconnues (test + sur un bit: 0 ou 1 en entrée ou sortie selon la donnée connue). + La différence entre la moyenne des 2 ensembles correspond à + l'influence des données traitées (du moins un bit des + données) sur la consommation. Dans le cas où l'hypothèse est + fausse, l'oracle ne peut déterminer la donnée inconnue, et + donc ne peux classer les traces en fonction. La séparation en 2 + ensembles est quasi-aléatoire, par conséquent leur moyenne ne + présente pas de différence notable. En testant successivement + toutes les hypothèses possibles concernant un sous problème + (recherche exhaustive sur ensemble très réduit), il est possible + de détecter l'hypothèse la plus vraisemblable, celle qui + correspond à la séparation en 2 sous ensembles très différents et + d'en déduire la valeur du secret manipulé. Appliquée à + chaque sous problème, cette méthode permet d'extraire, selon + l'algorithme, tout ou partie du secret manipulé. + +
+ + La consommation varie en fonction du clair + + +
+ + Dans le cas d'un chiffrement DES, on peut + s'intéresser à la consommation de courant durant le 16ème + tour. Chaque tour utilise une sous clef (48b) dérivée de la clef + maitre (56b). La sous clef est elle même découpée en 8 morceaux + de 6 bits, qui sont utilisés pour produire les données de sortie + du tour, qui correspond, dans le cas du dernier tour, au message + chiffré. La corrélation existant entre les données en entrée, + restreintes à un bit b impliquant le morceau de sous clef cherché + et la consommation va permettre de deviner la clef. En effet, la + fonction permettant de retrouver le bit source à partir du + chiffré utilise le morceau de sous clef cherché. + + En premier lieu, il est nécessaire de récupérer des traces + de consommation électrique (consommation en fonction du temps), + associées au chiffré obtenu. Ensuite on choisit une valeur K pour + le morceau de sous clef à trouver. Cette valeur permet, à + l'aide d'une fonction permettant d'inverser + l'effet du dernier tour de DES, de trouver une partie de la + valeur d'entrée de ce tour, dont le bit b. On sépare les + traces suivant que ce bit est estimé a 0 ou 1. On calcule la + trace moyenne pour chaque groupe, puis la différence des 2 traces + moyennes. A partir de la trace différentielle, il est possible de + voir si la valeur K de la clé choisie est correcte. Explications: + si K est faux, la probabilité que le bit b, calculé à partir de K + et du chiffré, soit exacte est environ 1/2. Dans ce cas, la + séparation faite entre les traces de consommation est aléatoire, + les moyennes effectuées dans chaque sous groupe n'ont pas + de raison de différer, la trace différentielle est donc proche de + 0 (présence de bruit). Par contre, si la valeur de K est + correcte, alors b est calculé correctement, et les sous groupes + sont bien classés en fonction de l'entrée. Dans ce cas la + trace différentielle présente des pics aux endroits où la valeur + de b influe sur la consommation electrique (car la consommation + est liée aux valeurs d'entrée). + +
+ + Différence caractéristique et validité de la clé + + +
+ + Un morceau de sous clef ne comportant que 6 bits, il est + nécessaire de tester 64 possibilités pour découvrir un morceau de + sous clef. En appliquant cette méthode pour chacun des 8 morceaux + de sous clef, il est possible de la deviner avec un nombre + d'opérations finalement assez restreint. On peut ensuite en + déduire la clef maitresse, par force brute par exemple. + + + + + + Attaque par corrélation + + L'attaque par DPA permet de trouver la clé, mais elle + nécessite un nombre élevé de traces de mesures. En effet, + c'est l'influence d'un seul bit sur la + consommation qui est prise en compte. L'influence des autres + bits est alors considérée comme du bruit, qui se résorbe avec + l'augmentation du nombre de courbes. Par ailleurs, la + détection des pics au cours de la DPA est rendue difficile par + l'apparition fréquente de "pics fantômes". Ces + pics se manifestent à coté du pic principal, ou bien + apparaissent même si l'hypothèse sur la clé est fausse. La + hauteur de ces pics peut dépasser celle du pic principal, + engendrant des erreurs dans l'interprétation du résultat. + L'efficacité de la DPA repose en fait sur + l'indépendance du bit obsvervé avec les autres bits du même + mot, et sur l'absence de lien entre la consommation et le + bit observé, sauf au moment ou celui ci est effectivement + observé. Or il apparait que ces pré-requis ne sont pas respectés. + Les valeurs des bits ne sont pas indépendantes, car elle sont + assujetties au design des S-Box (dans le cas du DES), et sont + donc possiblement corrélées. Par ailleurs, les bits ne sont pas + manipulés qu'une seule fois, et leur influence se diffuse + dans le temps. Ces raisons expliquent la présence des pics + fantômes. + + Pour parer ce phénomène particulièrement génant a été + introduit le concept de CPA, ou Correlation Power Analysis (voir + ). L'idée est de mieux exploiter + le modèle de fuite, en remarquant que celui-ci crée une relation + linéaire liant la consommation et la distance de hamming entre les + données manipulées et une valeur constante, cette constante dépendant de + l'architecture. La prise en compte de cette linéarité + autorise la détection de la bonne hypothèse de sous clé (le + fonctionnement global de la DPA est inchangé) simplement par + l'observation du coefficient de corrélation maximum. + + + + L'application de la CPA suit les étapes suivantes, + lorsqu'elle est appliquée à l'algorithme DES: + + + + + Choix d'un tour (généralement le premier ou le + dernier, selon que l'on dispose de l'accès aux + messages clairs ou aux messages chiffrés) et d'une + S-Box + + + + + + Énumération des hypothèses concernant la valeur + d'une sous clé pour ce tour. + + + + + + Prendre une valeur de sous clé, calculer la valeur + des données manipulées en fonction de cette hypothèse, puis + la distance de Hamming entre cette valeur et la constante. + On obtient alors une distance Di pour chaque courbe + i. + + + + + + Calculer, pour chaque instant t, le coefficient de + corrélation entre les Di et les valeurs des courbes i à cet + instant t. Le maximum de la courbe des coefficients de + corrélation en fonction du temps est alors associé à + l'hypothèse. + + + + + + Lorsque chaque hypothèse a été traitée, + l'hypothèse qui est associée au coefficient de + corrélation le plus élevé est considérée comme la bonne + hypothèse. Un morceau de sous clé est alors trouvé. + + + + + + Les morceaux de sous clé restants sont obtenus en + réitérant les précédentes étapes sur les autres S-Box, tout + comme dans le cas de la DPA. + + + + + + + + La CPA est une approche qui permet de réduire la quantité + de courbes nécessaire tout en facilitant la détection des bonnes + hypothèses, c'est pourquoi nous avons souhaité + l'introduire dons notre laboratoire d'attaques. + + + + + + + + Conclusion + + A l'issue de ce projet, nous pouvons mettre à la disposition + d'Ingenico notre étude documentaire, ainsi qu'une implémentation + sous le logiciel Matlab des attaques par DPA et CPA. Cet ensemble + représente une part non négligeable du laboratoire d'attaques, mais il + doit toutefois, pour son utilisation en production, être associé à la + chaine d'acquisition réalisée par la seconde équipe d'élèves ingénieurs, + et disposer d'une interface de commande, qu'il reste à développer. + + Ce projet de fin d'étude a été pour nous l'occasion de nous investir + une nouvelle fois dans un projet dont l'envergure dépasse celle des + incontournables (mais néanmoins formateurs) travaux pratiques. Au contact + d'une entreprise, nous avons dû faire montre, en plus de nos compétences + techniques, de qualité d'organisation et de communication. Via la mise en + place des outils de travail collaboratif, la rédaction d'un cahier des + charges précis et le suivi régulier de la documentation et des réunions, + nous avons fait preuve du sérieux et du professionnalisme qu'Ingenico + était en droit d'attendre de notre part. + + En outre, et concernant plus particulièrement le sujet de ce projet, + nous avons découvert un pan entier de la cryptanalyse que nous ne + connaissions pas. En tant qu'étudiant spécialisé dans la sécurité + des systèmes, cela représentait un manque flagrant, surtout lorsque l'on + prend en compte l'efficacité de ces attaques par canaux secondaires. + Grâce à ce projet, nous avons pu nous documenter et implémenter nous même + avec succès quelques unes de ces attaques. Retrouver une clé DES 56 bits en + seulement vingt minutes est une expérience qui aiguisera notre perception + de la sécurité globale d'un système, et nous rappelera le soin qu'il est + nécessaire d'apporter, dans ce domaine, à tous les détails. + + + + + + Bibliographie + + Ci-dessous la liste des références utilisées lors de notre + projet. + + + + + + KOCHER + + P. , + + JAFFE + + J. , + + JUN + + B. + <emphasis>Differential Power Analysis.</emphasis> + + Cryptography Research Inc. + [en ligne]. + 1998. + + http://www.cryptography.com/resources/whitepapers/DPA.pdf + + + + + KELSEY + + J., + + SCHNEIER + + B., + + WAGNER + + D., + + HALL + + C.. + <emphasis>Side Channel Cryptanalysis of Product + Ciphers.</emphasis> + + [en ligne]. + 2000. + + http://www.schneier.com/paper-side-channel.html + + + + + BAR-EL + + H. + <emphasis>Introduction to Side Channel + Attacks.</emphasis> + + Discretix. + [en ligne]. + 2000. + + http://www.hbarel.com/publications/Introduction_To_Side_Channel_Attacks.pdf + + + + + PERCIVAL + + C. + <emphasis>Cache missing for fun and + profit.</emphasis> + + [en ligne]. + http://www.daemonology.net/papers/htt.pdf + + + + + MESSERGES + + T. S., + + DABBISH + + Ezzy A., + + SLOAN + + R. H.. + <emphasis>Investigations of Power Analysis Attacks on + Smartcards.</emphasis> + + [en ligne]. + 1999. + + http://www.usenix.org/events/smartcard99/full_papers/messerges/messerges.pdf + + + + + BRIER + + E., + + CLAVIER + + C., + + OLIVIER + + F.. + + Gemplus Card International France Security Technology + Department. + <emphasis>Correlation Power Analysis with a Leakage + Model.</emphasis> + + [en ligne]. + 2004. + + https://projects.itix.fr/studies/DPA/files/springerCryptoHardwareAndEmbeddedSystemsCHES2004.pdf + + + + + + + + + Schémas électroniques + + Sur la les broches du + port B sont préchargées par l'utilisateur à une valeur de son + choix. (Source: + http://www.fairchildsemi.com/ms/MS/MS-523.pdf) + +
+ + Bus préchargé + + +
+ + + + + Glossaire + La plupart de ces définitions sont tirées du projet Wikipedia (). + + Analyse de courant + + En cryptanalyse de matériel cryptographique, l'analyse de consommation consiste à étudier les courants et tensions entrants et sortants d'un circuit dans le but de découvrir des informations secrètes comme la clé de chiffrement. + + + + ARM + + Les processeurs ARM, Acorn RISC Machines, sont basés sur une architecture RISC 32 bits. C'est une architecture simple et performante qui a été développée par la société ARM Ltd.. + + + + Attaque par canal secondaire + + Les attaques par canaux secondaires font partie d'une vaste famille de techniques cryptanalytiques qui exploitent des propriétés inattendues d'un algorithme de cryptographie lors de son implémentation logicielle ou matérielle. + Cf. . + + + + CPA + + Correlation Power Analysis (Analyse de courant par corrélation, en français). + Cf. . + + + + DPA + + Differential Power Analysis (Analyse différentielle de courant, en français). + Cf. . + + + + Power analysis + + Voir + + + + Side Channel Attack + + Voir . + + + + SPA + + Simple Power Analysis (Analyse simple de courant). + Cf. . + + + + + + + Ce document a été rédigé avec l'éditeur de texte Emacs en utilisant le langage de description de publication Docbook, version 4.2 XML . Les différents documents ou publications en résultant ont été générés grâce, entre autres, aux logiciels libres suivants: + + + + Apache-Xerces , un analyseur XML + + + + + Apache-Xalan , un processeur de transformation XSLT + + + + + Apache-Fop , un outil de rendu dirigé par XSL + + + + + Ainsi que d'autres bibliothèques du groupe de projets XML d'Apache + + + + + + + diff --git a/doc/doc-dpa/xsl/fo.xsl b/doc/doc-dpa/xsl/fo.xsl new file mode 100755 index 0000000..5e23e01 --- /dev/null +++ b/doc/doc-dpa/xsl/fo.xsl @@ -0,0 +1,152 @@ + + + + + + + + + + + + + + + + + + + 6, bd maréchal Juin + F-14050 Caen Cedex 4 + Spécialité informatique + Option Monétique + 3e année + + + + + + + + + + + + + + + 192, Avenue Charles de Gaulle + 92200 Neuilly-Sur-Seine + http://www.ingenico.fr/ + + + + + + + + + + + + + + + + + + + + + + + Suivi Ensicaen : + OTMANI Ayoub + Suivi Entreprise : + NACCACHE David + + + + + 1er semestre 2006-2007 + + + + + + + + + + + + + + + + titlepage-even + titlepage-odd + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + diff --git a/doc/doc-dpa/xsl/html-chunked.xsl b/doc/doc-dpa/xsl/html-chunked.xsl new file mode 100755 index 0000000..4eefab5 --- /dev/null +++ b/doc/doc-dpa/xsl/html-chunked.xsl @@ -0,0 +1,9 @@ + + + + + + diff --git a/doc/doc-dpa/xsl/html-onepage.xsl b/doc/doc-dpa/xsl/html-onepage.xsl new file mode 100755 index 0000000..e927b78 --- /dev/null +++ b/doc/doc-dpa/xsl/html-onepage.xsl @@ -0,0 +1,9 @@ + + + + + + diff --git a/doc/doc-dpa/xsl/xhtml-chunked.xsl b/doc/doc-dpa/xsl/xhtml-chunked.xsl new file mode 100755 index 0000000..564c1c6 --- /dev/null +++ b/doc/doc-dpa/xsl/xhtml-chunked.xsl @@ -0,0 +1,9 @@ + + + + + + diff --git a/doc/doc-dpa/xsl/xhtml-onepage.xsl b/doc/doc-dpa/xsl/xhtml-onepage.xsl new file mode 100755 index 0000000..13406f2 --- /dev/null +++ b/doc/doc-dpa/xsl/xhtml-onepage.xsl @@ -0,0 +1,9 @@ + + + + + + diff --git a/doc/globals/Makefile b/doc/globals/Makefile new file mode 100755 index 0000000..63857e9 --- /dev/null +++ b/doc/globals/Makefile @@ -0,0 +1,124 @@ +# Environment variables +export PATH := $(HOME)/bin/fop:$(PATH) +export CLASSPATH := xsl/xsl-stylesheets/extensions/xalan25.jar + +# Do you need a proxy ? +#export FOP_OPTS := -Dhttp.proxyHost=193.100.252.20 -Dhttp.proxyPort=8080 + +# Or any setting +export FOP_OPTS := -Xmx1G -Djava.awt.headless=true + +# Target filenames +PDF_FILE := book.pdf +RTF_FILE := book.rtf +TXT_FILE := book.txt +PS_FILE := book.ps +XHTML_DIR := book-xhtml +XHTML1_DIR := onepage-xhtml +HTML_DIR := book-html +HTML1_DIR := onepage-html +XHTML_ARCH := book-xhtml.tar.bz2 +HTML_ARCH := book-html.tar.bz2 +XHTML1_ARCH := onepage-xhtml.tar.bz2 +HTML1_ARCH := onepage-html.tar.bz2 +VALIDITY_FILE := validity + + + +# Source filenames +XSL_FO_FILE := xsl/fo.xsl +XSL_XHTML_FILE := xsl/xhtml-chunked.xsl +XSL_HTML_FILE := xsl/html-chunked.xsl +XSL_XHTML1_FILE := xsl/xhtml-onepage.xsl +XSL_HTML1_FILE := xsl/html-onepage.xsl +DB_FILE := main.xml + +# Titlepage customization +TP_SPEC_FILE := xsl/titlepage.spec.xml +TP_XSL_FILE := xsl/titlepage.xsl +TP_TEMPLATE_FILE := ../globals/xsl-stylesheets/template/titlepage.xsl + +# Do you have a custom titlepage ? +TP_XSL_REAL := $(shell if test -f $(TP_SPEC_FILE); then echo $(TP_XSL_FILE); fi) + +# FOP configuration +FOP := fop +FOP_CONF := fop.xconf + +# XSLT configuration +XSLTPROC := xsltproc + +# Validity check +VALIDATOR := xmllint --noout --valid + +# Extract external entities +XML_FILES := $(wildcard include/*.xml) +DEPENDENCIES := $(TP_XSL_REAL) $(VALIDITY_FILE) + +# Default target +all: $(PDF_FILE) $(RTF_FILE) $(TXT_FILE) $(PS_FILE) $(XHTML_ARCH) $(HTML_ARCH) $(XHTML1_ARCH) $(HTML1_ARCH) + +$(VALIDITY_FILE): $(DB_FILE) $(XML_FILES) + $(VALIDATOR) $< + touch $(VALIDITY_FILE) + +$(PDF_FILE): $(DB_FILE) $(XSL_FO_FILE) $(DEPENDENCIES) + $(FOP) -c $(FOP_CONF) -xsl $(XSL_FO_FILE) -xml $< -pdf $@ + +$(RTF_FILE): $(DB_FILE) $(XSL_FO_FILE) $(DEPENDENCIES) + $(FOP) -c $(FOP_CONF) -xsl $(XSL_FO_FILE) -xml $< -rtf $@ + +$(TXT_FILE): $(DB_FILE) $(XSL_FO_FILE) $(DEPENDENCIES) + $(FOP) -c $(FOP_CONF) -xsl $(XSL_FO_FILE) -xml $< -txt $@ + +$(PS_FILE): $(DB_FILE) $(XSL_FO_FILE) $(DEPENDENCIES) + $(FOP) -c $(FOP_CONF) -xsl $(XSL_FO_FILE) -xml $< -ps $@ + +$(XHTML_DIR): $(DB_FILE) $(XSL_XHTML_FILE) $(DEPENDENCIES) + if [ ! -e $(XHTML_DIR) ]; then mkdir $(XHTML_DIR); ln -s ../img $(XHTML_DIR)/img; \ + ln -s ../../globals/xsl-stylesheets/images $(XHTML_DIR)/std-img; fi + $(XSLTPROC) $(XSL_XHTML_FILE) $< + touch $(XHTML_DIR) + +$(HTML_DIR): $(DB_FILE) $(XSL_HTML_FILE) $(DEPENDENCIES) + if [ ! -e $(HTML_DIR) ]; then mkdir $(HTML_DIR); ln -s ../img $(HTML_DIR)/img; \ + ln -s ../../globals/xsl-stylesheets/images $(HTML_DIR)/std-img; fi + $(XSLTPROC) $(XSL_HTML_FILE) $< + touch $(HTML_DIR) + +$(XHTML1_DIR): $(DB_FILE) $(XSL_XHTML1_FILE) $(DEPENDENCIES) + if [ ! -e $(XHTML_DIR) ]; then mkdir $(XHTML1_DIR); ln -s ../img $(XHTML1_DIR)/img; \ + ln -s ../../globals/xsl-stylesheets/images $(XHTML1_DIR)/std-img; fi + $(XSLTPROC) -output $@/index.xhtml $(XSL_XHTML1_FILE) $< + touch $(XHTML1_DIR) + +$(HTML1_DIR): $(DB_FILE) $(XSL_HTML1_FILE) $(DEPENDENCIES) + if [ ! -e $(HTML1_DIR) ]; then mkdir $(HTML1_DIR); ln -s ../img $(HTML1_DIR)/img; \ + ln -s ../../globals/xsl-stylesheets/images $(HTML1_DIR)/std-img; fi + $(XSLTPROC) -output $@/index.html $(XSL_HTML1_FILE) $< + touch $(HTML1_DIR) + +$(HTML_ARCH): $(HTML_DIR) + tar -jcv -h --exclude '.svn' --exclude '*.svg' -f $@ $< + +$(XHTML_ARCH): $(XHTML_DIR) + tar -jcv -h --exclude '.svn' --exclude '*.svg' -f $@ $< + +$(HTML1_ARCH): $(HTML1_DIR) + tar -jcv -h --exclude '.svn' --exclude '*.svg' -f $@ $< + +$(XHTML1_ARCH): $(XHTML1_DIR) + tar -jcv -h --exclude '.svn' --exclude '*.svg' -f $@ $< + +$(TP_XSL_FILE): $(TP_SPEC_FILE) + $(XSLTPROC) -output $@ $(TP_TEMPLATE_FILE) $< + +clean: + rm -f $(PDF_FILE) $(TP_XSL_FILE) $(VALIDITY_FILE) $(HTML_ARCH) $(XHTML_ARCH) $(RTF_FILE) $(TXT_FILE) $(PS_FILE) + rm -rf $(XHTML_DIR) $(HTML_DIR) $(HTML1_DIR) $(XHTML1_DIR) + +test: + @echo '$(XML_FILES)' + +.PHONY: all clean test + diff --git a/doc/globals/common-fo.xsl b/doc/globals/common-fo.xsl new file mode 100755 index 0000000..d110b50 --- /dev/null +++ b/doc/globals/common-fo.xsl @@ -0,0 +1,220 @@ + + + + + + + + + + + + + + + + + + + + ../globals/xsl-stylesheets/images/ + + 1em + 0.8em + 1.2em + 1em + 0.8em + 1.2em + dashed + .5pt + #555555 + #EEEEEE + 5pt + + + + + sans-serif + + + + + + + + + + + + + + + img/ + + + + + + + + + 90% + + + + #EEEEEE + + + + + + + + + + + + transparent + + + + ltr + rtl + + + + + + + + + + + + + + + + + + + + + + + 3pt + 1pt + + + + + + + + + bold + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + pt + + + + + + + + pt + + + + + + + + + pt + + + + + + + + pt + + + + + + + + pt + + + diff --git a/doc/globals/common-html-chunked.xsl b/doc/globals/common-html-chunked.xsl new file mode 100755 index 0000000..bc25612 --- /dev/null +++ b/doc/globals/common-html-chunked.xsl @@ -0,0 +1,36 @@ + + + + + + + + + + + + + + + + + + + std-img/ + + + + + + + + std-img/callouts/ + + + img/ + + + diff --git a/doc/globals/common-html-onepage.xsl b/doc/globals/common-html-onepage.xsl new file mode 100755 index 0000000..087e250 --- /dev/null +++ b/doc/globals/common-html-onepage.xsl @@ -0,0 +1,36 @@ + + + + + + + + + + + + + + + + + + + std-img/ + + + + + + + + std-img/callouts/ + + + img/ + + + diff --git a/doc/globals/common-xhtml-chunked.xsl b/doc/globals/common-xhtml-chunked.xsl new file mode 100755 index 0000000..9f60d73 --- /dev/null +++ b/doc/globals/common-xhtml-chunked.xsl @@ -0,0 +1,36 @@ + + + + + + + + + + + + + + + + + + + std-img/ + + + + + + + + std-img/callouts/ + + + img/ + + + diff --git a/doc/globals/common-xhtml-onepage.xsl b/doc/globals/common-xhtml-onepage.xsl new file mode 100755 index 0000000..d52154a --- /dev/null +++ b/doc/globals/common-xhtml-onepage.xsl @@ -0,0 +1,36 @@ + + + + + + + + + + + + + + + + + + + std-img/ + + + + + + + + std-img/callouts/ + + + img/ + + + diff --git a/doc/globals/fonts/addfont.sh b/doc/globals/fonts/addfont.sh new file mode 100755 index 0000000..377d335 --- /dev/null +++ b/doc/globals/fonts/addfont.sh @@ -0,0 +1,16 @@ +#!/bin/sh + +FOP_PREFIX="$HOME/bin/fop" +CLASSPATH="$FOP_PREFIX/build/fop.jar:$FOP_PREFIX/lib/xercesImpl.jar:$FOP_PREFIX/lib/xalan.jar" +CLASSPATH="$CLASSPATH:$FOP_PREFIX/lib/avalon-framework.jar:$FOP_PREFIX/lib/xml-apis.jar" +CLASSPATH="$CLASSPATH:$FOP_PREFIX/lib/commons-logging-1.0.4.jar:$FOP_PREFIX/lib/commons-io-1.1.jar" +CLASS="org.apache.fop.fonts.apps.TTFReader" +ENC="ansi" + +if [ $# -ne 1 ]; then + echo "Usage: $0 " + exit 1 +fi + +java -cp "$CLASSPATH" "$CLASS" -enc "$ENC" "$1" "$(echo "$1" |sed 's/\.[Tt][Tt][Ff]//').xml" + diff --git a/doc/globals/fonts/cour.ttf b/doc/globals/fonts/cour.ttf new file mode 100755 index 0000000..9b06e57 Binary files /dev/null and b/doc/globals/fonts/cour.ttf differ diff --git a/doc/globals/fonts/cour.xml b/doc/globals/fonts/cour.xml new file mode 100755 index 0000000..616d082 --- /dev/null +++ b/doc/globals/fonts/cour.xml @@ -0,0 +1 @@ +CourierNew571422832-300-21-67963710203500TRUETYPEWinAnsiEncoding0255 \ No newline at end of file diff --git a/doc/globals/fonts/courbd.ttf b/doc/globals/fonts/courbd.ttf new file mode 100755 index 0000000..9b8d4f0 Binary files /dev/null and b/doc/globals/fonts/courbd.ttf differ diff --git a/doc/globals/fonts/courbd.xml b/doc/globals/fonts/courbd.xml new file mode 100755 index 0000000..7b276ac --- /dev/null +++ b/doc/globals/fonts/courbd.xml @@ -0,0 +1 @@ +CourierNew,Bold592443832-300-46-71070112213500TRUETYPEWinAnsiEncoding0255 \ No newline at end of file diff --git a/doc/globals/fonts/courbi.ttf b/doc/globals/fonts/courbi.ttf new file mode 100755 index 0000000..106b2bf Binary files /dev/null and b/doc/globals/fonts/courbi.ttf differ diff --git a/doc/globals/fonts/courbi.xml b/doc/globals/fonts/courbi.xml new file mode 100755 index 0000000..b254ef2 --- /dev/null +++ b/doc/globals/fonts/courbi.xml @@ -0,0 +1 @@ +CourierNew,BoldItalic592443832-300-102-3768361003990-12TRUETYPEWinAnsiEncoding0255 \ No newline at end of file diff --git a/doc/globals/fonts/couri.ttf b/doc/globals/fonts/couri.ttf new file mode 100755 index 0000000..31b90ae Binary files /dev/null and b/doc/globals/fonts/couri.ttf differ diff --git a/doc/globals/fonts/couri.xml b/doc/globals/fonts/couri.xml new file mode 100755 index 0000000..427badc --- /dev/null +++ b/doc/globals/fonts/couri.xml @@ -0,0 +1 @@ +CourierNew,Italic571422832-300-67-2738001000990-12TRUETYPEWinAnsiEncoding0255 \ No newline at end of file diff --git a/doc/globals/fonts/georgia.ttf b/doc/globals/fonts/georgia.ttf new file mode 100755 index 0000000..c24d59b Binary files /dev/null and b/doc/globals/fonts/georgia.ttf differ diff --git a/doc/globals/fonts/georgia.xml b/doc/globals/fonts/georgia.xml new file mode 100755 index 0000000..ef4e0fd --- /dev/null +++ b/doc/globals/fonts/georgia.xml @@ -0,0 +1 @@ +Georgia692481916-219-173-21611669123300TRUETYPEWinAnsiEncoding0255 \ No newline at end of file diff --git a/doc/globals/fonts/georgiab.ttf b/doc/globals/fonts/georgiab.ttf new file mode 100755 index 0000000..2cfce23 Binary files /dev/null and b/doc/globals/fonts/georgiab.ttf differ diff --git a/doc/globals/fonts/georgiab.xml b/doc/globals/fonts/georgiab.xml new file mode 100755 index 0000000..138e9a4 --- /dev/null +++ b/doc/globals/fonts/georgiab.xml @@ -0,0 +1 @@ +Georgia,Bold692484916-219-190-21612959123300TRUETYPEWinAnsiEncoding0255 \ No newline at end of file diff --git a/doc/globals/fonts/georgiai.ttf b/doc/globals/fonts/georgiai.ttf new file mode 100755 index 0000000..27abc9d Binary files /dev/null and b/doc/globals/fonts/georgiai.ttf differ diff --git a/doc/globals/fonts/georgiai.xml b/doc/globals/fonts/georgiai.xml new file mode 100755 index 0000000..a88b2a7 --- /dev/null +++ b/doc/globals/fonts/georgiai.xml @@ -0,0 +1 @@ +Georgia,Italic692498916-219-195-2161196912970-13TRUETYPEWinAnsiEncoding0255 \ No newline at end of file diff --git a/doc/globals/fonts/georgiaz.ttf b/doc/globals/fonts/georgiaz.ttf new file mode 100755 index 0000000..f60957e Binary files /dev/null and b/doc/globals/fonts/georgiaz.ttf differ diff --git a/doc/globals/fonts/georgiaz.xml b/doc/globals/fonts/georgiaz.xml new file mode 100755 index 0000000..0e57bfb --- /dev/null +++ b/doc/globals/fonts/georgiaz.xml @@ -0,0 +1 @@ +Georgia,BoldItalic692508916-219-242-2161354914970-13TRUETYPEWinAnsiEncoding0255 \ No newline at end of file diff --git a/doc/globals/fop.xconf b/doc/globals/fop.xconf new file mode 100755 index 0000000..1e82e37 --- /dev/null +++ b/doc/globals/fop.xconf @@ -0,0 +1,149 @@ + + + + + + + . + + + ../globals/fonts + + + 300 + + 300 + + + + + + + + + + + flate + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + diff --git a/doc/template/Makefile b/doc/template/Makefile new file mode 120000 index 0000000..3a269a0 --- /dev/null +++ b/doc/template/Makefile @@ -0,0 +1 @@ +../globals/Makefile \ No newline at end of file diff --git a/doc/template/docbook b/doc/template/docbook new file mode 120000 index 0000000..42b7ae3 --- /dev/null +++ b/doc/template/docbook @@ -0,0 +1 @@ +../globals/docbook \ No newline at end of file diff --git a/doc/template/fop.xconf b/doc/template/fop.xconf new file mode 120000 index 0000000..9113e46 --- /dev/null +++ b/doc/template/fop.xconf @@ -0,0 +1 @@ +../globals/fop.xconf \ No newline at end of file diff --git a/doc/template/main.xml b/doc/template/main.xml new file mode 100755 index 0000000..6ece725 --- /dev/null +++ b/doc/template/main.xml @@ -0,0 +1,35 @@ + + + + + + Title + + JohnSMITH + + ACME corp. + IT dept. + + john@acme.com + + + 2000 + ACME corp. + + + + + Foreword + + + + + My First Document with Docbook + + What is docbook ? + A paragraph + + + + diff --git a/doc/template/xsl/fo.xsl b/doc/template/xsl/fo.xsl new file mode 100755 index 0000000..ab87913 --- /dev/null +++ b/doc/template/xsl/fo.xsl @@ -0,0 +1,11 @@ + + + + + + + + diff --git a/doc/template/xsl/html-chunked.xsl b/doc/template/xsl/html-chunked.xsl new file mode 100755 index 0000000..4eefab5 --- /dev/null +++ b/doc/template/xsl/html-chunked.xsl @@ -0,0 +1,9 @@ + + + + + + diff --git a/doc/template/xsl/html-onepage.xsl b/doc/template/xsl/html-onepage.xsl new file mode 100755 index 0000000..e927b78 --- /dev/null +++ b/doc/template/xsl/html-onepage.xsl @@ -0,0 +1,9 @@ + + + + + + diff --git a/doc/template/xsl/xhtml-chunked.xsl b/doc/template/xsl/xhtml-chunked.xsl new file mode 100755 index 0000000..564c1c6 --- /dev/null +++ b/doc/template/xsl/xhtml-chunked.xsl @@ -0,0 +1,9 @@ + + + + + + diff --git a/doc/template/xsl/xhtml-onepage.xsl b/doc/template/xsl/xhtml-onepage.xsl new file mode 100755 index 0000000..13406f2 --- /dev/null +++ b/doc/template/xsl/xhtml-onepage.xsl @@ -0,0 +1,9 @@ + + + + + + diff --git a/src/Java/DPA/README b/src/Java/DPA/README new file mode 100755 index 0000000..0a84fc0 --- /dev/null +++ b/src/Java/DPA/README @@ -0,0 +1,9 @@ +Ce dossier contient une tentative d'implémentation de l'attaque par DPA +sur RSA. + +Note: Les résultats obtenus sont FAUX ! + +La documentation (payante) est disponible à : +http://www.springerlink.com/content/4ugk06uu0y8hf5ue/ + + diff --git a/src/Java/DPA/src/dpa/RsaTest.java b/src/Java/DPA/src/dpa/RsaTest.java new file mode 100755 index 0000000..16cb754 --- /dev/null +++ b/src/Java/DPA/src/dpa/RsaTest.java @@ -0,0 +1,220 @@ + +package dpa; + +import java.math.*; +import java.io.*; + +/** Cette classe regroupe l'implémentation de la DPA sur RSA. + * Note: C'est une version de test ! + * + * Mode d'emploi: + * Il faut placer les traces de courant dans le répertoire "traces". + * + * Résultats: + * Les résultats sont FAUX. + * + * A faire: + * Voir pourquoi les résultats sont faux. La documentation (payante) + * est disponible à http://www.springerlink.com/content/4ugk06uu0y8hf5ue/ + * + * Les traces de courant sont disponibles sur + * https://projects.itix.fr/studies/DPA/trac/wiki/TracesDeCourant + * + * @author nicolas.masse + */ +public class RsaTest { + + public static void main(String[] args) { + + BigInteger[] msg = new BigInteger[5000]; + for (int i = 0; i < 5000; i++) { + try { + BufferedReader in = new BufferedReader(new FileReader("traces/msg_" + goodform(i+1) + ".dat")); + msg[i] = new BigInteger(in.readLine()); + } catch (IOException ex) { + ex.printStackTrace(); + System.exit(1); + } + + if ((i+1) % 1000 == 0) { + System.out.println("Loaded " + (i+1) + " clear messages..."); + } + } + + int [][] traces = new int[5000][3536]; + for (int i = 0; i < 5000; i++) { + try { + BufferedReader in = new BufferedReader(new FileReader("traces/SM_32_" + goodform(i+1) + ".dat")); + for (int j = 0; j < 3536; j++) { + traces[i][j] = Integer.parseInt(in.readLine()); + } + + } catch (IOException ex) { + ex.printStackTrace(); + System.exit(1); + } + + if ((i+1) % 1000 == 0) { + System.out.println("Loaded " + (i+1) + " traces..."); + } + } + + // The public key + BigInteger n = new BigInteger("115753540889062431344172474906327728114200335452658415236258067817852290090837"); + BigInteger e = new BigInteger("3"); + + System.out.println("n = " + n); + System.out.println("Checking n..."); + if (n.isProbablePrime(1024)) { + System.out.println(" n is probably a prime number."); + } else { + System.out.println(" n is definitely NOT a prime number."); + } + + System.out.println("e = " + e); + System.out.println("Checking e..."); + if (e.isProbablePrime(1024)) { + System.out.println(" e is probably a prime number."); + } else { + System.out.println(" e is definitely NOT a prime number."); + } + + System.out.println("Breaking the key..."); + BigInteger key = dpa(256, msg, traces, n); + //BigInteger key = new BigInteger("77169027259374954229448316604218485408995432318477845515909257059866234615730"); + + System.out.println(" d = " + key); + System.out.println("Checking the private key..."); + if (key.isProbablePrime(1024)) { + System.out.println(" the private key is probably a prime number."); + } else { + System.out.println(" the private key is definitely NOT a prime number."); + } + + System.out.println("Verifying (sign-verif)..."); + + BigInteger msg_orig = msg[0]; + BigInteger sign = msg_orig.modPow(key, n); + BigInteger msg_verif = sign.modPow(e, n); + + if (msg_orig.equals(msg_verif)) { + System.out.println(" The key is the good one !"); + } else { + System.out.println(" Sorry, this is not the good key..."); + System.out.println(" original message = " + msg_orig); + System.out.println(" verified message = " + msg_verif); + } + + //System.out.println("Verifying..."); + //BigInteger + } + + public static BigInteger dpa(int bit, BigInteger[] msg, int[][] traces, BigInteger n) { + BigInteger res = null; + + if (bit == 1) { + res = new BigInteger("1"); + } else { + BigInteger key = dpa(bit - 1, msg, traces, n); + key = key.multiply(new BigInteger("2")); + BigInteger key2 = key.multiply(new BigInteger("2")); + BigInteger key1 = key.add(BigInteger.ONE); + + boolean alreadyChosen = false; + if (dpaStep(key2, msg, traces, n)) { + res = key; + alreadyChosen = true; + } + + if (dpaStep(key1, msg, traces, n)) { + res = key1; + if (alreadyChosen) { + System.out.println("Error: can't decide, two matches !"); + System.exit(1); + } + alreadyChosen = true; + } + + if (!alreadyChosen) { + System.out.println("Error: can't decide, no match !"); + System.exit(1); + } + } + + System.out.println("bit = " + bit + ", key = " + res); + + return res; + } + + public static boolean dpaStep(BigInteger power, BigInteger[] msg, int[][] traces, BigInteger n) { + int tlen = traces[0].length; + int[] c0 = new int[tlen]; + int[] c1 = new int[tlen]; + int[] diffP = new int[tlen]; + + int n0 = 0; + int n1 = 0; + + for (int j = 0; j < traces.length; j++) { + BigInteger m = msg[j]; + + if (sel(m.modPow(power,n))) { + for (int k = 0; k < tlen; k++) { + c0[k] += traces[j][k]; + } + n0++; + } else { + for (int k = 0; k < tlen; k++) { + c1[k] += traces[j][k]; + } + n1++; + } + } + + // Mean computation + int sum = 0; + for (int k = 0; k < tlen; k++) { + diffP[k] = c0[k] / n0 - c1[k] / n1; + sum += diffP[k]; + } + double mean = sum / traces.length; + + // Standard deviation computation + double stddev = 0; + for (int k = 0; k < tlen; k++) { + stddev += (diffP[k] - mean) * (diffP[k] - mean); + } + stddev = Math.sqrt(stddev / traces.length); + + int max = 0; + for (int k = 0; k < tlen; k++) { + if (Math.abs(diffP[k]) > max) { + max = diffP[k]; + } + } + + boolean spike = false; + if (max > 5 * stddev) { + spike = true; + } + + return spike; + } + + public static boolean sel(BigInteger i) { + // bits are numbered from 0 + return i.testBit(26); + } + + public static String goodform(int i) { + String str = Integer.toString(i); + + int len = str.length(); + for (int j = 0; j < 5 - len; j++) { + str = "0" + str; + } + + return str; + } + +} diff --git a/src/Java/DPA/src/dpa/RsaTest2.java b/src/Java/DPA/src/dpa/RsaTest2.java new file mode 100755 index 0000000..808a7ee --- /dev/null +++ b/src/Java/DPA/src/dpa/RsaTest2.java @@ -0,0 +1,233 @@ + +package dpa; + +import java.math.