关键词: 密码学, 高级加密标准, S盒, 二次方程

Abstract:

As the only nonlinear component in most block ciphers, S-box is responsible for the security of block ciphers. In this paper, the existence of the quadratic equations on S-boxes is theoretically analyzed, and 55 linearly independent quadratic equations on the S-box of the Advanced Encryption Standard （AES） are proved existent in the GF（2⁸） region. All these equations are then given in the paper. Moreover, in order to avoid the algebraic attacks using these equations, such as the eXtended Sparse Linearization （XSL） attack, a new S-box design criterion is presented. In the new S-box there exists no quadratic equation that may be used for algebraic attacks.

Key words: cryptography, Advanced Encryption Standard, S-box, quadratic equation