Abstract-We present an extensive study of symmetric Boolean functions, especially of their cryptographic properties. Our main result establishes the link between the periodicity of the simplified value vector of a symmetric Boolean function and its degree. Besides the reduction of the amount of memory required for representing a symmetric function, this property has some consequences from a cryptographic point of view. For instance, it leads to a new general bound on the order of resiliency of symmetric functions, which improves Siegenthaler's bound. The propagation characteristics of these functions are also addressed and the algebraic normal forms of all their derivatives are given. We finally detail the characteristics of the symmetric functions of degree at most 7, for any number of variables. Most notably, we determine all balanced symmetric functions of degree less than or equal to 7.

Abstract.To improve the security of iterated block ciphers, the resistance against linear cryptanalysis has been formulated in terms of provable security which suggests the use of highly nonlinear functions as round functions. Here, we show that some properties of such functions enable to find a new upper bound for the degree of the product of its Boolean components. Such an improvement holds when all values occurring in the Walsh spectrum of the round function are divisible by a high power of 2. This result leads to a higher order differential attack on any 5-round Feistel ciphers using an almost bent substitution function. We also show that the use of such a function is precisely the origin of the weakness of a reduced version of MISTY1 reported in [23,1].

International audienceMixed Boolean-Arithmetic expressions are presented as a strong protection in the context of data flow obfuscation. As there is very little literature on the analysis of such obfus-cated expressions, two important subjects of interest are: to define what simplifying those expressions means, and how to design a simplification solution. We focus on evaluating the resilience of this technique, by giving theoretical elements to justify its efficiency and proposing a simplification algorithm using a pattern matching approach. The implementation of this solution is capable of simplifying the public examples of MBA-obfuscated expressions, demonstrating that at least a subset of MBA obfuscation lacks resilience against pattern matching analysis

In order to assess the security of cryptosystems based on the discrete logarithm problem in non-prime finite fields, as are the torus-based or pairing-based ones, we investigate thoroughly the case in F p 6 with the number field sieve. We provide new insights, improvements, and comparisons between different methods to select polynomials intended for a sieve in dimension 3 using a special-q strategy. We also take into account the Galois action to increase the relation productivity of the sieving phase. To validate our results, we ran several experiments and real computations for various polynomial selection methods and field sizes with our publicly available implementation of the sieve in dimension 3, with special-q and various enumeration strategies.

Abstract. The year 2013 has seen several major complexity advances for the discrete logarithm problem in multiplicative groups of smallcharacteristic finite fields. These outmatch, asymptotically, the Function Field Sieve (FFS) approach, which was so far the most efficient algorithm known for this task. Yet, on the practical side, it is not clear whether the new algorithms are uniformly better than FFS. This article presents the state of the art with regard to the FFS algorithm, and reports data from a record-sized discrete logarithm computation in a prime-degree extension field.