TOT, a Fast Multivariate Public Key Cryptosystem with Basic Secure Trapdoor

In this paper, we design a novel one-way trapdoor function, and then propose a new multivariate public key cryptosystem called TOT, which can be used for encryption, signature and authentication. Through analysis, we declare that TOT is secure, because it can resist current known algebraic attacks if its parameters are properly chosen. Some practical implementations for TOT are also given, and whose security level is at least 2. The comparison shows that TOT is more secure than HFE, HFEv and Quartz (when n ≥ 81 and DHFE ≥ 129, HFE is still secure), and it can reach almost the same speed of computing the secret map by C∗ and Sflash (even though C∗ was broken, its high speed has been affirmed).