*; +import java.io.*; + +/** Version multi-bits de la DPA sur RSA. + * Note: C'est une version de test ! + * + * Mode d'emploi: + * Il faut placer les traces de courant dans le répertoire "traces". + * + * Résultats: + * Les résultats sont FAUX. + * + * A faire: + * Voir pourquoi les résultats sont faux. La documentation (payante) + * est disponible à http://www.springerlink.com/content/4ugk06uu0y8hf5ue/ + * + * Les traces de courant sont disponibles sur + * https://projects.itix.fr/studies/DPA/trac/wiki/TracesDeCourant + * + * @author nicolas.masse + */ +public class RsaTest2 { + + public static void main(String[] args) { + + + int ntraces = 5000; + + BigInteger[] msg = new BigInteger[ntraces]; + for (int i = 0; i < ntraces; i++) { + try { + BufferedReader in = new BufferedReader(new FileReader("traces/msg_" + goodform(i+1) + ".dat")); + msg[i] = new BigInteger(in.readLine()); + } catch (IOException ex) { + ex.printStackTrace(); + System.exit(1); + } + + if ((i+1) % 1000 == 0) { + System.out.println("Loaded " + (i+1) + " clear messages..."); + } + } + + int [][] traces = new int[ntraces][3536]; + for (int i = 0; i < ntraces; i++) { + try { + BufferedReader in = new BufferedReader(new FileReader("traces/SM_32_" + goodform(i+1) + ".dat")); + for (int j = 0; j < 3536; j++) { + traces[i][j] = Integer.parseInt(in.readLine()); + } + + } catch (IOException ex) { + ex.printStackTrace(); + System.exit(1); + } + + if ((i+1) % 1000 == 0) { + System.out.println("Loaded " + (i+1) + " traces..."); + } + } + + // The public key + BigInteger n = new BigInteger("115753540889062431344172474906327728114200335452658415236258067817852290090837"); + BigInteger e = new BigInteger("3"); + + System.out.println("n = " + n); + System.out.println("Checking n..."); + if (n.isProbablePrime(1024)) { + System.out.println(" n is probably a prime number."); + } else { + System.out.println(" n is definitely NOT a prime number."); + } + + System.out.println("e = " + e); + System.out.println("Checking e..."); + if (e.isProbablePrime(1024)) { + System.out.println(" e is probably a prime number."); + } else { + System.out.println(" e is definitely NOT a prime number."); + } + + System.out.println("Breaking the key..."); + BigInteger key = dpa(256, msg, traces, n); + //BigInteger key = new BigInteger("77169027259374954229448316604218485408995432318477845515909257059866234615730"); + + System.out.println(" d = " + key); + System.out.println("Checking the private key..."); + if (key.isProbablePrime(1024)) { + System.out.println(" the private key is probably a prime number."); + } else { + System.out.println(" the private key is definitely NOT a prime number."); + } + + System.out.println("Verifying (sign-verif)..."); + + BigInteger msg_orig = msg[0]; + BigInteger sign = msg_orig.modPow(key, n); + BigInteger msg_verif = sign.modPow(e, n); + + if (msg_orig.equals(msg_verif)) { + System.out.println(" The key is the good one !"); + } else { + System.out.println(" Sorry, this is not the good key..."); + System.out.println(" original message = " + msg_orig); + System.out.println(" verified message = " + msg_verif); + } + + //System.out.println("Verifying..."); + //BigInteger + } + + public static BigInteger dpa(int bit, BigInteger[] msg, int[][] traces, BigInteger n) { + BigInteger res = null; + + if (bit == 1) { + res = new BigInteger("1"); + } else { + BigInteger key = dpa(bit - 1, msg, traces, n); + key = key.multiply(new BigInteger("2")); + BigInteger key2 = key.multiply(new BigInteger("2")); + BigInteger key1 = key.add(BigInteger.ONE); + + boolean alreadyChosen = false; + if (dpaStep(key2, msg, traces, n)) { + res = key; + alreadyChosen = true; + } + + if (dpaStep(key1, msg, traces, n)) { + res = key1; + if (alreadyChosen) { + System.out.println("Error: can't decide, two matches !"); + System.exit(1); + } + alreadyChosen = true; + } + + if (!alreadyChosen) { + System.out.println("Error: can't decide, no match !"); + System.exit(1); + } + } + + System.out.println("bit = " + bit + ", key = " + res); + + return res; + } + + public static boolean dpaStep(BigInteger power, BigInteger[] msg, int[][] traces, BigInteger n) { + int tlen = traces[0].length; + int[] c0 = new int[tlen]; + int[] c1 = new int[tlen]; + int[] diffP = new int[tlen]; + + int n0 = 0; + int n1 = 0; + + for (int j = 0; j < traces.length; j++) { + BigInteger m = msg[j]; + + int sel = sel(m.modPow(power,n)); + if (sel > 0) { + for (int k = 0; k < tlen; k++) { + c0[k] += traces[j][k]; + } + n0++; + } else if (sel < 0) { + for (int k = 0; k < tlen; k++) { + c1[k] += traces[j][k]; + } + n1++; + } + } + + // Mean computation + int sum = 0; + for (int k = 0; k < tlen; k++) { + diffP[k] = c0[k] / n0 - c1[k] / n1; + sum += diffP[k]; + } + double mean = sum / (n0 + n1); + + // Standard deviation computation + double stddev = 0; + for (int k = 0; k < tlen; k++) { + stddev += (diffP[k] - mean) * (diffP[k] - mean); + } + stddev = Math.sqrt(stddev / (n0 + n1)); + + int max = 0; + for (int k = 0; k < tlen; k++) { + if (Math.abs(diffP[k]) > max) { + max = diffP[k]; + } + } + + boolean spike = false; + if (max > 5 * stddev) { + spike = true; + } + + return spike; + } + + public static int sel(BigInteger i) { + // bits are numbered from 0 + + int res = 0; + + if (i.testBit(26) && i.testBit(25) && i.testBit(24)) { + res = 1; + } else if (!(i.testBit(26) || i.testBit(25) || i.testBit(24)) ) { + res = -1; + } + + return res; + } + + public static String goodform(int i) { + String str = Integer.toString(i); + + int len = str.length(); + for (int j = 0; j < 5 - len; j++) { + str = "0" + str; + } + + return str; + } + +} diff --git a/src/Java/DPA/traces b/src/Java/DPA/traces new file mode 120000 index 0000000..469e9a9 --- /dev/null +++ b/src/Java/DPA/traces @@ -0,0 +1 @@ +../../Mathematica/DPA-RSA/traces \ No newline at end of file diff --git a/src/Mathematica/README b/src/Mathematica/README new file mode 100755 index 0000000..6d13dd8 --- /dev/null +++ b/src/Mathematica/README @@ -0,0 +1,10 @@ +Ces deux feuilles de calcul Mathematica sont des essais d'implémentation +de la DPA suite à l'intervention de M.PAILLIER à l'université de CAEN. + +Les traces de courant sont disponibles à +https://projects.itix.fr/studies/DPA/trac/wiki/TracesDeCourant + +Etat d'avancement: les résultats sont probablement FAUX. + +Note: ces deux feuilles sont grandement basées sur le travail de M.PAILLIER. + diff --git a/src/Mathematica/dpa-mb.nb b/src/Mathematica/dpa-mb.nb new file mode 100755 index 0000000..3aba1b5 --- /dev/null +++ b/src/Mathematica/dpa-mb.nb @@ -0,0 +1,8422 @@ +(************** Content-type: application/mathematica ************** + CreatedBy='Mathematica 5.2' + + Mathematica-Compatible Notebook + +This notebook can be used with any Mathematica-compatible +application, such as Mathematica, MathReader or Publicon. The data +for the notebook starts with the line containing stars above. + +To get the notebook into a Mathematica-compatible application, do +one of the following: + +* Save the data starting with the line of stars above into a file + with a name ending in .nb, then open the file inside the + application; + +* Copy the data starting with the line of stars above to the + clipboard, then use the Paste menu command inside the application. + +Data for notebooks contains only printable 7-bit ASCII and can be +sent directly in email or through ftp in text mode. Newlines can be +CR, LF or CRLF (Unix, Macintosh or MS-DOS style). + +NOTE: If you modify the data for this notebook not in a Mathematica- +compatible application, you must delete the line below containing +the word CacheID, otherwise Mathematica-compatible applications may +try to use invalid cache data. + +For more information on notebooks and Mathematica-compatible +applications, contact Wolfram Research: + web: http://www.wolfram.com + email: info@wolfram.com + phone: +1-217-398-0700 (U.S.) + +Notebook reader applications are available free of charge from +Wolfram Research. +*******************************************************************) + +(*CacheID: 232*) + + +(*NotebookFileLineBreakTest +NotebookFileLineBreakTest*) +(*NotebookOptionsPosition[ 507252, 8309]*) +(*NotebookOutlinePosition[ 507880, 8331]*) +(* CellTagsIndexPosition[ 507836, 8327]*) +(*WindowFrame->Normal*) + + + +Notebook[{ + +Cell[CellGroupData[{ +Cell[BoxData[ + \(SetDirectory["\"]\)], "Input"], + 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1157535408890624313441724749063277281142003354526584152362580678178522\ +90090837;\)\)], "Input"], + +Cell[CellGroupData[{ + +Cell[BoxData[ + \(PrimeQ@n\)], "Input"], + +Cell[BoxData[ + \(False\)], "Output"] +}, Open ]], + +Cell[BoxData[ + \(\(Sel[ + a_Integer] := \((\[IndentingNewLine]res\ = \ + 0; \[IndentingNewLine]If[\[IndentingNewLine]\(IntegerDigits[a, 2, + 256]\)[\([27]\)]\ \[Equal] \ + 0\ \ && \ \ \(IntegerDigits[a, 2, + 256]\)[\([26]\)]\ \[Equal] \ + 0\ \ && \ \(IntegerDigits[a, 2, + 256]\)[\([25]\)]\ \[Equal] \ + 0\ , \[IndentingNewLine]res\ = \ + 1, \ \[IndentingNewLine]\(If[\[IndentingNewLine]\(IntegerDigits[ + a, 2, 256]\)[\([\)\(27\)\(]\)]\ \[Equal] \ + 1\ \ && \ \ \(IntegerDigits[a, 2, + 256]\)[\([\)\(26\)\(]\)]\ \[Equal] \ + 1\ \ && \ \(IntegerDigits[a, 2, + 256]\)[\([\)\(25\)\(]\)]\ \[Equal] \ + 1\ , \[IndentingNewLine]res\ = \ \(-1\)];\)\ +\[IndentingNewLine]]; \[IndentingNewLine]res\[IndentingNewLine])\);\)\)], \ +"Input"], + +Cell[BoxData[ + \(DpaStep[ + power_Integer]\ := \ \((\[IndentingNewLine]C0 = + Table[0, {3536}]; \[IndentingNewLine]C1 = + Table[0, {3536}]; \[IndentingNewLine]n0 = + 0; \[IndentingNewLine]n1 = + 0; \n\[IndentingNewLine]Do[\[IndentingNewLine]m = + msg[\([j]\)]; \[IndentingNewLine]s\ = \ + Sel[PowerMod[m, power, + n]]; \[IndentingNewLine]If[\[IndentingNewLine]s\ < \ + 0, \[IndentingNewLine]C0 += \ + cons[\([j]\)]; \ +\[IndentingNewLine]\(n0++\);\[IndentingNewLine]]; \[IndentingNewLine]If[\ +\[IndentingNewLine]s\ > \ 0, \[IndentingNewLine]C1 += + cons[\([j]\)]; \ +\[IndentingNewLine]\(n1++\);\[IndentingNewLine]];\[IndentingNewLine], {j, 1, + 5000}]; \[IndentingNewLine]C0 = C0/n0; \[IndentingNewLine]C1 = + C1/n1; \[IndentingNewLine]DiffP\ = \ + C0\ - \ C1; \[IndentingNewLine]std\ = \ + StandardDeviation[DiffP]; \[IndentingNewLine]Max[Abs[DiffP]]\ > \ + std\ *\ 5\[IndentingNewLine])\)\)], "Input"], + +Cell[CellGroupData[{ + +Cell[BoxData[ + \(DpaStep[4]\)], "Input"], + +Cell[BoxData[ + \(True\)], "Output"] +}, Open ]], + +Cell[BoxData[{ + \(\(Print["\"\ <> \ ToString[n0]\ <> \ "\<, n1 = \>"\ <> \ + ToString[n1]];\)\), "\[IndentingNewLine]", + \(\(p\ = \ PowerMod[m, power, n];\)\), "\n", + \(\(Print[ + ToString[\(IntegerDigits[p, 2, 256]\)[\([\)\(27\)\(]\)]]\ <> \ + ToString[\(IntegerDigits[p, 2, 256]\)[\([\)\(26\)\(]\)]]\ <> \ + ToString[\(IntegerDigits[p, 2, + 256]\)[\([\)\(25\)\(]\)]]];\)\)}], "Input"], + +Cell[BoxData[ + \(\(\(Dpa[ + bit_Integer]\ := \ \((\[IndentingNewLine]If[\[IndentingNewLine]bit\ \ +\[Equal] \ + 1, \[IndentingNewLine]\[IndentingNewLine]1, \[IndentingNewLine]\ +\[IndentingNewLine]key\ = \ Dpa[bit\ - \ 1]; \[IndentingNewLine]key\ *= \ + 2; \[IndentingNewLine]Which[\[IndentingNewLine]DpaStep[ + key*2], \ \ Print["\"\ \ <> \ ToString[key]]; \ + key, \[IndentingNewLine]DpaStep[ + key + 1], \ \ Print["\"\ \ <> \ + ToString[key\ + \ 1]]; key + \ 1, \[IndentingNewLine]True, \ + Print["\"\ <> \ ToString[key]]; \ + 0\[IndentingNewLine]]\[IndentingNewLine]]\[IndentingNewLine])\)\)\ +\(\[IndentingNewLine]\) + \)\)], "Input"], + +Cell[CellGroupData[{ + +Cell[BoxData[ + \($RecursionLimit\ = \ 1024\)], "Input"], + +Cell[BoxData[ + \(1024\)], "Output"] +}, Open ]], + +Cell[CellGroupData[{ + +Cell[BoxData[ + \(Dpa[256]\)], "Input"], + +Cell[BoxData[ + \("key = 2"\)], "Print"], + +Cell[BoxData[ + \("key = 5"\)], "Print"], + +Cell[BoxData[ + \("key = 10"\)], "Print"], + +Cell[BoxData[ + \("key = 21"\)], "Print"], + +Cell[BoxData[ + \("key = 42"\)], "Print"], + +Cell[BoxData[ + \("key = 85"\)], "Print"], + +Cell[BoxData[ + \("key = 170"\)], "Print"], + +Cell[BoxData[ + \("key = 341"\)], "Print"], + +Cell[BoxData[ + \("key = 682"\)], "Print"], + +Cell[BoxData[ + \("key = 1364"\)], "Print"], + +Cell[BoxData[ + \("key = 2729"\)], "Print"], + +Cell[BoxData[ + \("key = 5458"\)], "Print"], + +Cell[BoxData[ + \("bug: key = 10916"\)], "Print"], + +Cell[BoxData[ + RowBox[{\(Power::"infy"\), \(\(:\)\(\ \)\), "\<\"Infinite expression \ +\\!\\(1\\/0\\) encountered. \\!\\(\\*ButtonBox[\\\"More\[Ellipsis]\\\", \ +ButtonStyle->\\\"RefGuideLinkText\\\", ButtonFrame->None, \ +ButtonData:>\\\"Power::infy\\\"]\\)\"\>"}]], "Message"], + +Cell[BoxData[ + RowBox[{\(\[Infinity]::"indet"\), \(\(:\)\(\ \)\), "\<\"Indeterminate \ +expression \\!\\(0\\\\ ComplexInfinity\\) encountered. \ +\\!\\(\\*ButtonBox[\\\"More\[Ellipsis]\\\", ButtonStyle->\\\"RefGuideLinkText\ +\\\", ButtonFrame->None, ButtonData:>\\\"General::indet\\\"]\\)\"\>"}]], \ +"Message"], + +Cell[BoxData[ + RowBox[{\(\[Infinity]::"indet"\), \(\(:\)\(\ \)\), "\<\"Indeterminate \ +expression \\!\\(0\\\\ ComplexInfinity\\) encountered. \ +\\!\\(\\*ButtonBox[\\\"More\[Ellipsis]\\\", ButtonStyle->\\\"RefGuideLinkText\ +\\\", ButtonFrame->None, ButtonData:>\\\"General::indet\\\"]\\)\"\>"}]], \ +"Message"], + +Cell[BoxData[ + RowBox[{\(\[Infinity]::"indet"\), \(\(:\)\(\ \)\), "\<\"Indeterminate \ +expression \\!\\(0\\\\ ComplexInfinity\\) encountered. \ +\\!\\(\\*ButtonBox[\\\"More\[Ellipsis]\\\", ButtonStyle->\\\"RefGuideLinkText\ +\\\", ButtonFrame->None, ButtonData:>\\\"General::indet\\\"]\\)\"\>"}]], \ +"Message"], + +Cell[BoxData[ + RowBox[{\(General::"stop"\), \(\(:\)\(\ \)\), "\<\"Further output of \ +\\!\\(\[Infinity] :: \\\"indet\\\"\\) will be suppressed during this \ +calculation. \\!