Algebraic Attacks over GF(2k), Application to HFE Challenge 2 and Sflash-v2

The problem MQ of solving a system of multivariate quadratic equations over a finite field is relevant to the security of AES and for several public key cryptosystems. For example Sflash, the fastest known signature scheme (cf. [1]), is based on MQ equations over GF(27), and Patarin’s 500 $ HFE Challenge 2 is over GF(24). Similarly, the fastest alleged algebraic attack on AES due to Courtois, Pieprzyk, Murphy and Robshaw uses a MQ system over GF(28).

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