Inverting HFE Is Quasipolynomial

In the last ten years, multivariate cryptography has emerged as a possible alternative to public key cryptosystems based on hard computational problems from number theory. Notably, the HFE scheme [17] appears to combine efficiency and resistance to attacks, as expected from any public key scheme. However, its security is not yet completely understood. On one hand, since the security is related to the hardness of solving quadratic systems of multivariate binary equations, an NP complete problem, there were hopes that the system could be immune to subexponential attacks. On the other hand, several lines of attacks have been explored, based on so-called relinearization techniques [12, 5], or on the use of Gr

• Type: Conference
• Year: 2006
• Where: CRYPTO
• Authors: Louis Granboulan, Antoine Joux, Jacques Stern
• Keywords: CRYPTO 2006, Cryptology, Decryption Attack, Gr¨obner Basis, Public Key