\\(\\*ButtonBox[\\\"More\[Ellipsis]\\\", \ +ButtonStyle->\\\"RefGuideLinkText\\\", ButtonFrame->None, \ +ButtonData:>\\\"General::stop\\\"]\\)\"\>"}]], "Message"], + +Cell[BoxData[ + \(Which[ + DpaStep[4\ Which[ + DpaStep[4\ Which[ + DpaStep[ + 4\ Which[ + DpaStep[ + 4\ Which[ + DpaStep[ + 4\ Which[ + DpaStep[ + 4\ Which[ + DpaStep[ + 4\ Which[ + DpaStep[4\ Which[ + DpaStep[4\ Which[DpaStep[ + 4\ Which[DpaStep[4\ Which[DpaStep[ + 4\ Which[DpaStep[4\ Which[DpaStep[ + 4\ Which[DpaStep[4\ Which[DpaStep[ + 4\ Which[DpaStep[4\ Which[DpaStep[ + 4\ Which[DpaStep[4\ Which[DpaStep[ + 4\ Which[DpaStep[4\ Which[DpaStep[ + 4\ Which[DpaStep[4\ Which[DpaStep[ + 4\ Which[DpaStep[4\ Which[DpaStep[ + 4\ Which[DpaStep[4\ Which[DpaStep[ + 4\ Which[DpaStep[4\ Which[DpaStep[ + 4\ Which[DpaStep[4\ Which[DpaStep[ + 4\ Which[DpaStep[4\ Which[DpaStep[ + 4\ Which[DpaStep[4\ Which[DpaStep[ + 4\ Which[DpaStep[4\ Which[DpaStep[ + 4\ Which[DpaStep[4\ Which[DpaStep[ + 4\ Which[DpaStep[4\ Which[DpaStep[ + 4\ Which[DpaStep[4\ Which[DpaStep[ + 4\ Which[DpaStep[4\ Which[DpaStep[ + 4\ Which[DpaStep[4\ Which[DpaStep[ + 4\ Which[DpaStep[4\ Which[DpaStep[ + 4\ Which[DpaStep[4\ Which[DpaStep[ + 4\ Which[DpaStep[4\ Which[DpaStep[ + 4\ Which[DpaStep[4\ Which[DpaStep[ + 4\ Which[DpaStep[4\ Which[DpaStep[ + 4\ Which[DpaStep[4\ Which[DpaStep[ + 4\ Which[DpaStep[4\ Which[DpaStep[ + 4\ Which[DpaStep[4\ Which[DpaStep[ + 4\ Which[DpaStep[4\ Which[DpaStep[ + 4\ Which[DpaStep[4\ Which[DpaStep[ + 4\ Which[DpaStep[4\ Which[DpaStep[ + 4\ Which[DpaStep[4\ Which[DpaStep[ + 4\ Which[DpaStep[4\ Which[DpaStep[ + 4\ Which[DpaStep[4\ Which[DpaStep[ + 4\ Which[DpaStep[4\ Which[DpaStep[ + 4\ Which[DpaStep[4\ Which[DpaStep[ + 4\ Which[DpaStep[4\ Which[DpaStep[ + 4\ Which[DpaStep[4\ Which[DpaStep[ + 4\ Which[DpaStep[4\ Which[DpaStep[ + 4\ Which[DpaStep[4\ Which[DpaStep[ + 4\ Which[DpaStep[4\ Which[DpaStep[ + 4\ Which[DpaStep[4\ Which[DpaStep[ + 4\ Which[DpaStep[4\ Which[DpaStep[ + 4\ Which[DpaStep[4\ Which[DpaStep[ + 4\ Which[DpaStep[4\ Which[DpaStep[ + 4\ Which[DpaStep[4\ Which[DpaStep[ + 4\ Which[DpaStep[4\ Which[DpaStep[ + 4\ Which[DpaStep[4\ Which[DpaStep[ + 4\ Which[DpaStep[4\ Which[DpaStep[ + 4\ Which[DpaStep[4\ Which[DpaStep[ + 4\ Which[DpaStep[4\ Which[DpaStep[ + 4\ Which[DpaStep[4\ Which[DpaStep[ + 4\ Which[DpaStep[4\ Which[DpaStep[ + 4\ Which[DpaStep[4\ Which[DpaStep[ + 4\ Which[DpaStep[4\ Which[DpaStep[ + 4\ Which[DpaStep[4\ Which[DpaStep[ + 4\ Which[DpaStep[4\ Which[DpaStep[ + 4\ Which[DpaStep[4\ Which[DpaStep[ + 4\ Which[DpaStep[4\ Which[DpaStep[ + 4\ Which[DpaStep[4\ Which[DpaStep[ + 4\ Which[DpaStep[4\ Which[DpaStep[ + 4\ Which[DpaStep[4\ Which[DpaStep[ + 4\ Which[DpaStep[4\ Which[DpaStep[ + 4\ Which[DpaStep[4\ Which[DpaStep[ + 4\ Which[DpaStep[4\ Which[DpaStep[ + 4\ Which[DpaStep[4\ Which[DpaStep[ + 4\ Which[DpaStep[4\ Which[DpaStep[ + 4\ Which[DpaStep[4\ Which[DpaStep[ + 4\ Which[DpaStep[4\ Which[DpaStep[ + 4\ Which[DpaStep[4\ Which[DpaStep[ + 4\ Which[DpaStep[4\ Which[DpaStep[ + 4\ Which[DpaStep[4\ Which[DpaStep[ + 4\ Which[DpaStep[4\ Which[DpaStep[ + 4\ Which[DpaStep[4\ Which[DpaStep[ + 4\ Which[DpaStep[4\ Which[DpaStep[ + 4\ Which[DpaStep[4\ Which[DpaStep[ + 4\ Which[DpaStep[4\ Which[DpaStep[ + 4\ Which[DpaStep[4\ Which[DpaStep[ + 4\ Which[DpaStep[4\ Which[DpaStep[ + 4\ Which[DpaStep[4\ Which[DpaStep[ + 4\ Which[DpaStep[4\ Which[DpaStep[ + 4\ Which[DpaStep[4\ Which[DpaStep[ + 4\ Which[DpaStep[4\ Which[DpaStep[ + 4\ Which[DpaStep[4\ Which[DpaStep[ + 4\ Which[DpaStep[4\ Which[DpaStep[ + 4\ Which[DpaStep[4\ Which[DpaStep[ + 4\ Which[DpaStep[4\ Which[DpaStep[ + 4\ Which[DpaStep[4\ Which[DpaStep[ + 4\ Which[DpaStep[4\ Which[DpaStep[ + 4\ Which[DpaStep[4\ Which[DpaStep[ + 4\ Which[DpaStep[4\ Which[DpaStep[ + 4\ Which[DpaStep[4\ Which[DpaStep[ + 4\ Which[DpaStep[4\ Which[DpaStep[ + 4\ Which[DpaStep[4\ Which[DpaStep[ + 4\ Which[DpaStep[4\ Which[DpaStep[ + 4\ Which[DpaStep[4\ Which[DpaStep[ + 4\ Which[DpaStep[4\ Which[DpaStep[ + 4\ Which[DpaStep[4\ Which[DpaStep[ + 4\ Which[DpaStep[4\ Which[DpaStep[ + 4\ Which[DpaStep[4\ Which[DpaStep[ + 4\ Which[DpaStep[4\ Which[DpaStep[ + 4\ Which[DpaStep[4\ Which[DpaStep[ + 4\ Which[DpaStep[4\ Which[DpaStep[ + 4\ Which[DpaStep[4\ Which[DpaStep[ + 4\ Which[DpaStep[4\ Which[DpaStep[ + 4\ Which[DpaStep[4\ Which[DpaStep[ + 4\ Which[DpaStep[4\ Which[DpaStep[ + 4\ Which[DpaStep[4\ Which[DpaStep[ + 4\ Which[DpaStep[4\ Which[DpaStep[ + 4\ Which[DpaStep[4\ Which[DpaStep[ + 4\ Which[DpaStep[4\ Which[DpaStep[ + 4\ Which[DpaStep[4\ Which[DpaStep[ + 4\ Which[DpaStep[4\ Which[DpaStep[ + 4\ Which[DpaStep[4\ Which[DpaStep[ + 4\ Which[DpaStep[4\ Which[DpaStep[ + 4\ Which[DpaStep[4\ Which[DpaStep[ + 4\ Which[DpaStep[4\ Which[ + Indeterminate > Indeterminate, + Print["key = " <> ToString[key]]; + key, DpaStep[key + 1], + Print["key = " <> ToString[key + 1]]; + key + 1, True, Print["bug: key = " <> + ToString[key]]; 0]], Print["key = " <> + ToString[key]]; key, DpaStep[key + + 1], Print["key = " <> ToString[key + + 1]]; key + 1, True, + Print["bug: key = " <> + ToString[key]]; 0]], Print["key = " <> + ToString[key]]; key, DpaStep[key + + 1], Print["key = " <> ToString[key + + 1]]; key + 1, True, + Print["bug: key = " <> + ToString[key]]; 0]], Print["key = " <> + ToString[key]]; key, DpaStep[key + + 1], Print["key = " <> ToString[key + + 1]]; key + 1, True, + Print["bug: key = " <> + ToString[key]]; 0]], Print["key = " <> + ToString[key]]; key, DpaStep[key + + 1], Print["key = " <> ToString[key + + 1]]; key + 1, True, + Print["bug: key = " <> + ToString[key]]; 0]], Print["key = " <> + ToString[key]]; key, DpaStep[key + + 1], Print["key = " <> ToString[key + + 1]]; key + 1, True, + Print["bug: key = " <> + ToString[key]]; 0]], Print["key = " <> + ToString[key]]; key, DpaStep[key + + 1], Print["key = " <> ToString[key + + 1]]; key + 1, True, + Print["bug: key = " <> + ToString[key]]; 0]], Print["key = " <> + ToString[key]]; key, DpaStep[key + + 1], Print["key = " <> ToString[key + + 1]]; key + 1, True, + Print["bug: key = " <> + ToString[key]]; 0]], Print["key = " <> + ToString[key]]; key, DpaStep[key + + 1], Print["key = " <> ToString[key + + 1]]; key + 1, True, + Print["bug: key = " <> + ToString[key]]; 0]], Print["key = " <> + ToString[key]]; key, DpaStep[key + + 1], Print["key = " <> ToString[key + + 1]]; key + 1, True, + Print["bug: key = " <> + ToString[key]]; 0]], Print["key = " <> + ToString[key]]; key, DpaStep[key + + 1], Print["key = " <> ToString[key + + 1]]; key + 1, True, + Print["bug: key = " <> + ToString[key]]; 0]], Print["key = " <> + ToString[key]]; key, DpaStep[key + + 1], Print["key = " <> ToString[key + + 1]]; key + 1, True, + Print["bug: key = " <> + ToString[key]]; 0]], Print["key = " <> + ToString[key]]; key, DpaStep[key + + 1], Print["key = " <> ToString[key + + 1]]; key + 1, True, + Print["bug: key = " <> + ToString[key]]; 0]], Print["key = " <> + ToString[key]]; key, DpaStep[key + + 1], Print["key = " <> ToString[key + + 1]]; key + 1, True, + Print["bug: key = " <> + ToString[key]]; 0]], Print["key = " <> + ToString[key]]; key, DpaStep[key + + 1], Print["key = " <> ToString[key + + 1]]; key + 1, True, + Print["bug: key = " <> + ToString[key]]; 0]], Print["key = " <> + ToString[key]]; key, DpaStep[key + + 1], Print["key = " <> ToString[key + + 1]]; key + 1, True, + Print["bug: key = " <> + ToString[key]]; 0]], Print["key = " <> + ToString[key]]; key, DpaStep[key + + 1], Print["key = " <> ToString[key + + 1]]; key + 1, True, + Print["bug: key = " <> + ToString[key]]; 0]], Print["key = " <> + ToString[key]]; key, DpaStep[key + + 1], Print["key = " <> ToString[key + + 1]]; key + 1, True, + Print["bug: key = " <> + ToString[key]]; 0]], Print["key = " <> + ToString[key]]; key, DpaStep[key + + 1], Print["key = " <> ToString[key + + 1]]; key + 1, True, + Print["bug: key = " <> + ToString[key]]; 0]], Print["key = " <> + ToString[key]]; key, DpaStep[key + + 1], Print["key = " <> ToString[key + + 1]]; key + 1, True, + Print["bug: key = " <> + ToString[key]]; 0]], Print["key = " <> + ToString[key]]; key, DpaStep[key + + 1], Print["key = " <> ToString[key + + 1]]; key + 1, True, + Print["bug: key = " <> + ToString[key]]; 0]], Print["key = " <> + ToString[key]]; key, DpaStep[key + + 1], Print["key = " <> ToString[key + + 1]]; key + 1, True, + Print["bug: key = " <> + ToString[key]]; 0]], Print["key = " <> + ToString[key]]; key, DpaStep[key + + 1], Print["key = " <> ToString[key + + 1]]; key + 1, True, + Print["bug: key = " <> + ToString[key]]; 0]], Print["key = " <> + ToString[key]]; key, DpaStep[key + + 1], Print["key = " <> ToString[key + + 1]]; key + 1, True, + Print["bug: key = " <> + ToString[key]]; 0]], Print["key = " <> + ToString[key]]; key, DpaStep[key + + 1], Print["key = " <> ToString[key + + 1]]; key + 1, True, + Print["bug: key = " <> + ToString[key]]; 0]], Print["key = " <> + ToString[key]]; key, DpaStep[key + + 1], Print["key = " <> ToString[key + + 1]]; key + 1, True, + Print["bug: key = " <> + ToString[key]]; 0]], Print["key = " <> + ToString[key]]; key, DpaStep[key + + 1], Print["key = " <> ToString[key + + 1]]; key + 1, True, + Print["bug: key = " <> + ToString[key]]; 0]], Print["key = " <> + ToString[key]]; key, DpaStep[key + + 1], Print["key = " <> ToString[key + + 1]]; key + 1, True, + Print["bug: key = " <> + ToString[key]]; 0]], Print["key = " <> + ToString[key]]; key, DpaStep[key + + 1], Print["key = " <> ToString[key + + 1]]; key + 1, True, + Print["bug: key = " <> + ToString[key]]; 0]], Print["key = " <> + ToString[key]]; key, DpaStep[key + + 1], Print["key = " <> ToString[key + + 1]]; key + 1, True, + Print["bug: key = " <> + ToString[key]]; 0]], Print["key = " <> + ToString[key]]; key, DpaStep[key + + 1], Print["key = " <> ToString[key + + 1]]; key + 1, True, + Print["bug: key = " <> + ToString[key]]; 0]], Print["key = " <> + ToString[key]]; key, DpaStep[key + + 1], Print["key = " <> ToString[key + + 1]]; key + 1, True, + Print["bug: key = " <> + ToString[key]]; 0]], Print["key = " <> + ToString[key]]; key, DpaStep[key + + 1], Print["key = " <> ToString[key + + 1]]; key + 1, True, + Print["bug: key = " <> + ToString[key]]; 0]], Print["key = " <> + ToString[key]]; key, DpaStep[key + + 1], Print["key = " <> ToString[key + + 1]]; key + 1, True, + Print["bug: key = " <> + ToString[key]]; 0]], Print["key = " <> + ToString[key]]; key, DpaStep[key + + 1], Print["key = " <> ToString[key + + 1]]; key + 1, True, + Print["bug: key = " <> + ToString[key]]; 0]], Print["key = " <> + ToString[key]]; key, DpaStep[key + + 1], Print["key = " <> ToString[key + + 1]]; key + 1, True, + Print["bug: key = " <> + ToString[key]]; 0]], Print["key = " <> + ToString[key]]; key, DpaStep[key + + 1], Print["key = " <> ToString[key + + 1]]; key + 1, True, + Print["bug: key = " <> + ToString[key]]; 0]], Print["key = " <> + ToString[key]]; key, DpaStep[key + + 1], Print["key = " <> ToString[key + + 1]]; key + 1, True, + Print["bug: key = " <> + ToString[key]]; 0]], Print["key = " <> + ToString[key]]; key, DpaStep[key + + 1], Print["key = " <> ToString[key + + 1]]; key + 1, True, + Print["bug: key = " <> + ToString[key]]; 0]], Print["key = " <> + ToString[key]]; key, DpaStep[key + + 1], Print["key = " <> ToString[key + + 1]]; key + 1, True, + Print["bug: key = " <> + ToString[key]]; 0]], Print["key = " <> + ToString[key]]; key, DpaStep[key + + 1], Print["key = " <> ToString[key + + 1]]; key + 1, True, + Print["bug: key = " <> + ToString[key]]; 0]], Print["key = " <> + ToString[key]]; key, DpaStep[key + + 1], Print["key = " <> ToString[key + + 1]]; key + 1, True, + Print["bug: key = " <> + ToString[key]]; 0]], Print["key = " <> + ToString[key]]; key, DpaStep[key + + 1], Print["key = " <> ToString[key + + 1]]; key + 1, True, + Print["bug: key = " <> + ToString[key]]; 0]], Print["key = " <> + ToString[key]]; key, DpaStep[key + + 1], Print["key = " <> ToString[key + + 1]]; key + 1, True, + Print["bug: key = " <> + ToString[key]]; 0]], Print["key = " <> + ToString[key]]; key, DpaStep[key + + 1], Print["key = " <> ToString[key + + 1]]; key + 1, True, + Print["bug: key = " <> + ToString[key]]; 0]], Print["key = " <> + ToString[key]]; key, DpaStep[key + + 1], Print["key = " <> ToString[key + + 1]]; key + 1, True, + Print["bug: key = " <> + ToString[key]]; 0]], Print["key = " <> + ToString[key]]; key, DpaStep[key + + 1], Print["key = " <> ToString[key + + 1]]; key + 1, True, + Print["bug: key = " <> + ToString[key]]; 0]], Print["key = " <> + ToString[key]]; key, DpaStep[key + + 1], Print["key = " <> ToString[key + + 1]]; key + 1, True, + Print["bug: key = " <> + ToString[key]]; 0]], Print["key = " <> + ToString[key]]; key, DpaStep[key + + 1], Print["key = " <> ToString[key + + 1]]; key + 1, True, + Print["bug: key = " <> + ToString[key]]; 0]], Print["key = " <> + ToString[key]]; key, DpaStep[key + + 1], Print["key = " <> ToString[key + + 1]]; key + 1, True, + Print["bug: key = " <> + ToString[key]]; 0]], Print["key = " <> + ToString[key]]; key, DpaStep[key + + 1], Print["key = " <> ToString[key + + 1]]; key + 1, True, + Print["bug: key = " <> + ToString[key]]; 0]], Print["key = " <> + ToString[key]]; key, DpaStep[key + + 1], Print["key = " <> ToString[key + + 1]]; key + 1, True, + Print["bug: key = " <> + ToString[key]]; 0]], Print["key = " <> + ToString[key]]; key, DpaStep[key + + 1], Print["key = " <> ToString[key + + 1]]; key + 1, True, + Print["bug: key = " <> + ToString[key]]; 0]], Print["key = " <> + ToString[key]]; key, DpaStep[key + + 1], Print["key = " <> ToString[key + + 1]]; key + 1, True, + Print["bug: key = " <> + ToString[key]]; 0]], Print["key = " <> + ToString[key]]; key, DpaStep[key + + 1], Print["key = " <> ToString[key + + 1]]; key + 1, True, + Print["bug: key = " <> + ToString[key]]; 0]], Print["key = " <> + ToString[key]]; key, DpaStep[key + + 1], Print["key = " <> ToString[key + + 1]]; key + 1, True, + Print["bug: key = " <> + ToString[key]]; 0]], Print["key = " <> + ToString[key]]; key, DpaStep[key + + 1], Print["key = " <> ToString[key + + 1]]; key + 1, True, + Print["bug: key = " <> + ToString[key]]; 0]], Print["key = " <> + ToString[key]]; key, DpaStep[key + + 1], Print["key = " <> ToString[key + + 1]]; key + 1, True, + Print["bug: key = " <> + ToString[key]]; 0]], Print["key = " <> + ToString[key]]; key, DpaStep[key + + 1], Print["key = " <> ToString[key + + 1]]; key + 1, True, + Print["bug: key = " <> + ToString[key]]; 0]], Print["key = " <> + ToString[key]]; key, DpaStep[key + + 1], Print["key = " <> ToString[key + + 1]]; key + 1, True, + Print["bug: key = " <> + ToString[key]]; 0]], Print["key = " <> + ToString[key]]; key, DpaStep[key + + 1], Print["key = " <> ToString[key + + 1]]; key + 1, True, + Print["bug: key = " <> + ToString[key]]; 0]], Print["key = " <> + ToString[key]]; key, DpaStep[key + + 1], Print["key = " <> ToString[key + + 1]]; key + 1, True, + Print["bug: key = " <> + ToString[key]]; 0]], Print["key = " <> + ToString[key]]; key, DpaStep[key + + 1], Print["key = " <> ToString[key + + 1]]; key + 1, True, + Print["bug: key = " <> + ToString[key]]; 0]], Print["key = " <> + ToString[key]]; key, DpaStep[key + + 1], Print["key = " <> ToString[key + + 1]]; key + 1, True, + Print["bug: key = " <> + ToString[key]]; 0]], Print["key = " <> + ToString[key]]; key, DpaStep[key + + 1], Print["key = " <> ToString[key + + 1]]; key + 1, True, + Print["bug: key = " <> + ToString[key]]; 0]], Print["key = " <> + ToString[key]]; key, DpaStep[key + + 1], Print["key = " <> ToString[key + + 1]]; key + 1, True, + Print["bug: key = " <> + ToString[key]]; 0]], Print["key = " <> + ToString[key]]; key, DpaStep[key + + 1], Print["key = " <> ToString[key + + 1]]; key + 1, True, + Print["bug: key = " <> + ToString[key]]; 0]], Print["key = " <> + ToString[key]]; key, DpaStep[key + + 1], Print["key = " <> ToString[key + + 1]]; key + 1, True, + Print["bug: key = " <> + ToString[key]]; 0]], Print["key = " <> + ToString[key]]; key, DpaStep[key + + 1], Print["key = " <> ToString[key + + 1]]; key + 1, True, + Print["bug: key = " <> + ToString[key]]; 0]], Print["key = " <> + ToString[key]]; key, DpaStep[key + + 1], Print["key = " <> ToString[key + + 1]]; key + 1, True, + Print["bug: key = " <> + ToString[key]]; 0]], Print["key = " <> + ToString[key]]; key, DpaStep[key + + 1], Print["key = " <> ToString[key + + 1]]; key + 1, True, + Print["bug: