No description available.

The thesis focuses on an algebraic description of S-boxes by the special type of quadratic equations, defined as biaffine equations. Biaffine equations satisfying S-boxes of higher order may not even exist. However, the special type of S-boxes en- ables to find such equations also for S-boxes of higher order. The S-box in the block cipher Rijndael, composed of the inverse function and the affine transformation, is an example of such special type of S-boxes. The thesis proves that a number of biaffine equations satisfying an S-box of this type does not depend on the affine function. The thesis also proves that for every S-box of order n formed by the in- verse function there exist at least 3n − 1 biaffine equations satisfying this S-box. 1

Les travaux de recherche de cette thèse s’inscrivent dans le cadre de la sécurité par chaos des réseaux locaux sans fil, en particulier les réseaux de capteurs sans fil. L’originalité de cette thèse consiste à proposer des cryptosystèmes à base de chaos plus adaptés aux réseaux de capteurs, en termes de consommation d’énergie, que les algorithmes conventionnels et à réaliser une implémentation sur une plateforme réelle. Nous présentons en premier lieu un état de l’art des réseaux, les menaces, les contraintes limitant le processus de sécurité des informations ainsi que les principales techniques de cryptographie. Nous donnons un aperçu sur la théorie de chaos et nous validons l’aspect aléatoire de plusieurs suites chaotiques par les tests statistiques du NIST. Nous proposons ensuite des nouvelles méthodes de construction de S-Box chaotiques tout en prouvant leur robustesse contre les attaques traditionnelles. Nous proposons enfin un nouvel algorithme de cryptage d’image dédié au réseau de capteurs sans fil. La validation de nos contributions est effectuée par simulation et par des mesures expérimentales sur une plateforme de réseaux de capteurs réels (SensLab). / The security of wireless sensor network is a growing field of research hampered by limited battery life time and computing constraints. The originality of this thesis is to provide Low Power chaotic cryptosystems for sensor networks more suitable than conventional algorithms and achieve an implementation on a real platform.. We present first a state of the art of wireless networks, threats and constraints of the security process as well as conventional cryptographic techniques. We give an overview of the chaos theory and we validate the randomness of several chaotic maps by the NIST statistical tests. Then, we propose new methods of chaotic S-Box construction, while demonstrating their robustness against traditional attacks. Finally, we propose a new image encryption algorithm dedicated to wireless sensor network. Validation of our contributions is performed by simulation and experimental measurements on a platform of real sensor networks (SensLab).

In this thesis, we examine a family of vectorial boolean functions on F22m inspired by Kim function, in order to find new APN permutations on F22m for m > 2. The functions of this family are defined as F(X) = X3 + bX3q + cX2q+1 + dXq+2 , where parameters b, c and d are from F2m . Necessary and sufficient conditions for this functions to be APN or equivalent to a permutation are presented in this thesis. To find conditions for being APN, Trace-0/Trace-1 decomposition method is used. A method using exponential sums is used to deduce which functions of this family is CCZ-equivalent to a certain type of permutation. These results were then used to search for APN permutations on F26 and F210 . 1

This thesis introduces a new chaos-based Advanced Encryption Standard (AES). The AES is a well-known encryption algorithm that was standardized by U.S National Institute of Standard and Technology (NIST) in 2001. The thesis investigates and explores the behavior of the AES algorithm by replacing two of its original modules, namely the S-Box and the Key Schedule, with two other chaos- based modules. Three chaos systems are considered in designing the new modules which are Lorenz system with multiplication nonlinearity, Chen system with sign modules nonlinearity, and 1D multiscroll system with stair case nonlinearity. The three systems are evaluated on their sensitivity to initial conditions and as Pseudo Random Number Generators (PRNG) after applying a post-processing technique to their output then performing NIST SP. 800-22 statistical tests. The thesis presents a hardware implementation of dynamic S-Boxes for AES that are populated using the three chaos systems. Moreover, a full MATLAB package to analyze the chaos generated S-Boxes based on graphical analysis, Walsh-Hadamard spectrum analysis, and image encryption analysis is developed. Although these S-Boxes are dynamic, meaning they are regenerated whenever the encryption key is changed, the analysis results show that such S-Boxes exhibit good properties like the Strict Avalanche Criterion (SAC) and the nonlinearity and in the application of image encryption. Furthermore, the thesis presents a new Lorenz-chaos-based key expansion for the AES. Many researchers have pointed out that there are some defects in the original key expansion of AES and thus have motivated such chaos-based key expansion proposal. The new proposed key schedule is analyzed and assessed in terms of confusion and diffusion by performing the frequency and SAC test respectively. The obtained results show that the new proposed design is more secure than the original AES key schedule and other proposed designs in the literature. The proposed design is then enhanced to increase the operating speed using the divide- and-conquer concept. Such enhancement, did not only make the AES algorithm more secure, but also enabled the AES to be faster, as it can now operate on higher frequencies, and more area-efficient.

