HFE Attacks
There are two famous recent attacks on HFE:
01. Shamir-Kipnis: Recover the Private Key.
The key point of this attack is to recover the private key as sparse univariate polynomials over the extension field . The attack only works for basic HFE and fails for all its variations.
02. Faugere: Fast Gröbner Bases.
The idea of Faugere's attacks is to use fast algorithm to compute a Gröbner basis of the system of polynomial equations. Faugere broke the HFE challenge 1 in 96 hours in 2002 and in 2003 Faugere and Joux worked together on the security of HFE.
Read more about this topic: Hidden Field Equations
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