key = " <> + ToString[key]]; 0]], Print["key = " <> + ToString[key]]; key, DpaStep[key + + 1], Print["key = " <> ToString[key + + 1]]; key + 1, True, + Print["bug: key = " <> + ToString[key]]; 0]], Print["key = " <> + ToString[key]]; key, DpaStep[key + + 1], Print["key = " <> ToString[key + + 1]]; key + 1, True, + Print["bug: key = " <> + ToString[key]]; 0]], Print["key = " <> + ToString[key]]; key, DpaStep[key + + 1], Print["key = " <> ToString[key + + 1]]; key + 1, True, + Print["bug: key = " <> + ToString[key]]; 0]], Print["key = " <> + ToString[key]]; key, DpaStep[key + + 1], Print["key = " <> ToString[key + + 1]]; key + 1, True, + Print["bug: key = " <> + ToString[key]]; 0]], Print["key = " <> + ToString[key]]; key, DpaStep[key + + 1], Print["key = " <> ToString[key + + 1]]; key + 1, True, + Print["bug: key = " <> + ToString[key]]; 0]], Print["key = " <> + ToString[key]]; key, DpaStep[key + + 1], Print["key = " <> ToString[key + + 1]]; key + 1, True, + Print["bug: key = " <> + ToString[key]]; 0]], Print["key = " <> + ToString[key]]; key, DpaStep[key + + 1], Print["key = " <> ToString[key + + 1]]; key + 1, True, + Print["bug: key = " <> + ToString[key]]; 0]], Print["key = " <> + ToString[key]]; key, DpaStep[key + + 1], Print["key = " <> ToString[key + + 1]]; key + 1, True, + Print["bug: key = " <> + ToString[key]]; 0]], Print["key = " <> + ToString[key]]; key, DpaStep[key + + 1], Print["key = " <> ToString[key + + 1]]; key + 1, True, + Print["bug: key = " <> + ToString[key]]; 0]], Print["key = " <> + ToString[key]]; key, DpaStep[key + + 1], Print["key = " <> ToString[key + + 1]]; key + 1, True, + Print["bug: key = " <> + ToString[key]]; 0]], Print["key = " <> + ToString[key]]; key, DpaStep[key + + 1], Print["key = " <> ToString[key + + 1]]; key + 1, True, + Print["bug: key = " <> + ToString[key]]; 0]], Print["key = " <> + ToString[key]]; key, DpaStep[key + + 1], Print["key = " <> ToString[key + + 1]]; key + 1, True, + Print["bug: key = " <> + ToString[key]]; 0]], Print["key = " <> + ToString[key]]; key, DpaStep[key + + 1], Print["key = " <> ToString[key + + 1]]; key + 1, True, + Print["bug: key = " <> + ToString[key]]; 0]], Print["key = " <> + ToString[key]]; key, DpaStep[key + + 1], Print["key = " <> ToString[key + + 1]]; key + 1, True, + Print["bug: key = " <> + ToString[key]]; 0]], Print["key = " <> + ToString[key]]; key, DpaStep[key + + 1], Print["key = " <> ToString[key + + 1]]; key + 1, True, + Print["bug: key = " <> + ToString[key]]; 0]], Print["key = " <> + ToString[key]]; key, DpaStep[key + + 1], Print["key = " <> ToString[key + + 1]]; key + 1, True, + Print["bug: key = " <> + ToString[key]]; 0]], Print["key = " <> + ToString[key]]; key, DpaStep[key + + 1], Print["key = " <> ToString[key + + 1]]; key + 1, True, + Print["bug: key = " <> + ToString[key]]; 0]], Print["key = " <> + ToString[key]]; key, DpaStep[key + + 1], Print["key = " <> ToString[key + + 1]]; key + 1, True, + Print["bug: key = " <> + ToString[key]]; 0]], Print["key = " <> + ToString[key]]; key, DpaStep[key + + 1], Print["key = " <> ToString[key + + 1]]; key + 1, True, + Print["bug: key = " <> + ToString[key]]; 0]], Print["key = " <> + ToString[key]]; key, DpaStep[key + + 1], Print["key = " <> ToString[key + + 1]]; key + 1, True, + Print["bug: key = " <> + ToString[key]]; 0]], Print["key = " <> + ToString[key]]; key, DpaStep[key + + 1], Print["key = " <> ToString[key + + 1]]; key + 1, True, + Print["bug: key = " <> + ToString[key]]; 0]], Print["key = " <> + ToString[key]]; key, DpaStep[key + + 1], Print["key = " <> ToString[key + + 1]]; key + 1, True, + Print["bug: key = " <> + ToString[key]]; 0]], Print["key = " <> + ToString[key]]; key, DpaStep[key + + 1], Print["key = " <> ToString[key + + 1]]; key + 1, True, + Print["bug: key = " <> + ToString[key]]; 0]], Print["key = " <> + ToString[key]]; key, DpaStep[key + + 1], Print["key = " <> ToString[key + + 1]]; key + 1, True, + Print["bug: key = " <> + ToString[key]]; 0]], Print["key = " <> + ToString[key]]; key, DpaStep[key + + 1], Print["key = " <> ToString[key + + 1]]; key + 1, True, + Print["bug: key = " <> + ToString[key]]; 0]], Print["key = " <> + ToString[key]]; key, DpaStep[key + + 1], Print["key = " <> ToString[key + + 1]]; key + 1, True, + Print["bug: key = " <> + ToString[key]]; 0]], Print["key = " <> + ToString[key]]; key, DpaStep[key + + 1], Print["key = " <> ToString[key + + 1]]; key + 1, True, + Print["bug: key = " <> + ToString[key]]; 0]], Print["key = " <> + ToString[key]]; key, DpaStep[key + + 1], Print["key = " <> ToString[key + + 1]]; key + 1, True, + Print["bug: key = " <> + ToString[key]]; 0]], Print["key = " <> + ToString[key]]; key, DpaStep[key + + 1], Print["key = " <> ToString[key + + 1]]; key + 1, True, + Print["bug: key = " <> + ToString[key]]; 0]], Print["key = " <> + ToString[key]]; key, DpaStep[key + + 1], Print["key = " <> ToString[key + + 1]]; key + 1, True, + Print["bug: key = " <> + ToString[key]]; 0]], Print["key = " <> + ToString[key]]; key, DpaStep[key + + 1], Print["key = " <> ToString[key + + 1]]; key + 1, True, + Print["bug: key = " <> + ToString[key]]; 0]], Print["key = " <> + ToString[key]]; key, DpaStep[key + + 1], Print["key = " <> ToString[key + + 1]]; key + 1, True, + Print["bug: key = " <> + ToString[key]]; 0]], Print["key = " <> + ToString[key]]; key, DpaStep[key + + 1], Print["key = " <> ToString[key + + 1]]; key + 1, True, + Print["bug: key = " <> + ToString[key]]; 0]], Print["key = " <> + ToString[key]]; key, DpaStep[key + + 1], Print["key = " <> ToString[key + + 1]]; key + 1, True, + Print["bug: key = " <> + ToString[key]]; 0]], Print["key = " <> + ToString[key]]; key, DpaStep[key + + 1], Print["key = " <> ToString[key + + 1]]; key + 1, True, + Print["bug: key = " <> + ToString[key]]; 0]], Print["key = " <> + ToString[key]]; key, DpaStep[key + + 1], Print["key = " <> ToString[key + + 1]]; key + 1, True, + Print["bug: key = " <> + ToString[key]]; 0]], Print["key = " <> + ToString[key]]; key, DpaStep[key + + 1], Print["key = " <> ToString[key + + 1]]; key + 1, True, + Print["bug: key = " <> + ToString[key]]; 0]], Print["key = " <> + ToString[key]]; key, DpaStep[key + + 1], Print["key = " <> ToString[key + + 1]]; key + 1, True, + Print["bug: key = " <> + ToString[key]]; 0]], Print["key = " <> + ToString[key]]; key, DpaStep[key + + 1], Print["key = " <> ToString[key + + 1]]; key + 1, True, + Print["bug: key = " <> + ToString[key]]; 0]], Print["key = " <> + ToString[key]]; key, DpaStep[key + + 1], Print["key = " <> ToString[key + + 1]]; key + 1, True, + Print["bug: key = " <> + ToString[key]]; 0]], Print["key = " <> + ToString[key]]; key, DpaStep[key + + 1], Print["key = " <> ToString[key + + 1]]; key + 1, True, + Print["bug: key = " <> + ToString[key]]; 0]], Print["key = " <> + ToString[key]]; key, DpaStep[key + + 1], Print["key = " <> ToString[key + + 1]]; key + 1, True, + Print["bug: key = " <> + ToString[key]]; 0]], Print["key = " <> + ToString[key]]; key, DpaStep[key + + 1], Print["key = " <> ToString[key + + 1]]; key + 1, True, + Print["bug: key = " <> + ToString[key]]; 0]], Print["key = " <> + ToString[key]]; key, DpaStep[key + + 1], Print["key = " <> ToString[key + + 1]]; key + 1, True, + Print["bug: key = " <> + ToString[key]]; 0]], Print["key = " <> + ToString[key]]; key, DpaStep[key + + 1], Print["key = " <> ToString[key + + 1]]; key + 1, True, + Print["bug: key = " <> + ToString[key]]; 0]], Print["key = " <> + ToString[key]]; key, DpaStep[key + + 1], Print["key = " <> ToString[key + + 1]]; key + 1, True, + Print["bug: key = " <> + ToString[key]]; 0]], Print["key = " <> + ToString[key]]; key, DpaStep[key + + 1], Print["key = " <> ToString[key + + 1]]; key + 1, True, + Print["bug: key = " <> + ToString[key]]; 0]], Print["key = " <> + ToString[key]]; key, DpaStep[key + + 1], Print["key = " <> ToString[key + + 1]]; key + 1, True, + Print["bug: key = " <> + ToString[key]]; 0]], Print["key = " <> + ToString[key]]; key, DpaStep[key + + 1], Print["key = " <> ToString[key + + 1]]; key + 1, True, + Print["bug: key = " <> + ToString[key]]; 0]], Print["key = " <> + ToString[key]]; key, DpaStep[key + + 1], Print["key = " <> ToString[key + + 1]]; key + 1, True, + Print["bug: key = " <> + ToString[key]]; 0]], Print["key = " <> + ToString[key]]; key, DpaStep[key + + 1], Print["key = " <> ToString[key + + 1]]; key + 1, True, + Print["bug: key = " <> + ToString[key]]; 0]], Print["key = " <> + ToString[key]]; key, DpaStep[key + + 1], Print["key = " <> ToString[key + + 1]]; key + 1, True, + Print["bug: key = " <> + ToString[key]]; 0]], Print["key = " <> + ToString[key]]; key, DpaStep[key + + 1], Print["key = " <> ToString[key + + 1]]; key + 1, True, + Print["bug: key = " <> + ToString[key]]; 0]], Print["key = " <> + ToString[key]]; key, DpaStep[key + + 1], Print["key = " <> ToString[key + + 1]]; key + 1, True, + Print["bug: key = " <> + ToString[key]]; 0]], Print["key = " <> + ToString[key]]; key, DpaStep[key + + 1], Print["key = " <> ToString[key + + 1]]; key + 1, True, + Print["bug: key = " <> + ToString[key]]; 0]], Print["key = " <> + ToString[key]]; key, DpaStep[key + + 1], Print["key = " <> ToString[key + + 1]]; key + 1, True, + Print["bug: key = " <> + ToString[key]]; 0]], Print["key = " <> + ToString[key]]; key, DpaStep[key + + 1], Print["key = " <> ToString[key + + 1]]; key + 1, True, + Print["bug: key = " <> + ToString[key]]; 0]], Print["key = " <> + ToString[key]]; key, DpaStep[key + + 1], Print["key = " <> ToString[key + + 1]]; key + 1, True, + Print["bug: key = " <> + ToString[key]]; 0]], Print["key = " <> + ToString[key]]; key, DpaStep[key + + 1], Print["key = " <> ToString[key + + 1]]; key + 1, True, + Print["bug: key = " <> + ToString[key]]; 0]], Print["key = " <> + ToString[key]]; key, DpaStep[key + + 1], Print["key = " <> ToString[key + + 1]]; key + 1, True, + Print["bug: key = " <> + ToString[key]]; 0]], Print["key = " <> + ToString[key]]; key, DpaStep[key + + 1], Print["key = " <> ToString[key + + 1]]; key + 1, True, + Print["bug: key = " <> + ToString[key]]; 0]], Print["key = " <> + ToString[key]]; key, DpaStep[key + + 1], Print["key = " <> ToString[key + + 1]]; key + 1, True, + Print["bug: key = " <> + ToString[key]]; 0]], Print["key = " <> + ToString[key]]; key, DpaStep[key + + 1], Print["key = " <> ToString[key + + 1]]; key + 1, True, + Print["bug: key = " <> + ToString[key]]; 0]], Print["key = " <> + ToString[key]]; key, DpaStep[key + + 1], Print["key = " <> ToString[key + + 1]]; key + 1, True, + Print["bug: key = " <> + ToString[key]]; 0]], Print["key = " <> + ToString[key]]; key, DpaStep[key + + 1], Print["key = " <> ToString[key + + 1]]; key + 1, True, + Print["bug: key = " <> + ToString[key]]; 0]], Print["key = " <> + ToString[key]]; key, DpaStep[key + + 1], Print["key = " <> ToString[key + + 1]]; key + 1, True, + Print["bug: key = " <> + ToString[key]]; 0]], Print["key = " <> + ToString[key]]; key, DpaStep[key + + 1], Print["key = " <> ToString[key + + 1]]; key + 1, True, + Print["bug: key = " <> + ToString[key]]; 0]], Print["key = " <> + ToString[key]]; key, DpaStep[key + + 1], Print["key = " <> ToString[key + + 1]]; key + 1, True, + Print["bug: key = " <> + ToString[key]]; 0]], Print["key = " <> + ToString[key]]; key, DpaStep[key + + 1], Print["key = " <> ToString[key + + 1]]; key + 1, True, + Print["bug: key = " <> + ToString[key]]; 0]], Print["key = " <> + ToString[key]]; key, DpaStep[key + + 1], Print["key = " <> ToString[key + + 1]]; key + 1, True, + Print["bug: key = " <> + ToString[key]]; 0]], Print["key = " <> + ToString[key]]; key, DpaStep[key + + 1], Print["key = " <> ToString[key + + 1]]; key + 1, True, + Print["bug: key = " <> + ToString[key]]; 0]], Print["key = " <> + ToString[key]]; key, DpaStep[key + + 1], Print["key = " <> ToString[key + + 1]]; key + 1, True, + Print["bug: key = " <> + ToString[key]]; 0]], Print["key = " <> + ToString[key]]; key, DpaStep[key + + 1], Print["key = " <> ToString[key + + 1]]; key + 1, True, + Print["bug: key = " <> + ToString[key]]; 0]], Print["key = " <> + ToString[key]]; key, DpaStep[key + + 1], Print["key = " <> ToString[key + + 1]]; key + 1, True, + Print["bug: key = " <> + ToString[key]]; 0]], Print["key = " <> + ToString[key]]; key, DpaStep[key + + 1], Print["key = " <> ToString[key + + 1]]; key + 1, True, + Print["bug: key = " <> + ToString[key]]; 0]], Print["key = " <> + ToString[key]]; key, DpaStep[key + + 1], Print["key = " <> ToString[key + + 1]]; key + 1, True, + Print["bug: key = " <> + ToString[key]]; 0]], Print["key = " <> + ToString[key]]; key, DpaStep[key + + 1], Print["key = " <> ToString[key + + 1]]; key + 1, True, + Print["bug: key = " <> + ToString[key]]; 0]], Print["key = " <> + ToString[key]]; key, DpaStep[key + + 1], Print["key = " <> ToString[key + + 1]]; key + 1, True, + Print["bug: key = " <> + ToString[key]]; 0]], Print["key = " <> + ToString[key]]; key, DpaStep[key + + 1], Print["key = " <> ToString[key + + 1]]; key + 1, True, + Print["bug: key = " <> + ToString[key]]; 0]], Print["key = " <> + ToString[key]]; key, DpaStep[key + + 1], Print["key = " <> ToString[key + + 1]]; key + 1, True, + Print["bug: key = " <> + ToString[key]]; 0]], Print["key = " <> + ToString[key]]; key, DpaStep[key + + 1], Print["key = " <> ToString[key + + 1]]; key + 1, True, + Print["bug: key = " <> + ToString[key]]; 0]], Print["key = " <> + ToString[key]]; key, DpaStep[key + + 1], Print["key = " <> ToString[key + + 1]]; key + 1, True, + Print["bug: key = " <> + ToString[key]]; 0]], Print["key = " <> + ToString[key]]; key, DpaStep[key + + 1], Print["key = " <> ToString[key + + 1]]; key + 1, True, + Print["bug: key = " <> + ToString[key]]; 0]], Print["key = " <> + ToString[key]]; key, DpaStep[key + + 1], Print["key = " <> ToString[key + + 1]]; key + 1, True, + Print["bug: key = " <> + ToString[key]]; 0]], Print["key = " <> + ToString[key]]; key, DpaStep[key + + 1], Print["key = " <> ToString[key + + 1]]; key + 1, True, + Print["bug: key = " <> + ToString[key]]; 0]], Print["key = " <> + ToString[key]]; key, DpaStep[key + + 1], Print["key = " <> ToString[key + + 1]]; key + 1, True, + Print["bug: key = " <> + ToString[key]]; 0]], Print["key = " <> + ToString[key]]; key, DpaStep[key + + 1], Print["key = " <> ToString[key + + 1]]; key + 1, True, + Print["bug: key = " <> + ToString[key]]; 0]], Print["key = " <> + ToString[key]]; key, DpaStep[key + + 1], Print["key = " <> ToString[key + + 1]]; key + 1, True, + Print["bug: key = " <> + ToString[key]]; 0]], Print["key = " <> + ToString[key]]; key, DpaStep[key + + 1], Print["key = " <> ToString[key + + 1]]; key + 1, True, + Print["bug: key = " <> + ToString[key]]; 0]], Print["key = " <> + ToString[key]]; key, DpaStep[key + + 1], Print["key = " <> ToString[key + + 1]]; key + 1, True, + Print["bug: key = " <> + ToString[key]]; 0]], Print["key = " <> + ToString[key]]; key, DpaStep[key + + 1], Print["key = " <> ToString[key + + 1]]; key + 1, True, + Print["bug: key = " <> + ToString[key]]; 0]], Print["key = " <> + ToString[key]]; key, DpaStep[key + + 1], Print["key = " <> ToString[key + + 1]]; key + 1, True, + Print["bug: key = " <> + ToString[key]]; 0]], Print["key = " <> + ToString[key]]; key, DpaStep[key + + 1], Print["key = " <> ToString[key + + 1]]; key + 1, True, + Print["bug: key = " <> + ToString[key]]; 0]], Print["key = " <> + ToString[key]]; key, DpaStep[key + + 1], Print["key = " <> ToString[key + + 1]]; key + 1, True, + Print["bug: key = " <> + ToString[key]]; 0]], Print["key = " <> + ToString[key]]; key, DpaStep[key + + 1], Print["key = " <> ToString[key + + 1]]; key + 1, True, + Print["bug: key = " <> + ToString[key]]; 0]], Print["key = " <> + ToString[key]]; key, DpaStep[key + + 1], Print["key = " <> ToString[key + + 1]]; key + 1, True, + Print["bug: key = " <> + ToString[key]]; 0]], Print["key = " <> + ToString[key]]; key, DpaStep[key + + 1], Print["key = " <> ToString[key + + 1]]; key + 1, True, + Print["bug: key = " <> + ToString[key]]; 0]], Print["key = " <> + ToString[key]]; key, DpaStep[key + + 1], Print["key = " <> ToString[key + + 1]]; key + 1, True, + Print["bug: key = " <> + ToString[key]]; 0]], Print["key = " <> + ToString[key]]; key, DpaStep[key + + 1], Print["key = " <> ToString[key + + 1]]; key + 1, True, + Print["bug: key = " <> + ToString[key]]; 0]], Print["key = " <> + ToString[key]]; key, DpaStep[key + + 1], Print["key = " <> ToString[key + + 1]]; key + 1, True, + Print["bug: key = " <> + ToString[key]]; 0]], Print["key = " <> + ToString[key]]; key, DpaStep[key + + 1], Print["key = " <> ToString[key + + 1]]; key + 1, True, + Print["bug: key = " <> + ToString[key]]; 0]], Print["key = " <> + ToString[key]]; key, DpaStep[key + + 1], Print["key = " <> ToString[key + + 1]]; key + 1, True, + Print["bug: key = " <> + ToString[key]]; 0]], Print["key = " <> + ToString[key]]; key, DpaStep[key + + 1], Print["key = " <> ToString[key + + 1]]; key + 1, True, + Print["bug: key = " <> + ToString[key]]; 0]], Print["key = " <> + ToString[key]]; key, DpaStep[key + + 1], Print["key = " <> ToString[key + + 1]]; key + 1, True, + Print["bug: key = " <> + ToString[key]]; 0]], Print["key = " <> + ToString[key]]; key, DpaStep[key + + 1], Print["key = " <> ToString[key + + 1]]; key + 1, True, + Print["bug: key = " <> + ToString[key]]; 0]], Print["key = " <> + ToString[key]]; key, DpaStep[key + + 1], Print["key = " <> ToString[key + + 1]]; key + 1, True, + Print["bug: key = " <> + ToString[key]]; 0]], Print["key = " <> + ToString[key]]; key, DpaStep[key + + 1], Print["key = " <> ToString[key + + 1]]; key + 1, True, + Print["bug: key = " <> + ToString[key]]; 0]], Print["key = " <> + ToString[key]]; key, DpaStep[key + + 1], Print["key = " <> ToString[key + + 1]]; key + 1, True, + Print["bug: key = " <> + ToString[key]]; 0]], Print["key = " <> + ToString[key]]; key, DpaStep[key + + 1], Print["key = " <> ToString[key + + 1]]; key + 1, True, + Print["bug: key = " <> + ToString[key]]; 0]], Print["key = " <> + ToString[key]]; key, DpaStep[key + + 1], Print["key = " <> ToString[key + + 1]]; key + 1, True, + Print["bug: key = " <> + ToString[key]]; 0]], Print["key = " <> + ToString[key]]; key, DpaStep[key + + 1], Print["key = " <> ToString[key + + 1]]; key + 1, True, + Print["bug: key = " <> + ToString[key]]; 0]], Print["key = " <> + ToString[key]]; key, DpaStep[key + + 1], Print["key = " <> ToString[key + + 1]]; key + 1, True, + Print["bug: key = " <> + ToString[key]]; 0]], Print["key = " <> + ToString[key]]; key, DpaStep[key + + 1], Print["key = " <> ToString[key + + 1]]; key + 1, True, + Print["bug: key = " <> + ToString[key]]; 0]], Print["key = " <> + ToString[key]]; key, DpaStep[key + + 1], Print["key = " <> ToString[key + + 1]]; key + 1, True, + Print["bug: key = " <> + ToString[key]]; 0]], Print["key = " <> + ToString[key]]; key, DpaStep[key + + 1], Print["key = " <> ToString[key + + 1]]; key + 1, True, + Print["bug: key = " <> + ToString[key]]; 0]], Print["key = " <> + ToString[key]]; key, DpaStep[key + + 1], Print["key = " <> ToString[key + + 1]]; key + 1, True, + Print["bug: key = " <> + ToString[key]]; 0]], Print["key = " <> + ToString[key]]; key, DpaStep[key + + 1], Print["key = " <> ToString[key + + 1]]; key + 1, True, + Print["bug: key = " <> + ToString[key]]; 0]], Print["key = " <> + ToString[key]]; key, DpaStep[key + + 1], Print["key = " <> ToString[key + + 1]]; key + 1, True, + Print["bug: key = " <> + ToString[key]]; 0]], Print["key = " <> + ToString[key]]; key, DpaStep[key + + 1], Print["key = " <> ToString[key + + 1]]; key + 1, True, + Print["bug: key = " <> + ToString[key]]; 0]], Print["key = " <> + ToString[key]]; key, DpaStep[key + + 1], Print["key = " <> ToString[key + + 1]]; key + 1, True, + Print["bug: key = " <> + ToString[key]]; 0]], Print["key = " <> + ToString[key]]; key, DpaStep[key + + 1], Print["key = " <> ToString[key + + 1]]; key + 1, True, + Print["bug: key = " <> + ToString[key]]; 0]], Print["key = " <> + ToString[key]]; key, DpaStep[key + + 1], Print["key = " <> ToString[key + + 1]]; key + 1, True, + Print["bug: key = " <> + ToString[key]]; 0]], Print["key = " <> + ToString[key]]; key, DpaStep[key + + 1], Print["key = " <> ToString[key + + 1]]; key + 1, True, + Print["bug: key = " <> + ToString[key]]; 0]], Print["key = " <> + ToString[key]]; key, DpaStep[key + + 1], Print["key = " <> ToString[key + + 1]]; key + 1, True, + Print["bug: key = " <> + ToString[key]]; 0]], Print["key = " <> + ToString[key]]; key, DpaStep[key + + 1], Print["key = " <> ToString[key + + 1]]; key + 1, True, + Print["bug: key = " <> + ToString[key]]; 0]], Print["key = " <> + ToString[key]]; key, DpaStep[key + + 1], Print["key = " <> ToString[key + + 1]]; key + 1, True, + Print["bug: key = " <> + ToString[key]]; 0]], Print["key = " <> + ToString[key]]; key, DpaStep[key + + 1], Print["key = " <> ToString[key + + 1]]; key + 1, True, + Print["bug: key = " <> + ToString[key]]; 0]], Print["key = " <> + ToString[key]]; key, DpaStep[key + + 1], Print["key = " <> ToString[key + + 1]]; key + 1, True, + Print["bug: key = " <> + ToString[key]]; 0]], Print["key = " <> + ToString[key]]; key, DpaStep[key + + 1], Print["key = " <> ToString[key + + 1]]; key + 1, True, + Print["bug: key = " <> + ToString[key]]; 0]], Print["key = " <> + ToString[key]]; key, DpaStep[key + + 1], Print["key = " <> ToString[key + + 1]]; key + 1, True, + Print["bug: key = " <> + ToString[key]]; 0]], Print["key = " <> + ToString[key]]; key, DpaStep[key + + 1], Print["key = " <> ToString[key + + 1]]; key + 1, True, + Print["bug: key = " <> + ToString[key]]; 0]], Print["key = " <> + ToString[key]]; key, DpaStep[key + + 1], Print["key = " <> ToString[key + + 1]]; key + 1, True, + Print["bug: key = " <> + ToString[key]]; 0]], Print["key = " <> + ToString[key]]; key, DpaStep[key + + 1], Print["key = " <> ToString[key + + 1]]; key + 1, True, + Print["bug: key = " <> + ToString[key]]; 0]], Print["key = " <> + ToString[key]]; key, DpaStep[key + + 1], Print["key = " <> ToString[key + + 1]]; key + 1, True, + Print["bug: key = " <> + ToString[key]]; 0]], Print["key = " <> + ToString[key]]; key, DpaStep[key + + 1], Print["key = " <> ToString[key + + 1]]; key + 1, True, + Print["bug: key = " <> + ToString[key]]; 0]], Print["key = " <> + ToString[key]]; key, DpaStep[key + + 1], Print["key = " <> ToString[key + + 1]]; key + 1, True, + Print["bug: key = " <> + ToString[key]]; 0]], Print["key = " <> + ToString[key]]; key, DpaStep[key + + 1], Print["key = " <> ToString[key + + 1]]; key + 1, True, + Print["bug: key = " <> + ToString[key]]; 0]], Print["key = " <> + ToString[key]]; key, DpaStep[key + + 1], Print["key = " <> ToString[key + + 1]]; key + 1, True, + Print["bug: key = " <> + ToString[key]]; 0]], Print["key = " <> + ToString[key]]; key, DpaStep[key + + 1], Print["key = " <> ToString[key + + 1]]; key + 1, True, + Print["bug: key = " <> + ToString[key]]; 0]], Print["key = " <> + ToString[key]]; key, DpaStep[key + + 1], Print["key = " <> ToString[key + + 1]]; key + 1, True, + Print["bug: key = " <> + ToString[key]]; 0]], Print["key = " <> + ToString[key]]; key, DpaStep[key + + 1], Print["key = " <> ToString[key + + 1]]; key + 1, True, + Print["bug: key = " <> + ToString[key]]; 0]], Print["key = " <> + ToString[key]]; key, DpaStep[key + + 1], Print["key = " <> ToString[key + + 1]]; key + 1, True, + Print["bug: key = " <> + ToString[key]]; 0]], Print["key = " <> + ToString[key]]; key, DpaStep[key + + 1], Print["key = " <> ToString[key + + 1]]; key + 1, True, + Print["bug: key = " <> + ToString[key]]; 0]], Print["key = " <> + ToString[key]]; key, DpaStep[key + + 1], Print["key = " <> ToString[key + + 1]]; key + 1, True, + Print["bug: key = " <> + ToString[key]]; 0]], Print["key = " <> + ToString[key]]; key, DpaStep[key + + 1], Print["key = " <> ToString[key + + 1]]; key + 1, True, + Print["bug: key = " <> + ToString[key]]; 0]], Print["key = " <> + ToString[key]]; key, DpaStep[key + + 1], Print["key = " <> ToString[key + + 1]]; key + 1, True, + Print["bug: key = " <> + ToString[key]]; 0]], Print["key = " <> + ToString[key]]; key, DpaStep[key + + 1], Print["key = " <> ToString[key + + 1]]; key + 1, True, + Print["bug: key = " <> + ToString[key]]; 0]], Print["key = " <> + ToString[key]]; key, DpaStep[key + + 1], Print["key = " <> ToString[key + + 1]]; key + 1, True, + Print["bug: key = " <> + ToString[key]]; 0]], Print["key = " <> + ToString[key]]; key, DpaStep[key + + 1], Print["key = " <> ToString[key + + 1]]; key + 1, True, + Print["bug: key = " <> + ToString[key]]; 0]], Print["key = " <> + ToString[key]]; key, DpaStep[key + + 1], Print["key = " <> ToString[key + + 1]]; key + 1, True, + Print["bug: key = " <> + ToString[key]]; 0]], Print["key = " <> + ToString[key]]; key, DpaStep[key + + 1], Print["key = " <> ToString[key + + 1]]; key + 1, True, + Print["bug: key = " <> + ToString[key]]; 0]], Print["key = " <> + ToString[key]]; key, DpaStep[key + + 1], Print["key = " <> ToString[key + + 1]]; key + 1, True, + Print["bug: key = " <> + ToString[key]]; 0]], Print["key = " <> + ToString[key]]; key, DpaStep[key + + 1], Print["key = " <> ToString[key + + 1]]; key + 1, True, + Print["bug: key = " <> + ToString[key]]; 0]], Print["key = " <> + ToString[key]]; key, DpaStep[key + + 1], Print["key = " <> ToString[key + + 1]]; key + 1, True, + Print["bug: key = " <> + ToString[key]]; 0]], Print["key = " <> + ToString[key]]; key, DpaStep[key + + 1], Print["key = " <> ToString[key + + 1]]; key + 1, True, + Print["bug: key = " <> + ToString[key]]; 0]], Print["key = " <> + ToString[key]]; key, DpaStep[key + + 1], Print["key = " <> ToString[key + + 1]]; key + 1, True, + Print["bug: key = " <> + ToString[key]]; 0]], Print["key = " <> + ToString[key]]; key, DpaStep[key + + 1], Print["key = " <> ToString[key + + 1]]; key + 1, True, + Print["bug: key = " <> + ToString[key]]; 0]], Print["key = " <> + ToString[key]]; key, DpaStep[key + + 1], Print["key = " <> ToString[key + + 1]]; key + 1, True, + Print["bug: key = " <> + ToString[key]]; 0]], Print["key = " <> + ToString[key]]; key, DpaStep[key + + 1], Print["key = " <> ToString[key + + 1]]; key + 1, True, + Print["bug: key = " <> + ToString[key]]; 0]], Print["key = " <> + ToString[key]]; key, DpaStep[key + + 1], Print["key = " <> ToString[key + + 1]]; key + 1, True, + Print["bug: key = " <> + ToString[key]]; 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+max_corr_sample_id = zeros(1,8); +best_guess = zeros(1,8); + + +% preloading the curves data (40 * 50ko curves) +curves = cpa_load_curves(directory_name, variant, max_curve_num); + +num_curve = size(curves, 1); +num_sample = size(curves, 2); + +% computing standarg deviation among curves same timestep samples; +std_curve_sample = std(curves); +mean_curve_sample = mean(curves, 1); + + +% iterating over all the possible guess +for guess = 0:63 + disp(guess); + % get the hamming weight assotiated with the cleartexts, one column per + % sbox + weights = cpa_get_hamming_weigth(directory_name, guess, num_curve); + + % computing standard deviation and mean + std_hamming = std(weights); + mean_hamming = mean(weights, 1); + + + %iterating over sbox + for sbox = 1:8 + w = weights(:, sbox); + + max_corr = 0; + max_corr_id = 0; + + %iterating over samples to compute correlation curve + for i = 1:num_sample + std_curve_sample_i = std_curve_sample(i); + std_hamming_sbox = std_hamming(sbox); + if std_curve_sample_i ~= 0 & std_hamming_sbox ~= 0 + correlation_factor= (mean(curves(:,i) .* w, 1) - (mean_curve_sample(i) * mean_hamming(sbox))) / (std_curve_sample_i * std_hamming_sbox); + + if correlation_factor > max_corr + max_corr = correlation_factor; + max_corr_id = i; + end + end + end + + if max_corr > max_corr_factor(sbox) + max_corr_factor(sbox) = max_corr; + max_corr_sample_id(sbox) = max_corr_id; + best_guess(sbox) = guess; + end + end +end \ No newline at end of file diff --git a/src/Matlab/CPA/cpa_get_hamming_weigth.m b/src/Matlab/CPA/cpa_get_hamming_weigth.m new file mode 100755 index 0000000..4ba5b72 --- /dev/null +++ b/src/Matlab/CPA/cpa_get_hamming_weigth.m @@ -0,0 +1,10 @@ +function [weights] = cpa_get_hamming_weigth(directory_name, guess, num_curve) +%CPA_GET_HAMMING_WEIGHT(DIRECTORY_NAME, GUESS) +% return array containing the hamming weigth of +% the handled cleartext when the given guess is used, one line per sbox + +weights = []; + +for sbox = 1:8 + weights = [weights, cpa_get_hamming_weigth_per_sbox(directory_name, sbox, guess, num_curve)]; +end \ No newline at end of file diff --git a/src/Matlab/CPA/cpa_get_hamming_weigth_per_sbox.m b/src/Matlab/CPA/cpa_get_hamming_weigth_per_sbox.m new file mode 100755 index 0000000..d5181f4 --- /dev/null +++ b/src/Matlab/CPA/cpa_get_hamming_weigth_per_sbox.m @@ -0,0 +1,21 @@ +function [weights] = cpa_get_hamming_weigth_per_sbox(directory_name, sbox, guess, num_curve) +%CPA_GET_HAMMING_WEIGHT_PER_SBOX(DIRECTORY_NAME, SBOX, GUESS) +% return an array containing the hamming weigth of +% the handled cleartext when the given sbox and guess is used + + + +filename = [directory_name, '/cpa/', 'S', num2str(sbox), '/outbox.64_4.s', num2str(sbox), '.p00.g', num2str(guess, '%02d')]; +fid = fopen(filename, 'r'); + +weights = []; +i = 0; + +while i < num_curve & ~ feof(fid) + str = fgetl(fid); + data = sscanf(str, '%d%d'); + weights = [weights; data(2)]; + i = i + 1; +end + +fclose(fid); \ No newline at end of file diff --git a/src/Matlab/CPA/cpa_load_curves.m b/src/Matlab/CPA/cpa_load_curves.m new file mode 100755 index 0000000..290f1b9 --- /dev/null +++ b/src/Matlab/CPA/cpa_load_curves.m @@ -0,0 +1,23 @@ +function [curves] = cpa_load_curves(directory_name, variant, max_curve_num) +%CPA_LOAD_CURVES(DIRECTORY_NAME, VARIANT, MAX_CURVE_NUM) +% a null max_num_curve lead to load all the curves in the specified directory +% return an array (size: [num_curves, num_sample_per_curve]) + + +curves = []; +num_curve = 0; + +filename = [directory_name, '/curves/00/', variant, '.', num2str(num_curve, '%05d')]; +fid = fopen(filename,'r'); + + +% try to load max_curve_num curve files in the directory +while ((max_curve_num == 0) | (num_curve < max_curve_num)) & fid ~= -1 + + curves = [curves; fread(fid, inf, 'uint8')']; + fclose(fid); + + num_curve = num_curve + 1; + filename = [directory_name, '/curves/00/', variant, '.', num2str(num_curve, '%05d')]; + fid = fopen(filename,'r'); +end diff --git a/src/Matlab/DPA/dpa_des_block2hexstr.m b/src/Matlab/DPA/dpa_des_block2hexstr.m new file mode 100755 index 0000000..339af16 --- /dev/null +++ b/src/Matlab/DPA/dpa_des_block2hexstr.m @@ -0,0 +1,16 @@ +function [ str ] = dpa_des_block2hexstr(block) +%DES_DPA(BLOCK) to display a block in hexadecimal format. block length must +% be a multiple of 8. Return a string + +numblock = (size(block, 2) / 8) - 1; + +str = ''; + +p2 = 2 .