Features of constructing nonlinear transformations of block symmetric ciphers

Abstract

The article is devoted to the peculiarities of constructing nonlinear transformations of block symmetric ciphers. The history of the emergence of nonlinear transformations of block symmetric ciphers is briefly reviewed and the evolution of block symmetric ciphers after DES. The paper analyzes the methods of constructing S-blocks (Substitution-boxes), which are the main component that implements nonlinear substitutions and ensures cryptographic stability of the block symmetric cipher. The authors investigate and compare four main types of S-blocks: deterministic (fixed), dynamic (key-dependent), chaotically generated and random ones. The article analyzes in detail the advantages and disadvantages of each approach, as well as the key cryptographic properties ensuring that ensure stable nonlinear transformations, such as high nonlinearity, low differential homogeneity, bijectivity, avalanche effect, balance, high algebraic degree. The influence of post-quantum cryptography conditions is considered, in particular, the opposition to the Grover algorithm. The authors conclude that the choice of the S-block structure is a compromise between security, performance and ease of implementation. In the context of post-quantum symmetric block ciphers, the use of verified, fixed S-blocks combined with a key length sufficient to protect against quantum attacks is preferred. The reasons are the same as in the classical case: the complexity of security analysis, the computational cost of generation, and the problems associated with reproducibility. However, hybrid approaches combining algebraic and heuristic methods can also be used to achieve optimal results.