Ces travaux de thèse se concentrent sur l'étude des attaques par canaux cachés et les implications sur les mesures à prendre pour un concepteur de circuits sécurisés. Nous nous intéressons d'abord aux différentes attaques par canaux cachés en proposant une amélioration pour un type d'attaque générique particulièrement intéressante : l'attaque par analyse d'information mutuelle. Nous étudions l'effet des différentes techniques d'estimation d'entropie sur les résultats de l'attaque. Nous proposons l'utilisation de fonctions B-splines comme estimateurs étant donné qu'elles sont bien adaptées à notre scénario d'attaques par canaux cachés. Nous étudions aussi l'impact que peut avoir ce type d'attaques sur un cryptosystème symétrique connu, l'Advanced Encryption Standard (AES), en proposant une contre-mesure basée sur la structure algébrique de l'AES. L'opération principale de la majorité des systèmes ECC est la multiplication scalaire qui consiste à additionner un certain nombre de fois un point de courbe elliptique avec lui-même. Dans une deuxième partie, nous nous intéressons à la sécurisation de cette opération. Nous proposons un algorithme de multiplication scalaire à la fois efficace et résistant face aux principales attaques par canaux cachés. Nous étudions enfin les couplages, une construction mathématique basée sur les courbes elliptiques, qui possède des propriétés intéressantes pour la création de nouveaux protocoles cryptographiques. Nous évaluons finalement la résistance aux attaques par canaux cachés de ces constructions. / This thesis focuses on the study of side-channel attacks as well as their consequences on the secure implementation of cryptographic algorithms. We first analyze different side-channel attacks and we propose an improvement of a particularly interesting generic attack: the mutual information analysis. We study the effect of state of the art entropy estimation techniques on the results of the attack. We propose the use of B-spline funtions as estimators as they are well suited to the side-channel attack scenario. We also investigate the consequences of this kind of attack on a well known symmetric cryptosystem, the Advanced Encryption Standard (AES), and we propose a countermeasure based on the algebraic structure of AES. The main operation of ECC is the scalar multiplication that consists of adding an elliptic curve point to itself a certain number of times. In the second part, we investigate how to secure this operation. We propose a scalar multiplication algorithm that is both efficient and secure against main side-channel attacks. We then study pairings, a mathematical construction based on elliptic curves. Pairings have many interesting properties that allow the creation of new cryptographic protocols. We finally evaluate the side-channel resistance of pairings.

Cette thèse se concentre sur les problèmes liés à l’authentification dans la technologie RFID. Cette technologie est l’une des technologies les plus prometteuses dans le domaine de l’informatique ubiquitaire, elle est souvent désignée comme la prochaine révolution après Internet. Cependant, à cause des ressources très limitées en termes de calcul, mémoire et énergie sur les étiquettes RFID, les algorithmes classiques de sécurité ne peuvent pas être implémentés sur les étiquettes à bas coût rendant ainsi la sécurité et la vie privée un important sujet de recherche aujourd’hui. Dans un premier temps, nous étudions le passage à l’échelle dans les systèmes RFID à bas coût en développant un module pour ns-3 qui simule le standard EPC Class 1 Generation 2 pour établir un cadre stricte pour l’identification sécurisée des RFID à bas coût, ce qui nous conduit à l’utilisation de la cryptographie à clés publiques. Ensuite, nous proposons un protocole d’authentification basé sur une adaptation que nous avons introduit sur le célèbre cryptosystème NTRU. Ce protocole est spécialement conçu pour les RFID à bas coût comme les étiquettes n’implémentent que des opérations simples (xor, décalages, addition) et il garantit le passage à l’échelle. Enfin, nous considérons l’identification à divulgation nulle de connaissance, ce type d’approches est très utile dans de nombreuses applications RFID. Nous proposons deux protocoles à divulgation nulle de connaissance basés sur cryptoGPS et cryptoGPS randomisé. Ces approches consistent à stocker sur le serveur des coupons pré-calculés, ainsi la sécurité et la vie privée sont mieux supportées que dans les autres approches de ce type / This thesis focuses on issues related to authentication in low-cost radio frequency identification technology, more commonly referred to as RFID. This technology it is often referred to as the next technological revolution after the Internet. However, due to the very limited resources in terms of computation, memory and energy on RFID tags, conventional security algorithms cannot be implemented on low-cost RFID tags making security and privacy an important research subject today. First of all, we investigate the scalability in low-cost RFID systems by developing a ns-3 module to simulate the universal low-cost RFID standard EPC Class-1 Generation-2 in order to establish a strict framework for secure identification in low-cost RFID systems. We show that, the symmetrical key cryptography is excluded from being used in any scalable low-cost RFID standard. Then, we propose a scalable authentification protocol based on our adaptation of the famous public key cryptosystem NTRU. This protocol is specially designed for low-cost RFID systems, it can be efficiently implemented into low-cost tags. Finally, we consider the zero-knowledge identification i.e. when the no secret sharing between the tag and the reader is needed. Such identification approaches are very helpful in many RFID applications when the tag changes constantly the field of administration. We propose two lightweight zero-knowledge identification approaches based on GPS and randomized GPS schemes. The proposed approaches consist in storing in the back-end precomputed values in the form of coupons. So, the GPS-based variant can be private and the number of coupons can be much higher than in other approaches thus leading to higher resistance to denial of service attacks for cheaper tags