No description available.

No description available.

Les travaux de recherche de cette thèse s'inscrivent dans le cadre de la sécurité par chaos des réseaux locaux sans fil, en particulier les réseaux de capteurs sans fil. L'originalité de cette thèse consiste à proposer des cryptosystèmes à base de chaos plus adaptés aux réseaux de capteurs, en termes de consommation d'énergie, que les algorithmes conventionnels et à réaliser une implémentation sur une plateforme réelle. Nous présentons en premier lieu un état de l'art des réseaux, les menaces, les contraintes limitant le processus de sécurité des informations ainsi que les principales techniques de cryptographie. Nous donnons un aperçu sur la théorie de chaos et nous validons l'aspect aléatoire de plusieurs suites chaotiques par les tests statistiques du NIST. Nous proposons ensuite des nouvelles méthodes de construction de S-Box chaotiques tout en prouvant leur robustesse contre les attaques traditionnelles. Nous proposons enfin un nouvel algorithme de cryptage d'image dédié au réseau de capteurs sans fil. La validation de nos contributions est effectuée par simulation et par des mesures expérimentales sur une plateforme de réseaux de capteurs réels (SensLab).

The construction of a substitution box (S-box) with high nonlinearity and high resiliency is an important research area in cryptography. In this thesis, t-resilient nxm S-box construction methods depending on linear block codes presented in &quot / A Construction of Resilient Functions with High Nonlinearity&quot / by T. Johansson and E. Pasalic in 2000, and two years later in &quot / Linear Codes in Generalized Construction of Resilient Functions with Very High Nonlinearity&quot / by E. Pasalic and S. Maitra are compared and the former one is observed to be more promising in terms of nonlinearity. The first construction method uses a set of nonintersecting [n-d,m,t+1] linear block codes in deriving t-resilient S-boxes of nonlinearity 2^(n-1)-2^(n-d-1),where d is a parameter to be maximized for high nonlinearity. For some cases, we have found better results than the results of Johansson and Pasalic, using their construction. As a distinguished reference for nxn S-box construction methods, we study the paper &quot / Differentially Uniform Mappings for Cryptography&quot / presented by K.Nyberg in Eurocrypt 1993. One of the two constructions of this paper, i.e., the inversion mapping described by Nyberg but first noticed in 1957 by L. Carlitz and S. Uchiyama, is used in the S-box of Rijndael, which is chosen as the Advanced Encryption Standard. We complete the details of some theorem and proposition proofs given by Nyberg.

Two versions of SNOW, which are word-oriented stream ciphers proposed by P. Ekdahl and T. Johansson in 2000 and 2002, are studied together with cryptanalytic attacks on the first version. The reported attacks on SNOW1.0 are the &ldquo / guess-and-determine attack&rdquo / s by Hawkes and Rose and the &ldquo / distinguishing attack&rdquo / by Coppersmith, Halevi and Jutla in 2002. A review of the distinguishing attack on SNOW1.0 is given using the approach made by the designers of SNOW in 2002 on another cipher, SOBER-t32. However, since the calculation methods for the complexities of the attack are different, the values found with the method of the designers of SNOW are higher than the ones found by Coppersmith, Halevi and Jutla. The correlations in the finite state machine that make the distinguishing attack possible and how these correlations are affected by the operations in the finite state machine are investigated. Since the substitution boxes (S-boxes) play an important role in destroying the correlation and linearity caused by Linear Feedback Shift Register, the s-boxes of the two versions of SNOW are examined for the criteria of Linear Approximation Table (LAT), Difference Distribution Table (DDT) and Auto-correlation Table distributions. The randomness tests are performed using NIST statistical test suite for both of the ciphers. The results of the tests are presented.