Provable Security Against Differential Attacks for Generalized SPN Structures

Abstract

In the practice of block cipher design, designers usually choose linear functions over () n GF 2 with large branch numbers to achieve provable security against differential and linear attack. Recently, the Internet-of-Things gives rise to a number of applications that require Lightweight block ciphers, some new extensions of the diffusion layer were proposed, and these diffusion layers are designed by the matrices over commutative rings. Compared with the matrices which were defined over () n GF 2 , these matrices need less cost in hardware implementation and are thus more suitable for lightweight ciphers. In this work, we prove that the SPN structure with an extended diffusion layer provides a provable security against differential attack and linear attack. The probability of each differential of the SPS function is bounded by r p 1 , where p is the maximum differential probability of S-boxes used in the substitution layer, and r denotes the branch number of the diffusion layer. Similarly, the results of maximum linear hull bias could also be obtained. With the application of our method, we give the first security evaluation for some SPS structures with the matrix over () GF 2 against differential attack.