Designing cryptographically strong S-boxes with the use of cellular automata

Block ciphers are widely used in modern cryptography. Substitution boxes (S-boxes) are main elements of these types of ciphers. In this paper we propose a new method to create S-boxes, which is based on application of Cellular Automata (CA). We present the results of testing CA-based S-boxes. These results confirm that CA are able to realize efficiently the Boolean function corresponding to classical S-boxes the proposed CA-based S-boxes offer cryptographic properties comparable or better than classical S-box tables

Guaranteeing the diversity of number generators

A major problem in using iterative number generators of the form x_i=f(x_{i-1}) is that they can enter unexpectedly short cycles. This is hard to analyze when the generator is designed, hard to detect in real time when the generator is used, and can have devastating cryptanalytic implications. In this paper we define a measure of security, called_sequence_diversity_, which generalizes the notion of cycle-length for non-iterative generators. We then introduce the class of counter assisted generators, and show how to turn any iterative generator (even a bad one designed or seeded by an adversary) into a counter assisted generator with a provably high diversity, without reducing the quality of generators which are already cryptographically strong.Comment: Small update

Cryptographically strong permutations from the butterfly structure

Boomerang connectivity table is a new tool to characterize the vulnerability of cryptographic functions against boomerang attacks. Consequently, a cryptographic function is desired to have boomerang uniformity as low as its differential uniformity. Based on generalized butterfly structures recently introduced by Canteaut, Duval and Perrin, this paper presents infinite families of permutations of ${\mathbb {F}}_{2^{2n}}$ for a positive odd integer n, which have the best known nonlinearity and boomerang uniformity 4. Both open and closed butterfly structures are considered. The open butterflies, according to experimental results, appear not to produce permutations with boomerang uniformity 4. On the other hand, from the closed butterflies we derive a condition on coefficients $\alpha , \beta \in {\mathbb {F}}_{2^n}$ such that the functions $$\begin{aligned} V_i(x,y) := (R_i(x,y), R_i(y,x)), \end{aligned}$$ where $R_i(x,y)=(x+\alpha y)^{2^i+1}+\beta y^{2^i+1}$ and $\gcd (i,n)=1$, permute ${{\mathbb {F}}}_{2^n}^2$ and have boomerang uniformity 4. In addition, experimental results for $n=3, 5$ indicate that the proposed condition seems to cover all such permutations $V_i(x,y)$ with boomerang uniformity 4.acceptedVersio

Nonlinearity and propagation characteristics of balanced boolean functions

Three of the most important criteria for cryptographically strong Boolean functions are the balancedness, the nonlinearity and the propagation criterion. The main contribution of this paper is to reveal a number of interesting properties of balancedness and nonlinearity, and to study systematic methods for constructing Boolean functions satisfying some or all of the three criteria. We show that concatenating, splitting, modifying and multiplying (in the sense of Kronecker) sequences can yield balanced Boolean functions with a very high nonlinearity. In particular, we show that balanced Boolean functions obtained by modifying and multiplying sequences achieve a nonlinearity higher than that attainable by any previously known construction method. We also present methods for constructing balanced Boolean functions that are highly nonlinear and satisfy the strict avalanche criterion (SAC). Furthermore we present methods for constructing highly nonlinear balanced Boolean functions satisfying the propagation criterion with respect to all but one or three vectors. A technique is developed to transform the vectors where the propagation criterion is not satisfied in such a way that the functions constructed satisfy the propagation criterion of high degree while preserving the balancedness and nonlinearity of the functions. The algebraic degrees of functions constructed are also discussed, together with examples illustrating the various constructions