Cryptanalysis Of A Type Of White-Box Implementations Of The SM4 Block Cipher

The SM4 block cipher is a Chinese national standard and an ISO international standard. Since white-box cryptography has many real-life applications nowadays, a few white-box implementations of SM4 has been proposed, among which a type of constructions is dominated, which uses a linear or affine diagonal block encoding to protect the original three 32-bit branches entering a round function and uses its inverse as the input encoding to the S-box layer. In this paper, we analyse the security of this type of constructions against Lepoint et al.'s collision-based attack method. Our experiment under a small fraction of (encodings, round key) combinations shows that the rank of the concerned linear system is much less than the number of the involved unknowns, meaning these white-box SM4 implementations should resist Lepoint et al.'s method, but we leave it as an open problem whether there are such encodings that the rank of the corresponding linear system is slightly less than the number of the involved unknowns, in which scenario Lepoint et al.'s method may be used to recover a round key for the case with linear encodings and to remove most white-box operations until mainly some Boolean masks for the case with affine encodings.