Reversed genetic algorithms for generation of bijective s-boxes with good cryptographic properties

Abstract

Abstract. Often S-boxes are the only nonlinear component in a block cipher and as such play an important role in ensuring its resistance to cryptanalysis. Cryptographic properties and constructions of S-boxes have been studied for many years. The most common techniques for constructing S-boxes are: algebraic constructions, pseudo-random generation and a variety of heuristic approaches. Among the latter are the genetic algorithms. In this paper, a genetic algorithm working in a reversed way is proposed. Using the algorithm we can rapidly and repeatedly generate a large number of strong bijective S-boxes of each dimension from (8 × 8) to (16 × 16), which have sub-optimal properties close to the ones of S-boxes based on finite field inversion, but have more complex algebraic structure and possess no linear redundancy.

Bijective S-boxes of different sizes obtained from quasi-cyclic codes

“…In our paper [3] we considered only the first construction technique and its application only in the case of 8 × 8 S-boxes. Now we extend our study to more construction methods with applications to bijective S-boxes of sizes 4,6,8,9,10,11,12,14,15,16 and 18.…”

Current implementation of advance encryption standard (AES) S-Box

“…The iteration will run several times and maximum time taken will be 10 days. While in [41], the same author introduced another biological approach method to construct S-Box.…”

S-Boxes from Binary Quasi-Cyclic Codes

“…The smallest possible value of δ in the case of bijective S-boxes (n = m) is 2. Summarized results for good S-boxes are presented in [5] and [6].…”

“…We have done the exhaustive search for m = 17, r = 15, and have concluded that there are 15 S-boxes with nonlinearity 112, and 601 S-boxes with nonlinearity 108. The most important parameters (see [6]) of these 15 S-boxes are presented in the following table. Note that the computed parameters coincide with the parameters of the S-box used in the block cipher AES.…”