^ [7:-1:0]; + +for i = [0 : numblock] + id = i * 8; + subblock = block(id + 1:id + 8); + val = subblock * p2'; + str = strcat(str, dec2hex(val,2)); +end \ No newline at end of file diff --git a/src/Matlab/DPA/dpa_des_deckeychunk2block.m b/src/Matlab/DPA/dpa_des_deckeychunk2block.m new file mode 100755 index 0000000..fde914c --- /dev/null +++ b/src/Matlab/DPA/dpa_des_deckeychunk2block.m @@ -0,0 +1,15 @@ +function [ block ] = dpa_des_deckeychunk2block(dec_key_chunks) +%DPA_DES_DECKEYCHUNK2BLOCK(DEC_KEY_CHUNKS) compute a round key block from an array +%of decimal values, one per sbox (value 1 for sbox 1 etc...) +%representation + + +num_chunks = size(dec_key_chunks, 2); + +block = []; +for chunk = dec_key_chunks + str = dec2bin(chunk,6); + for c = str + block = [block, str2num(c)]; + end +end \ No newline at end of file diff --git a/src/Matlab/DPA/dpa_des_display_mean.m b/src/Matlab/DPA/dpa_des_display_mean.m new file mode 100755 index 0000000..a8f7b33 --- /dev/null +++ b/src/Matlab/DPA/dpa_des_display_mean.m @@ -0,0 +1,160 @@ +function [g, b] = dpa_des_display_mean(num_samples, power_model_name, tested_sbox) +%DES_DISPLAY_MEAN COMPUTES A DPA ON ONE KEY CHUNK AND DISPLAY THE RESULTING PLOT) +% figure 1 resulting from a good key chunk, figure 2 resulting from afalse hypothesis +%on the key chunk; + + +key = round(rand(1,64)); +keys = des_key_schedule(key); +lastkey = keys(16,:); + +[pmodel spdetector] = dpa_des_power_model(power_model_name); + +% computing a dumb power trace to get its size +spower = size(pmodel(zeros(1,64)), 2); + +%tested_sbox = 1; +i = ((tested_sbox - 1) * 6) + 1; + +good_key_chunk = lastkey(i:i+5); + +bad_key_chunk = round(rand(1,6)); + +%good_key_chunk = bad_key_chunk; + +while all(bad_key_chunk == good_key_chunk) + bad_key_chunk = round(rand(i,i+5)); +end + +% GA = Good key chunk, tested bit = 0 +% GB = Good key chunk, tested bit = 1 +% BA = Bad key chunk, tested bit = 0 +% BB = Bad key chunk, tested bit = 1 + +trace_ga = zeros(1,spower); +trace_gb = zeros(1,spower); +trace_ba = zeros(1,spower); +trace_bb = zeros(1,spower); + +s = num_samples; + +nga = 0; +ngb = 0; +nba = 0; +nbb = 0; + +tested_bit_index = 1 + (tested_sbox - 1) * 4; + +while s > 0 + + plaintext = round(rand(1,64)); + [ciphertext power] = dpa_des_pencryption(plaintext, keys, pmodel); + + + % oracle using the good key chunk + r = dpa_des_selection_function(ciphertext, tested_sbox, good_key_chunk); + + if r == 0 + trace_ga = trace_ga + power; + nga = nga + 1; + else + trace_gb = trace_gb + power; + ngb = ngb + 1; + end + + + % oracle using the erroneous key chunk + r = dpa_des_selection_function(ciphertext, tested_sbox, bad_key_chunk); + + if r == 0 + trace_ba = trace_ba + power; + nba = nba + 1; + else + trace_bb = trace_bb + power; + nbb = nbb + 1; + end + + s = s - 1; +end + + +if nga ~= 0 +trace_ga = trace_ga / nga; +end + +if ngb ~= 0 +trace_gb = trace_gb / ngb; +end + +if nba ~= 0 +trace_ba = trace_ba / nba; +end + +if nbb ~= 0 +trace_bb = trace_bb / nbb; +end + +g = trace_ga - trace_gb; +b = trace_ba - trace_bb; + +figure(1); +x = 1:size(g,2); + +n = 20; +f = ones(1, n) / n; + +lg = conv(f, g); +lb = conv(f, b); +lg = lg(1, 1 : spower); +lb = lb(1, 1 : spower); + +% Some statistics (mean and standard deviation) +mlg = mean(lg); +mlb = mean(lb); +slg = std(lg); +slb = std(lb); +disp('dpaspike'); +disp(dpa_des_spike(g)); +disp(dpa_des_spike(b)); +disp('/dpaspike'); +nstd = 10; + +% Plot the raw data +subplot(3,2,1); +plot(x, g, '-g'); +subplot(3,2,2); +plot(x, b, '-r'); + + + +% Plot the filtered (smoothed) data with the limits +subplot(3,2,3); +hold on; +plot(x, lg, '-g'); +plot([1 spower], [1 1] * nstd * (mlg - slg), '-b'); +plot([1 spower], [1 1] * nstd * (mlg + slg), '-b'); +subplot(3,2,4); +hold on; +plot(x, lb, '-r'); +plot([1 spower], [1 1] * nstd * (mlb - slb), '-b'); +plot([1 spower], [1 1] * nstd * (mlb + slb), '-b'); + + +subplot(3,2,5); +n2 = 40; +[n, xout] = hist(lg, n2); +sumi = 0; for i = [1 : n2]; sumi = sumi + n(i); n(i) = sumi / spower; end +hold on; +plot(xout, n, '-g'); +plot([1 1] * nstd * (mlg + slg), [0 1], '-b'); +plot([1 1] * nstd * (mlg - slg), [0 1], '-b'); +subplot(3,2,6); +[n, xout] = hist(lb, n2); +sumi = 0; for i = [1 : n2]; sumi = sumi + n(i); n(i) = sumi / spower; end +hold on; +plot(xout, n, '-r'); +plot([1 1] * nstd * (mlb + slb), [0 1], '-b'); +plot([1 1] * nstd * (mlb - slb), [0 1], '-b'); + +spdetector(g) +spdetector(b) diff --git a/src/Matlab/DPA/dpa_des_dpa.m b/src/Matlab/DPA/dpa_des_dpa.m new file mode 100755 index 0000000..1c02eed --- /dev/null +++ b/src/Matlab/DPA/dpa_des_dpa.m @@ -0,0 +1,77 @@ +function [ keys ] = dpa_des_dpa(traces, ciphers, spike_detector) +%DES_DPA(TRACES,CIPHERS,CLEARS) Simple version of the DPA on DES +% Returns the possible keys, using the provided traces and ciphers + +n_traces = size(traces, 1); +n_samples = size(traces, 2); +sbox_num = 8; + +hypothesis_spike_max = zeros(1, sbox_num); +hypothesis_subkey = zeros(1, sbox_num); + +% we iterate over the 64 possible subkeys +for ikey = [0 : 63] + fprintf(1, 'test sous clé %d\n', ikey); + + %if mod(i,16) == 0 + % figure((i / 16) + 1); + %end + + % compute the key chunk block + key_chunk = dec2bin(ikey, 6) == '1'; + + % place to store 8 parallele dpa over the 8 s-box + trace_a = zeros(sbox_num, n_samples); + trace_b = zeros(sbox_num, n_samples); + + na = zeros(1,sbox_num); + nb = zeros(1,sbox_num); + + % iterate over all the trace + for n_trace = [1 : n_traces] + + % iterate over the 8 sbox + for n_sbox = [1:sbox_num] + r = dpa_des_selection_function(ciphers(n_trace,:), n_sbox, key_chunk); + + if r == 0 + trace_a(n_sbox,:) = trace_a(n_sbox,:) + traces(n_trace,:); + na(n_sbox) = na(n_sbox) + 1; + else + trace_b(n_sbox,:) = trace_b(n_sbox,:) + traces(n_trace,:); + nb(n_sbox) = nb(n_sbox) + 1; + end + end + end + + % iterate over the 8 sbox + for n_sbox = [1:sbox_num] + if na(n_sbox) ~= 0 + trace_a(n_sbox,:) = trace_a(n_sbox,:) / na(n_sbox); + end + + if nb(n_sbox) ~= 0 + trace_b(n_sbox,:) = trace_b(n_sbox,:) / nb(n_sbox); + end + + spike_value = spike_detector(trace_a(n_sbox,:) - trace_b(n_sbox,:)); + %if spike_value == 2 + % fprintf(1, 'key chunk num: %d found, %s\n', n_sbox,dec2bin(ikey,6)) ; + %end + + if spike_value > hypothesis_spike_max(n_sbox) + hypothesis_spike_max(n_sbox) = spike_value; + hypothesis_subkey(n_sbox) = ikey; + end + end +end + +% rebuild the last key using the chosen subkey +computed_last_key = []; +for n_sbox = [1:sbox_num] + k = dec2bin(hypothesis_subkey(n_sbox), 6) == '1'; + computed_last_key = [computed_last_key k]; +end + +keys = dpa_des_reverse_ks(computed_last_key); +%keys = computed_last_key; diff --git a/src/Matlab/DPA/dpa_des_dpa_test.m b/src/Matlab/DPA/dpa_des_dpa_test.m new file mode 100755 index 0000000..d3b05cf --- /dev/null +++ b/src/Matlab/DPA/dpa_des_dpa_test.m @@ -0,0 +1,48 @@ +function [good_bit] = dpa_des_dpa_test(num_samples, power_model) +%DES_DPA_TEST(NUM_SAMPLES, POWER_MODEL) Tests the simple version of the DPA algorithm + +s = num_samples; + +% we build a random key +key = round(rand(1,64)); +% raz parity bit of the key. reverse key schedule do the same +key(8:8:64) = 0; + +keys = des_key_schedule(key); + + +[pmodel spdetector] = dpa_des_power_model(power_model); + +traces = []; +ciphers = []; +clears = []; + +while s > 0 + plaintext = round(rand(1,64)); + [ciphertext power] = dpa_des_pencryption(plaintext, keys, pmodel); + + clears = [clears ; plaintext]; + ciphers = [ciphers ; ciphertext]; + traces = [traces ; power]; + + s = s - 1; +end + +returned_keys = dpa_des_dpa(traces, ciphers, spdetector); + + +%if all(returned_keys == keys(16,:)) +% disp('La clé est trouvée'); +%end + + + +fprintf(1, 'original key:\t%s\n', dpa_des_block2hexstr(key)); + +for i = [1 : size(returned_keys, 1)] + %disp(sum(returned_keys(i, :) == key) - 8); + k = returned_keys(i, :); + if all(k == key) + fprintf(1, 'found key\t%s\n', dpa_des_block2hexstr(k)); + end +end diff --git a/src/Matlab/DPA/dpa_des_expand_key_chunk.m b/src/Matlab/DPA/dpa_des_expand_key_chunk.m new file mode 100755 index 0000000..9d40c4f --- /dev/null +++ b/src/Matlab/DPA/dpa_des_expand_key_chunk.m @@ -0,0 +1,6 @@ +function key48 = des_expand_key_ckunk(key_chunk, key_chunk_number ) +%DES_EXPAND_KEY_CHUNK(KEY_CHUNK, KEY_CHUNK_NUMBER) +% compute a 48 bits key based on the provided chunk (6 bits), concatenate with 0 +% key_chunk_number indicate where will be the chunk in the key48 (1 <= x <= 8) + +key48 = horzcat(zeros(1, (key_chunk_number - 1) * 6), key_chunk, zeros(1, 6 * (8 - key_chunk_number))); diff --git a/src/Matlab/DPA/dpa_des_get_power.m b/src/Matlab/DPA/dpa_des_get_power.m new file mode 100755 index 0000000..625c381 --- /dev/null +++ b/src/Matlab/DPA/dpa_des_get_power.m @@ -0,0 +1,25 @@ +function [ power ] = dpa_des_get_power( block ) +%DES_GET_POWER COMPUTES THE POWER TRACE FROM A BIT BLOCK) + +psize = 10000; + +%power = rand(1, psize) * 0.5; +power = rand(1, psize); + +for j = 1:64; + i = floor(j * psize / 65); + power(i : i + psize / 1000) = power(i : i + psize / 1000) + ((0.5 - block(j)) * 0.3); +end + +%{ + +on définit 64 morceau de 10 bits consécutifs sur la trace de courant +à chaque bit d'un morceau est ajouté la valeur (coefficientée) du bit du block +correspondant à ce morceau + +exemple, la valeur du bit 8 du bloc de données d'entrée +est ajoutée au 10 bits du 8ème bloc de la trace de courant, +c'est a dire les bits allant de 8 * (10000/65) a (10000/65) + 10 + +%} + diff --git a/src/Matlab/DPA/dpa_des_hexstr2block.m b/src/Matlab/DPA/dpa_des_hexstr2block.m new file mode 100755 index 0000000..8ec33e6 --- /dev/null +++ b/src/Matlab/DPA/dpa_des_hexstr2block.m @@ -0,0 +1,14 @@ +function [ block ] = dpa_des_hexstr2block(str) +%DPA_DES_HEXSTR2BLOCK(STR) compute a key block from an hexadecimal string +%representation + +block = []; + +for i = str + num = hex2dec(i); + bin = dec2bin(num,4); + + for i = bin + block = [block, str2num(i)]; + end +end \ No newline at end of file diff --git a/src/Matlab/DPA/dpa_des_oracle.m b/src/Matlab/DPA/dpa_des_oracle.m new file mode 100755 index 0000000..9328640 --- /dev/null +++ b/src/Matlab/DPA/dpa_des_oracle.m @@ -0,0 +1,18 @@ +function block = dpa_des_oracle( ciphertext, tested_sbox, key_chunk ) +%DES_ORACLE(CIPHERTEXT, TESTED_SBOX, KEY_CHUNK) +% +% Return the value, before the last des round, of the four bits +% modified by the specified key_chunk during the last round + +% expand the key chunk to a 48 bit key +key48 = dpa_des_expand_key_chunk(key_chunk, tested_sbox); + +% invert final permutation (aka initial permutation) to retrive +% last des round result +data = des_initial_permutation(ciphertext); + +% reapply last round +block = des_round(data, key48); + + + diff --git a/src/Matlab/DPA/dpa_des_oracle_test.m b/src/Matlab/DPA/dpa_des_oracle_test.m new file mode 100755 index 0000000..31ec251 --- /dev/null +++ b/src/Matlab/DPA/dpa_des_oracle_test.m @@ -0,0 +1,50 @@ +function [ good_response, false_response ] = dpa_des_oracle_test(number_of_test) +%DES_ORACLE_TEST(NUMBER_OF_TEST) Return the number of oracle's good and false response, after + +good_response = 0; +false_response = 0; + +for test = 1:number_of_test + +% choose a plaintext and a key to use in this test +keys = round(rand(1,64)); +plaintext = round(rand(1,64)); + + +if size(keys,1) == 1 + keys = des_key_schedule(keys); +end + +data = des_initial_permutation(plaintext); + +for rnd = 1:15 + data = des_round(data, keys(rnd,:)); + data = des_block_interchange(data); +end + +% store the value of the left block before applying last round +before_16_data = data(1:32); +before_16_data = dpa_des_reverse_permutation(before_16_data); + +data = des_round(data, keys(16,:)); + +ciphertext = des_final_permutation(data); + +lastkey48 = keys(16,:); + +for sbox_number = [1:8] + + id32 = ((sbox_number - 1) * 4) + 1; + id48 = ((sbox_number - 1) * 6) + 1; + + block = dpa_des_oracle(ciphertext, sbox_number, lastkey48(id48 : id48 + 5)); + + if all(block == before_16_data(id32:id32 + 3)) == 1 + good_response = good_response + 1; + else + false_response = false_response + 1; + end + +end + +end diff --git a/src/Matlab/DPA/dpa_des_pencryption.m b/src/Matlab/DPA/dpa_des_pencryption.m new file mode 100755 index 0000000..c43532c --- /dev/null +++ b/src/Matlab/DPA/dpa_des_pencryption.m @@ -0,0 +1,21 @@ +function [ ciphertext power ] = dpa_des_pencryption( plaintext, keys, model ) +%DES_PENCRYPTION(PLAINTEXT, KEYS, MODEL) +%Executes the DES algorithm and computes a power trace using the given model + +% compute subkeys if only master key is provided +if size(keys,1) == 1 + keys = des_key_schedule(keys); +end + +data = des_initial_permutation(plaintext); + +for round = 1:15 + data = des_round(data, keys(round,:)); + data = des_block_interchange(data); +end + +power = model(data); + +data = des_round(data, keys(16,:)); + +ciphertext = des_final_permutation(data); diff --git a/src/Matlab/DPA/dpa_des_power_model.m b/src/Matlab/DPA/dpa_des_power_model.m new file mode 100755 index 0000000..b15efa9 --- /dev/null +++ b/src/Matlab/DPA/dpa_des_power_model.m @@ -0,0 +1,14 @@ +function [power criteria] = dpa_des_power_model(model_name) +%DES_POWER_MODEL(MODEL_NAME) + +switch model_name + case 'des_power1' + power = @dpa_des_get_power; + criteria = @dpa_des_spike; + case 'des_power2' + power = @dpa_des_power_simplest_model; + criteria = @dpa_des_power_simplest_model_criteria; + otherwise + power = 0; + criteria = 0; +end diff --git a/src/Matlab/DPA/dpa_des_power_simplest_model.m b/src/Matlab/DPA/dpa_des_power_simplest_model.m new file mode 100755 index 0000000..ba2a207 --- /dev/null +++ b/src/Matlab/DPA/dpa_des_power_simplest_model.m @@ -0,0 +1,8 @@ +function [ power ] = dpa_des_power_simplest_model( block ) +%DES_POWER_SIMPLEST_MODEL( BLOCK ) Computes a simple "over-correlated" power trace +%from a bit 64 bits block. + + +power = zeros(1, size(block,2)); +power = (-2 * block) + 1; + diff --git a/src/Matlab/DPA/dpa_des_power_simplest_model_criteria.m b/src/Matlab/DPA/dpa_des_power_simplest_model_criteria.m new file mode 100755 index 0000000..bbf70c3 --- /dev/null +++ b/src/Matlab/DPA/dpa_des_power_simplest_model_criteria.m @@ -0,0 +1,4 @@ +function [ spike ] = dpa_des_power_simplest_model_criteria(mean) +%DES_POWER_SIMPLEST_MODEL_CRITERIA(MEAN ) return the peak height + +spike = max(mean); diff --git a/src/Matlab/DPA/dpa_des_reverse_ks.m b/src/Matlab/DPA/dpa_des_reverse_ks.m new file mode 100755 index 0000000..7443184 --- /dev/null +++ b/src/Matlab/DPA/dpa_des_reverse_ks.m @@ -0,0 +1,78 @@ +function [ masterKeys64 ] = dpa_des_reverse_ks( lastKey48 ) +%DES_REVERSE_KS(LAST_SUBKEY48) Recover a part of the master key using the +%last subkey. Returns the list of all possible subkeys. + +% IPC2 is the reverse of PC2, its computation can be done using : +%{ +IPC2 = zeros(1,56); +for i = [1:48]; IPC2(PC2(i)) = i; end +%} + +IPC2 = [5 24 7 16 6 10 20 18 0 12 3 15 23 1 9 19 2 0 14 22 11 0 13 4 0 17]; +IPC2 = [IPC2 21 8 47 31 27 48 35 41 0 46 28 0 39 32 25 44 0 37 34 43 29]; +IPC2 = [IPC2 36 38 45 33 26 42 0 30 40]; + +% We do not need to invert the shifts since C and D are 28bits wide and +% there are 28 shifts between C0 (resp. D0) and C16 (resp. D16). + +% IPC1 is the reverse of PC1, its computation can be done using : +%{ +IPC1 = zeros(1,64); +for i = [1:56]; IPC1(PC1(i)) = i; end +%} + +IPC1 = [8 16 24 56 52 44 36 0 7 15 23 55 51 43 35 0 6 14 22 54 50 42]; +IPC1 = [IPC1 34 0 5 13 21 53 49 41 33 0 4 12 20 28 48 40 32 0 3 11 19 27]; +IPC1 = [IPC1 47 39 31 0 2 10 18 26 46 38 30 0 1 9 17 25 45 37 29 0]; + +% Computes the composition "invP = IPC1 o IPC2" +invP = zeros(1,64); +for i = [1:64]; + j = IPC1(i); + if j ~= 0; + k = IPC2(j); + if k ~= 0; + invP(i) = k; + end + end +end + + +% Find the free variables +freePos = []; +for i = [1:64]; + if invP(i) == 0 && rem(i, 8) ~= 0; + freePos = [freePos i]; + end +end + +% Find 48 bits of the master key +incompleteKey = zeros(1,64); +for i = [1:64]; + if (invP(i) ~= 0); + incompleteKey(i) = lastKey48(invP(i)); + end +end + +% 256 keys +masterKeys64 = zeros(256, 64); + +% Find the 256 possible keys +for i = [0:255]; + v = bitget(uint8(i), 8:-1:1); + masterKeys64(i + 1, :) = incompleteKey; + for j = [1:8]; + masterKeys64(i + 1, freePos(j)) = v(j); + end +end + +%{ +key = 0; +keyRef = round(rand(1,64)); +keyRef(8:8:64) = 0; +keysRef = des_key_schedule(keyRef); +lastKeyRef = keysRef(16,:); +keys = dpa_des_reverse_ks(lastKeyRef); +for i = [1:256]; if all(keys(i,:) == keyRef); key = keys(i,:); break; end; end; +key +%} diff --git a/src/Matlab/DPA/dpa_des_reverse_permutation.m b/src/Matlab/DPA/dpa_des_reverse_permutation.m new file mode 100755 index 0000000..736fa04 --- /dev/null +++ b/src/Matlab/DPA/dpa_des_reverse_permutation.m @@ -0,0 +1,22 @@ +function [ outBlock32 ] = dpa_des_reverse_permutation( inBlock32 ) +%DES_INVERSE_PERMUTATION DO REVERSE OF THE IN-ROUND PERMUTATION) + +% Test case : +%{ +in = [1 : 32]; +ret = des_inverse_permutation(in); +ref = [16 7 20 21 29 12 28 17 1 15 23 26 5 18 31 10 2 8 24 14 32]; +ref = [ref 27 3 9 19 13 30 6 22 11 4 25]; +all(ret == ref) +%} + +P = [9 17 23 31 13 28 2 18 24 16 30 6 26 20 10 1 8 14]; +P = [P 25 3 4 29 11 19 32 12 22 7 5 27 15 21]; + +outBlock32 = zeros(1, 32); + +for i = [1 : 32] + outBlock32(i) = inBlock32(P(i)); +end + + diff --git a/src/Matlab/DPA/dpa_des_selection_function.m b/src/Matlab/DPA/dpa_des_selection_function.m new file mode 100755 index 0000000..d1bf5ac --- /dev/null +++ b/src/Matlab/DPA/dpa_des_selection_function.m @@ -0,0 +1,17 @@ +function result = dpa_des_selection_function(ciphertext, tested_sbox, key_chunk ) +%DES_SELECTION_FUNCTION(CIPHERTEXT, TESTED_SBOX, KEY_CHUNK) +% +% Return 0 or 1 depending of the value, before the round, of the first bit processed +% by the tested sbox. + + +block = dpa_des_oracle(ciphertext, tested_sbox, key_chunk); + + +% to keep bit processed by the sbox n in a contiguous block of bit +data = dpa_des_reverse_permutation(block(1:32)); + +tested_bit_index = 1 + (tested_sbox - 1) * 4; + +result = data(tested_bit_index); + diff --git a/src/Matlab/DPA/dpa_des_spike.m b/src/Matlab/DPA/dpa_des_spike.m new file mode 100755 index 0000000..fd27a6c --- /dev/null +++ b/src/Matlab/DPA/dpa_des_spike.m @@ -0,0 +1,27 @@ +function [ spike ] = dpa_des_spike( sample_mean ) +%DES_SPIKE(MEAN) Detects a spike in sample_mean, the higher the returned value is, the +% more important the spike is. + + +% The filter +n = 20; +f = ones(1, n) / n; + +spower = size(sample_mean, 2); + +% We filter the samples mean + +f_mean = conv(f, sample_mean); +f_mean = f_mean(1, 1 : spower); + +% Some statistics +s_std = std(f_mean); + +nstd = 10; + +tmp = abs(f_mean); + +spike = 0; +if any(tmp > nstd * s_std) + spike = max(tmp); +end diff --git a/src/Matlab/DataEncryptionStandard/des_block_interchange.m b/src/Matlab/DataEncryptionStandard/des_block_interchange.m new file mode 100755 index 0000000..4ee4046 --- /dev/null +++ b/src/Matlab/DataEncryptionStandard/des_block_interchange.m @@ -0,0 +1,12 @@ +function [ outBlock64 ] = des_block_interchange( inBlock64 ) +%DES_BLOCK_INTERCHANGE Exchange the parts of a 64 bits block + +% Test case : +%{ +ret = des_block_interchange(1:64); +ref = [33:64, 1:32]; +all(ret == ref) +%} + +outBlock64 = [inBlock64(33:64) inBlock64(1:32)]; + diff --git a/src/Matlab/DataEncryptionStandard/des_cipher_function.m b/src/Matlab/DataEncryptionStandard/des_cipher_function.m new file mode 100755 index 0000000..e9de8f1 --- /dev/null +++ b/src/Matlab/DataEncryptionStandard/des_cipher_function.m @@ -0,0 +1,17 @@ +function [ outBlock32 ] = des_cipher_function( inBlock32, subkey48 ) +%DES_CIPHER_FUNCTION Encrypt a 32 bits block using a 48 bits subkey + +% E function +inBlock48 = des_expand_box(inBlock32); + +% XOR +outBlock48 = xor(inBlock48, subkey48); + +% SBOXes +outBlock32 = zeros(1, 32); +for i = 1 : 8 + outBlock32(((i - 1) * 4) + 1 : i * 4) = des_sbox(outBlock48(((i - 1) * 6) + 1 : i * 6), i); +end + +% P +outBlock32 = des_permutation(outBlock32); diff --git a/src/Matlab/DataEncryptionStandard/des_decryption.m b/src/Matlab/DataEncryptionStandard/des_decryption.m new file mode 100755 index 0000000..c011c8a --- /dev/null +++ b/src/Matlab/DataEncryptionStandard/des_decryption.m @@ -0,0 +1,19 @@ +function plaintext = des_decryption(ciphertext, keys) +% DES_DECRYPTION 64 bit block ciphertext, keys +% compute the decryption of the input block + +% compute subkeys if only master key is provided +if size(keys,1) == 1 + keys = des_key_schedule(keys); +end + + +data = des_initial_permutation(ciphertext); + +for round = 1:15 + data = des_round(data, keys(17 - round,:)); + des_block_interchange(data); +end + +data = des_round(data, keys(1,:)); +plaintext = des_final_permutation(data); diff --git a/src/Matlab/DataEncryptionStandard/des_encryption.m b/src/Matlab/DataEncryptionStandard/des_encryption.m new file mode 100755 index 0000000..47038ba --- /dev/null +++ b/src/Matlab/DataEncryptionStandard/des_encryption.m @@ -0,0 +1,19 @@ +function ciphertext = des_encryption(plaintext, keys) +% DES_ENCRYPTION 64 bit block plaintext, keys +% compute the encryption of the input block + +% compute subkeys if only master key is provided +if size(keys,1) == 1 + keys = des_key_schedule(keys); +end + + +data = des_initial_permutation(plaintext); + +for round = 1:15 + data = des_round(data, keys(round,:)); + data = des_block_interchange(data); +end + +data = des_round(data, keys(16,:)); +ciphertext = des_final_permutation(data); diff --git a/src/Matlab/DataEncryptionStandard/des_expand_box.m b/src/Matlab/DataEncryptionStandard/des_expand_box.m new file mode 100755 index 0000000..8fa7750 --- /dev/null +++ b/src/Matlab/DataEncryptionStandard/des_expand_box.m @@ -0,0 +1,22 @@ +function [ block48 ] = des_expand_box( block32 ) +%DES_EXPAND_BOX Expand a 32 bits block into a 48 bits block + +% Test case : +%{ +in = [1 : 32]; +ret = des_expand_box(in); +ref = [32 1 2 3 4 5 4 5 6 7 8 9 8 9 10 11 12 13 12 13 14 15 16 17 16]; +ref = [ref 17 18 19 20 21 20 21 22 23 24 25 24 25 26 27 28 29 28 29]; +ref = [ref 30 31 32 1]; +all(ret == ref) +%} + +E = [32 1 2 3 4 5 4 5 6 7 8 9 8 9 10 11 12 13 12 13 14 15 16]; +E = [E 17 16 17 18 19 20 21 20 21 22 23 24 25 24 25 26 27 28 29 28 29 30]; +E = [E 31 32 1]; + +block48 = zeros(1, 48); + +for i = [1 : 48] + block48(i) = block32(E(i)); +end diff --git a/src/Matlab/DataEncryptionStandard/des_final_permutation.m b/src/Matlab/DataEncryptionStandard/des_final_permutation.m new file mode 100755 index 0000000..d93439e --- /dev/null +++ b/src/Matlab/DataEncryptionStandard/des_final_permutation.m @@ -0,0 +1,19 @@ +function [block64out] = des_final_permutation(block64in) +% DES_FINAL_PERMUTATION(BLOCK64IN), permute bit, used after applying des last round + +ip = [40, 8, 48, 16, 56, 24, 64, 32, 39, 7, 47, 15, 55, 23, 63, 31, 38, 6, 46, 14, 54, 22, 62, 30, 37, 5, 45, 13, 53, 21, 61, 29, 36, 4, 44, 12, 52, 20, 60, 28, 35, 3, 43, 11, 51, 19, 59, 27, 34, 2, 42, 10, 50, 18, 58, 26, 33, 1, 41, 9, 49, 17, 57, 25]; + +for i = 1:numel(ip); + block64out(i) = block64in(ip(i)); +end + + +%{ +to test this function: +call it with block64in an array containing the 64 first strictly positive integer, +with the final permutation table as defined in fips 46-3, page 10. + +block64out = des_final_permutation(1:64); +result = all(block64out == ip); + +%} diff --git a/src/Matlab/DataEncryptionStandard/des_initial_permutation.m b/src/Matlab/DataEncryptionStandard/des_initial_permutation.m new file mode 100755 index 0000000..e1ca384 --- /dev/null +++ b/src/Matlab/DataEncryptionStandard/des_initial_permutation.m @@ -0,0 +1,19 @@ +function [block64out] = des_initial_permutation(block64in) +% DES_INITIAL_PERMUTATION(BLOCK64IN), permute bit, used before applying des first round + +ip = [58, 50, 42, 34, 26, 18, 10, 2, 60, 52, 44, 36, 28, 20, 12, 4, 62, 54, 46, 38, 30, 22, 14, 6, 64, 56, 48, 40, 32, 24, 16, 8, 57, 49, 41, 33, 25, 17, 9, 1, 59, 51, 43, 35, 27, 19, 11, 3, 61, 53, 45, 37, 29, 21, 13, 5, 63, 55, 47, 39, 31, 23, 15, 7]; + +for i = 1:numel(ip); + block64out(i) = block64in(ip(i)); +end + + +%{ +to test this function: +call it with block64in an array containing the 64 first strictly positive integer, +with the initial permutation table as defined in fips 46-3, page 10. + +block64out = des_initial_permutation(1:64); +result = all(block64out == ip); + +%} diff --git a/src/Matlab/DataEncryptionStandard/des_key_schedule.m b/src/Matlab/DataEncryptionStandard/des_key_schedule.m new file mode 100755 index 0000000..ceb20da --- /dev/null +++ b/src/Matlab/DataEncryptionStandard/des_key_schedule.m @@ -0,0 +1,15 @@ +function [ keys ] = des_key_schedule( key64 ) +%DES_KEY_SCHEDULE Generate 16 subkeys from a 64 bits master key + +des_shift_number = [ 1 1 2 2 2 2 2 2 1 2 2 2 2 2 2 1 ]; + +[ Cn Dn ] = des_permuted_choice_1(key64); + +keys = zeros(16, 48); + +for i = [1 : 16] + Dn = des_shift(Dn, des_shift_number(i)); + Cn = des_shift(Cn, des_shift_number(i)); + keys(i, :) = des_permuted_choice_2(Cn, Dn); +end + diff --git a/src/Matlab/DataEncryptionStandard/des_permutation.m b/src/Matlab/DataEncryptionStandard/des_permutation.m new file mode 100755 index 0000000..1dfb11d --- /dev/null +++ b/src/Matlab/DataEncryptionStandard/des_permutation.m @@ -0,0 +1,21 @@ +function [ outBlock32 ] = des_permutation( inBlock32 ) +%DES_PERMUTATION Do the in-round permutation + +% Test case : +%{ +in = [1 : 32]; +ret = des_permutation(in); +ref = [16 7 20 21 29 12 28 17 1 15 23 26 5 18 31 10 2 8 24 14 32]; +ref = [ref 27 3 9 19 13 30 6 22 11 4 25]; +all(ret == ref) +%} + +P = [16 7 20 21 29 12 28 17 1 15 23 26 5 18 31 10 2 8 24 14 32 27 3 9]; +P = [P 19 13 30 6 22 11 4 25]; + +outBlock32 = zeros(1, 32); + +for i = [1 : 32] + outBlock32(i) = inBlock32(P(i)); +end + diff --git a/src/Matlab/DataEncryptionStandard/des_permuted_choice_1.m b/src/Matlab/DataEncryptionStandard/des_permuted_choice_1.m new file mode 100755 index 0000000..876027d --- /dev/null +++ b/src/Matlab/DataEncryptionStandard/des_permuted_choice_1.m @@ -0,0 +1,22 @@ +function [C0, D0] = des_permuted_choice_1(key64) +% DES_PERMUTED_CHOICE_1(k), where k is the 64 bits master key, compute C0 and D0 + +pc1_c = [57, 49, 41, 33, 25, 17, 9, 1, 58, 50, 42, 34, 26, 18, 10, 2, 59, 51, 43, 35, 27, 19, 11, 3, 60, 52, 44, 36]; +pc1_d = [63, 55, 47, 39, 31, 23, 15, 7, 62, 54, 46, 38, 30, 22, 14, 6, 61, 53, 45, 37, 29, 21, 13, 5, 28, 20, 12, 4]; + +for i = 1:numel(pc1_c); + C0(i) = key64(pc1_c(i)); + D0(i) = key64(pc1_d(i)); +end + + +%{ +to test this function: +call it with an array containing the 64 first strictly positive integer and +compare the output c and d with the permutation table as defined in fips 46-3, +page 19. + +[c,d] = des_permuted_choice_1(1:64); +result = all(c == permut_table1) and all(d == permut_table2); + +%} diff --git a/src/Matlab/DataEncryptionStandard/des_permuted_choice_2.m b/src/Matlab/DataEncryptionStandard/des_permuted_choice_2.m new file mode 100755 index 0000000..ef6fe31 --- /dev/null +++ b/src/Matlab/DataEncryptionStandard/des_permuted_choice_2.m @@ -0,0 +1,25 @@ +function [subkey48] = des_permuted_choice_2(c, d) +% DES_PERMUTED_CHOICE_2(C, D), where C and D come from shifted C0 and D0 + +pc2 = [14, 17, 11, 24, 1, 5, 3, 28, 15, 6, 21, 10, 23, 19, 12, 4, 26, 8, 16, 7, 27, 20, 13, 2, 41, 52, 31, 37, 47, 55, 30, 40, 51, 45, 33, 48, 44, 49, 39, 56, 34, 53, 46, 42, 50, 36, 29, 32]; + +for i = 1:numel(pc2); + bit_num = pc2(i); + if bit_num <= 28 + subkey48(i) = c(bit_num); + else + subkey48(i) = d(bit_num - 28); + end +end + + +%{ +to test this function: +call it with c an array containing the 24 first strictly positive integer, +d an array containing the 24 following integer and compare the output subkey +with the permutation table as defined in fips 46-3, page 21. + +subkey = des_permuted_choice_2(1:28, 29:56); +result = all(subkey == permut_table2); + +%} diff --git a/src/Matlab/DataEncryptionStandard/des_round.m b/src/Matlab/DataEncryptionStandard/des_round.m new file mode 100755 index 0000000..014a5ac --- /dev/null +++ b/src/Matlab/DataEncryptionStandard/des_round.m @@ -0,0 +1,10 @@ +function [ outBlock64 ] = des_round( inBlock64, subkey48 ) +%DES_ROUND Do a DES round + +% Test case : +%{ +res = des_round([des_cipher_function(zeros(1,32), zeros(1,48)) zeros(1,32)], zeros(1,48)) +all(res == zeros(1, 64)) +%} + +outBlock64 = [xor(des_cipher_function(inBlock64(33:64), subkey48), inBlock64(1:32)), inBlock64(33:64)]; diff --git a/src/Matlab/DataEncryptionStandard/des_sbox.m b/src/Matlab/DataEncryptionStandard/des_sbox.m new file mode 100755 index 0000000..b5fd92d --- /dev/null +++ b/src/Matlab/DataEncryptionStandard/des_sbox.m @@ -0,0 +1,76 @@ +function [ block4 ] = des_sbox( block6, sboxNumber ) +%DES_SBOX Returns a 4 bits block from a 6 bits block +% sbox_number is the number of the chosen sbox (1 .. 8) + +% Test case : +%{ +block6 = [ 0 1 1 0 1 1 ] +rowNumber = 1 +colNumber = 13 +%} + +% rowNumber is in [1 : 4] +rowNumber = (2 * block6(1) + block6(6)) + 1; + +% colNumber is in [1 : 16] +colNumber = sum(block6(2:5) .* [8 4 2 1]) + 1; + + +% S1 +S = [ +14 4 13 1 2 15 11 8 3 10 6 12 5 9 0 7 ; + 0 15 7 4 14 2 13 1 10 6 12 11 9 5 3 8 ; + 4 1 14 8 13 6 2 11 15 12 9 7 3 10 5 0 ; +15 12 8 2 4 9 1 7 5 11 3 14 10 0 6 13 ]; + +% S2 +S(:, :, 2) = [ +15 1 8 14 6 11 3 4 9 7 2 13 12 0 5 10; + 3 13 4 7 15 2 8 14 12 0 1 10 6 9 11 5; + 0 14 7 11 10 4 13 1 5 8 12 6 9 3 2 15; +13 8 10 1 3 15 4 2 11 6 7 12 0 5 14 9]; + +% S3 +S(:, :, 3) = [ +10 0 9 14 6 3 15 5 1 13 12 7 11 4 2 8; +13 7 0 9 3 4 6 10 2 8 5 14 12 11 15 1; +13 6 4 9 8 15 3 0 11 1 2 12 5 10 14 7; + 1 10 13 0 6 9 8 7 4 15 14 3 11 5 2 12]; + +% S4 +S(:, :, 4) = [ + 7 13 14 3 0 6 9 10 1 2 8 5 11 12 4 15; +13 8 11 5 6 15 0 3 4 7 2 12 1 10 14 9; +10 6 9 0 12 11 7 13 15 1 3 14 5 2 8 4; + 3 15 0 6 10 1 13 8 9 4 5 11 12 7 2 14]; + +% S5 +S(:, :, 5) = [ + 2 12 4 1 7 10 11 6 8 5 3 15 13 0 14 9; +14 11 2 12 4 7 13 1 5 0 15 10 3 9 8 6; + 4 2 1 11 10 13 7 8 15 9 12 5 6 3 0 14; +11 8 12 7 1 14 2 13 6 15 0 9 10 4 5 3]; + +% S6 +S(:, :, 6) = [ +12 1 10 15 9 2 6 8 0 13 3 4 14 7 5 11; +10 15 4 2 7 12 9 5 6 1 13 14 0 11 3 8; + 9 14 15 5 2 8 12 3 7 0 4 10 1 13 11 6; + 4 3 2 12 9 5 15 10 11 14 1 7 6 0 8 13]; + +% S7 +S(:, :, 7) = [ + 4 11 2 14 15 0 8 13 3 12 9 7 5 10 6 1; +13 0 11 7 4 9 1 10 14 3 5 12 2 15 8 6; + 1 4 11 13 12 3 7 14 10 15 6 8 0 5 9 2; + 6 11 13 8 1 4 10 7 9 5 0 15 14 2 3 12]; + +% S8 +S(:, :, 8) = [ +13 2 8 4 6 15 11 1 10 9 3 14 5 0 12 7; + 1 15 13 8 10 3 7 4 12 5 6 11 0 14 9 2; + 7 11 4 1 9 12 14 2 0 6 10 13 15 3 5 8; + 2 1 14 7 4 10 8 13 15 12 9 0 3 5 6 11]; + +retNumber = S(rowNumber, colNumber, sboxNumber); +block4 = bitget(uint8(retNumber), 4:-1:1); diff --git a/src/Matlab/DataEncryptionStandard/des_shift.m b/src/Matlab/DataEncryptionStandard/des_shift.m new file mode 100755 index 0000000..abb6704 --- /dev/null +++ b/src/Matlab/DataEncryptionStandard/des_shift.m @@ -0,0 +1,15 @@ +function [ outBlock28 ] = des_shift( inBlock28, shift ) +%DES_SHIFT Left shift of a 28 bits block +% shift is 1 or 2 + +% Test case : +%{ +all(des_shift(1:28, 2) == [3:28, 1:2]) +all(des_shift(1:28, 1) == [2:28, 1]) +%} + +if shift == 1 + outBlock28 = [inBlock28(2:28) inBlock28(1)]; +else % shift == 2 + outBlock28 = [inBlock28(3:28) inBlock28(1:2)]; +end diff --git a/src/Matlab/DataEncryptionStandard/test_des.sh b/src/Matlab/DataEncryptionStandard/test_des.sh new file mode 100755 index 0000000..4d18b0b --- /dev/null +++ b/src/Matlab/DataEncryptionStandard/test_des.sh @@ -0,0 +1,21 @@ +#!/bin/sh + +if [ $# -ne 2 ]; then + echo "Usage: $0 key data" + exit 1 +fi + +key="$1" +data="$2" + +echo "The key is '$key'." +echo "The data is '$data'." + +cmd=$(echo "$data" | sed -r "s/(..)(..)(..)(..)(..)(..)(..)(..)/awk 'BEGIN{ printf(\"%c%c%c%c%c%c%c%c\", 0x\1, 0x\2, 0x\3, 0x\4, 0x\5, 0x\6, 0x\7, 0x\8); exit; }'/") + +enc=$( (eval $cmd) | openssl des -des-ecb -K "$key" -iv '0000000000000000' -nosalt -nopad -e |od -t x1 | head -n 1 |cut -d" " -f 2- ) +dec=$( (eval $cmd) | openssl des -des-ecb -K "$key" -iv '0000000000000000' -nosalt -nopad -d |od -t x1 | head -n 1 |cut -d" " -f 2- ) + +echo "The encrypted data is '$enc'." +echo "The decrypted data is '$dec'." +