An Efficient Structural Analysis of SAS and its Application to White-Box Cryptography

Structural analysis is the study of finding component functions for a given function. In this paper, we proceed with structural analysis of structures consisting of the S (nonlinear Substitution) layer and the A (Affine or linear) layer. Our main interest is the S1AS2 structure with different substitution layers and large input/output sizes. The purpose of our structural analysis is to find the functionally equivalent oracle F* and its component functions for a given encryption oracle F(= S2 ∘ A ∘ S1). As a result, we can construct the decryption oracle F*−1 explicitly and break the one-wayness of the building blocks used in a White-box implementation. Our attack consists of two steps: S layer recovery using multiset properties and A layer recovery using differential properties. We present the attack algorithm for each step and estimate the time complexity. Finally, we discuss the applicability of S1AS2 structural analysis in a White-box Cryptography environment.