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Der Vortrag erläutert das Grundprinzip des Diffie-Hellman-Schlüsseltausches mithilfe des diskreten Logarithmus unter Zuhilfenahme elliptischer Kurven über endlichen Körpern.

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Given an elliptic curve E over Fp and an integer e ≥ 1, we define a new object, called “elliptic loop”, as the set of plane projective points over Z/p^e Z lying over E, endowed with an operation inherited by the curve addition. This object is proved to be a power-associative abelian algebraic loop. Its substructures are investigated by means of other algebraic cubics defined over the same ring, which we named “shadow curve” and “layers”. When E has trace 1, a distinctive behavior is detected and employed for producing an isomorphism attack to the discrete logarithm on this family of curves. Stronger properties are derived for small values of e, which lead to an explicit description of the infinity part and to characterizing the geometry of rational |E|-torsion points. / Data una curva ellittica E su Fp ed un intero e ≥ 1, definiamo un nuovo oggetto, chiamato "loop ellittico", come l'insieme dei punti nel piano proiettivo su Z/p^e Z che stanno sopra ad E, dotato di una operazione ereditata dalla somma di punti sulla curva. Questo oggetto si prova essere un loop algebrico con associatività delle potenze. Le sue sotto-strutture sono investigate utilizzando altre cubiche definite sullo stesso anello, che abbiamo chiamato "curva ombra" e "strati". Quando E ha traccia 1, un comportamento speciale viene notato e sfruttato per produrre un attacco di isomorfismo al problema del logaritmo discreto su questa famiglia di curve. Migliori proprietà vengono trovate per bassi valori di e, che portano ad una descrizione esplicita della parte all'infinito e alla caratterizzazione della geometria dei punti razionali di |E|-torsione.

Security of cryptographic algorithms relies on the computational difficulty of deriving the secret key using public information. Cryptanalysis, including logical and implementation attacks, plays an important role in allowing the security community to estimate their cost, based on the computational resources of an attacker. Practical implementations of cryptanalytic systems require complex designs that integrate multiple functional components with many parameters. In this thesis, methodologies are proposed to improve the design process of cryptanalytic systems and reduce the cost of design space exploration required for optimization. First, Bluespec, a rule-based HDL, is used to increase the abstraction level of hardware design and support efficient design space exploration. Bluespec is applied to implement a hardware-accelerated logical attack on ECC with optimized modular arithmetic components. The language features of Bluespec support exploration and this is demonstrated by applying Bluespec to investigate the speed area tradeoff resulting from various design parameters and demonstrating performance that is competitive with prior work. This work also proposes a testing environment for use in verifying the implementation attack resistance of secure systems. A modular design approach is used to provide separation between the device being tested and the test script, as well as portability, and openness. This yields an open-source solution that supports implementation attack testing independent of the system platform, implementation details, and type of attack under evaluation. The suitability of the proposed test environment for implementation attack vulnerability analysis is demonstrated by applying the environment to perform an implementation attack on AES. The design of complex cryptanalytic hardware can greatly benefit from better design methodologies and the results presented in this thesis advocate the importance of this aspect. / Master of Science

