Pitfalls in Designing Substitution Boxes

Proceedings of the 1st ACM conference on Computer and communications security - CCS '93, 1993

Mathematics

A Substitution box (S-box) is an important component used in symmetric key cryptosystems to satisfy Shannon’s property on confusion. As the only nonlinear operation, the S-box must be cryptographically strong to thwart any cryptanalysis tools on cryptosystems. Generally, the S-boxes can be constructed using any of the following approaches: the random search approach, heuristic/evolutionary approach or mathematical approach. However, the current S-box construction has some drawbacks, such as low cryptographic properties for the random search approach and the fact that it is hard to develop mathematical functions that can be used to construct a cryptographically strong S-box. In this paper, we explore the non-permutation function that was generated from the binomial operation of the power function to construct a cryptographically strong S-box. By adopting the method called the Redundancy Removal Algorithm, we propose some enhancement in the algorithm such that the desired result can b...

Proceedings 22nd International Conference on Distributed Computing Systems Workshops

2020

The results of studies of the properties of random permutations carried out with the participation of the authors are generalized. It is shown that random substitutions overwhelmingly have good cryptographic, and in particular, algebraic properties. The prospects of using random S-blocks to build block symmetric ciphers with improved dynamic rates of arrival to random substitution are substantiated. A refined model of random substitution and the corresponding criteria are proposed, with the help of which one can verify the suitability of substitutions generated randomly for use in modern cipher designs. It is a check, since with a very high probability the checked substitutions will be suitable.

Security and Communication Networks

In the literature, different algebraic techniques have been applied on Galois field GF(28) to construct substitution boxes. In this paper, instead of Galois field GF(28), we use a cyclic group C255 in the formation of proposed substitution box. The construction proposed S-box involves three simple steps. In the first step, we introduce a special type of transformation T of order 255 to generate C255. Next, we adjoin 0 to C255 and write the elements of C255∪0 in 16×16 matrix to destroy the initial sequence 0,1,2,…,255. In the 2nd step, the randomness in the data is increased by applying certain permutations of the symmetric group S16 on rows and columns of the matrix. In the last step we consider the symmetric group S256, and positions of the elements of the matrix obtained in step 2 are changed by its certain permutations to construct the suggested S-box. The strength of our S-box to work against cryptanalysis is checked through various tests. The results are then compared with the ...

International Journal of Advanced Computer Science and Applications, 2016

)Jennifer Seberry, Xian-Mo Zhang and Yuliang ZhengDepartment of Computer ScienceUniversity of Wollongong, Wollongong, NSW 2522, Australiafjennie, xianmo, yuliangg@cs.uow.edu.auAbstract. Two significant recent advances in cryptanalysis, namely thedifferential attack put forward by Biham and Shamir [3] and the linearattack by Matsui [7, 8], have had devastating impact on data encryptionalgorithms. An eminent problem that researchers are facing is to designS-boxes or substitution

AIP Advances, 2017

ETRI Journal, 2001