How Far Can We Go Beyond Linear Cryptanalysis?

Several generalizations of linear cryptanalysis have been proposed in the past, as well as very similar attacks in a statistical point of view. In this paper, we define a rigorous general statistical framework which allows to interpret most of these attacks in a simple and unified way. Then, we explicitely construct optimal distinguishers, we evaluate their performance, and we prove that a block cipher immune to classical linear cryptanalysis possesses some resistance to a wide class of generalized versions, but not all. Finally, we derive tools which are necessary to set up more elaborate extensions of linear cryptanalysis, and to generalize the notions of bias, characteristic, and piling-up lemma

Computing Expected Differential Probability of (Truncated) Differentials and Expected Linear Potential of (Multidimensional) Linear Hulls in SPN Block Ciphers

In this paper we introduce new algorithms that, based only on the independent round keys assumption, allow to practically compute the exact expected differential probability of (truncated) differentials and the expected linear potential of (multidimensional) linear hulls. That is, we can compute the exact sum of the probability or the potential of all characteristics that follow a given activity pattern. We apply our algorithms to various recent SPN ciphers and discuss the results

Statistical cryptanalysis of block ciphers

Since the development of cryptology in the industrial and academic worlds in the seventies, public knowledge and expertise have grown in a tremendous way, notably because of the increasing, nowadays almost ubiquitous, presence of electronic communication means in our lives. Block ciphers are inevitable building blocks of the security of various electronic systems. Recently, many advances have been published in the field of public-key cryptography, being in the understanding of involved security models or in the mathematical security proofs applied to precise cryptosystems. Unfortunately, this is still not the case in the world of symmetric-key cryptography and the current state of knowledge is far from reaching such a goal. However, block and stream ciphers tend to counterbalance this lack of "provable security" by other advantages, like high data throughput and ease of implementation. In the first part of this thesis, we would like to add a (small) stone to the wall of provable security of block ciphers with the (theoretical and experimental) statistical analysis of the mechanisms behind Matsui's linear cryptanalysis as well as more abstract models of attacks. For this purpose, we consider the underlying problem as a statistical hypothesis testing problem and we make a heavy use of the Neyman-Pearson paradigm. Then, we generalize the concept of linear distinguisher and we discuss the power of such a generalization. Furthermore, we introduce the concept of sequential distinguisher, based on sequential sampling, and of aggregate distinguishers, which allows to build sub-optimal but efficient distinguishers. Finally, we propose new attacks against reduced-round version of the block cipher IDEA. In the second part, we propose the design of a new family of block ciphers named FOX. First, we study the efficiency of optimal diffusive components when implemented on low-cost architectures, and we present several new constructions of MDS matrices; then, we precisely describe FOX and we discuss its security regarding linear and differential cryptanalysis, integral attacks, and algebraic attacks. Finally, various implementation issues are considered

Stochastic cryptanalysis of Crypton

Abstract. Crypton is a 12-round blockcipher proposed as an AES candidate by C.H. Lim in 1998. In this paper, we show how to exploit some statistical deficiencies of the Crypton round function to mount stochastic attacks on round-reduced versions of Crypton. Though more efficient than the best differential and linear attacks, our attacks do not endanger the practical security offered by Crypton.