Cette thèse porte sur l'étude, la conception matérielle, la validation théorique et pratique, et enfin la comparaison de différents opérateurs arithmétiques pour des cryptosystèmes basés sur les courbes elliptiques (ECC). Les solutions proposées doivent être robustes contre certaines attaques par canaux cachés tout en étant performantes en matériel, tant au niveau de la vitesse d'exécution que de la surface utilisée. Dans ECC, nous cherchons à protéger la clé secrète, un grand entier, utilisé lors de la multiplication scalaire. Pour nous protéger contre des attaques par observation, nous avons utilisé certaines représentations des nombres et des algorithmes de calcul pour rendre difficiles certaines attaques ; comme par exemple rendre aléatoires certaines représentations des nombres manipulés, en recodant certaines valeurs internes, tout en garantissant que les valeurs calculées soient correctes. Ainsi, l'utilisation de la représentation en chiffres signés, du système de base double (DBNS) et multiple (MBNS) ont été étudiés. Toutes les techniques de recodage ont été validées théoriquement, simulées intensivement en logiciel, et enfin implantées en matériel (FPGA et ASIC). Une attaque par canaux cachés de type template a de plus été réalisée pour évaluer la robustesse d'un cryptosystème utilisant certaines de nos solutions. Enfin, une étude au niveau matériel a été menée dans le but de fournir à un cryptosystème ECC un comportement régulier des opérations effectuées lors de la multiplication scalaire afin de se protéger contre certaines attaques par observation. / This PhD thesis focuses on the study, the hardware design, the theoretical and practical validation, and eventually the comparison of different arithmetic operators for cryptosystems based on elliptic curves (ECC). Provided solutions must be robust against some side-channel attacks, and efficient at a hardware level (execution speed and area). In the case of ECC, we want to protect the secret key, a large integer, used in the scalar multiplication. Our protection methods use representations of numbers, and behaviour of algorithms to make more difficult some attacks. For instance, we randomly change some representations of manipulated numbers while ensuring that computed values are correct. Redundant representations like signed-digit representation, the double- (DBNS) and multi-base number system (MBNS) have been studied. A proposed method provides an on-the-fly MBNS recoding which operates in parallel to curve-level operations and at very high speed. All recoding techniques have been theoretically validated, simulated extensively in software, and finally implemented in hardware (FPGA and ASIC). A side-channel attack called template attack is also carried out to evaluate the robustness of a cryptosystem using a redundant number representation. Eventually, a study is conducted at the hardware level to provide an ECC cryptosystem with a regular behaviour of computed operations during the scalar multiplication so as to protect against some side-channel attacks.

Protocolos de autenticação e de estabelecimento de chaves são peças fundamentais em implementações de segurança para comunicação de dispositivos eletrônicos. Em aplicações que envolvam dispositivos com poder computacional restrito (tais como smartphones ou tablets) comunicando-se com um servidor, é primordial a escolha de protocolos eficientes e que necessitem de uma infraestrutura mais simples. Neste trabalho selecionamos e implementamos protocolos de acordo de chave seguros nos modelos de criptografia de chave pública baseado em identidade (ID-based) e sem certificado (Certificateless) em plataformas com processadores ARM. Comparamos tempos de execução, utilização de memória e uso do canal de comunicação. / Protocols for authentication and key establishment are fundamental parts in security implementations for electronic devices communication. In applications involving devices with limited computational power (such as smartphones and tablets) communicating with a server, the choice of efficient protocols that require a simpler infrastructure is essential. In this work we select and implement secure key agreement protocols in ID-based and Certificateless public key cryptography models on ARM processor platforms. We also compare running times, memory and network usage.

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