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
Famous quotes containing the word attacks:
“Leadership does not always wear the harness of compromise. Once and again one of those great influences which we call a Cause arises in the midst of a nation. Men of strenuous minds and high ideals come forward.... The attacks they sustain are more cruel than the collision of arms.... Friends desert and despise them.... They stand alone and oftentimes are made bitter by their isolation.... They are doing nothing less than defy public opinion, and shall they convert it by blows. Yes.”
—Woodrow Wilson (1856–1924)