Novel Recursive Construction Method for Resilient S-Boxes

Abstract

Resilient S-boxes have many applications in quantum cryptographic key distribution, random sequence generation for stream ciphers, and fault-tolerant distributed computing. In this paper, we provide a novel method of constructing new resilient S-boxes from old ones. The proposed method is a simple modification on the recursive construction technique for resilient S-boxes due to Zhang and Zheng. The modified Zhang-Zheng construction has better performance since it increases the output dimensions of S-boxes, whereas having the same resiliency as the existing method. Using this new method, given an (n, m, t)-resilient S-box, one can construct an ((h+1)kn, (h+1)km, 2k(1+t) -1)-resilient S-box for all h = 2, 3,…, and k =1, 2,….