Abstract:

In a white-box attack model, the attacker can access the implementation process of the cryptographic algorithm, observe or modify the internal details of the cryptographic algorithm. Based on the concept of white-box cryptography, Yao-Chen’s white-box SM4 scheme presents a design idea for expanding the internal state of white-box SM4, but the scheme fails to resist the analysis of collision attack, and the time complexity of recovering the key is only O(2^23.02). In order to ensure the normal operation of white-box SM4 in the collision attack context, this paper proposed a white-box improvement scheme of SM4 for collision attack. This improvement scheme introduced more random affine transformations and random vectors to complicate the internal encoding to resist the collision attack. By using the counter proof method, it was proven that the round encryption function of the improved scheme couldn’t be converted into a collision function, and the analysis of collision attack couldn’t be carried out. In addition, this paper demonstrated that the scheme can also resist BGE attack, code extraction attacks and a combination of differential analysis and methods for solving systems of equations. For the attack method of differential analysis with adjusted affine constant, the key space size of the improved scheme was 61200×2¹²⁸, and the time complexity for affine equivalent attack was O(2⁹⁷).

Key words: white-box attack context, white-box cryptography, collision attack, complex coding