Abstract: This paper focuses on the number of algebraic equations, which describe the S-boxes of several famous block ciphers such of DES, AES, MARS and SERPENT. We compute the number of these algebraic equations from low degree to high degree. A comparison between the number of these equations and the theoretical minimum value is presented. Moreover, this paper introduces a kind of incomplete algebraic equations which are especially important to cryptanalysis. By comparing the number of these incomplete equations with that of a random S-box, a difference is shown between the S-boxes of these block ciphers and a random S-box.

Key words: block cipher, S-box, algebraic equations