International Association
for Cryptologic Research

In this paper, we design a novel one-way trapdoor function, and then propose a new multivariate public key cryptosystem called $\\rm TOT$, which can be used for encryption, signature and authentication. Through analysis, we declare that $\\rm TOT$ is secure, because it can resist current known algebraic attacks if its parameters are properly chosen. Some practical implementations for $\\rm TOT$ are also given, and whose security level is at least $2^{90}$. The comparison shows that $\\rm TOT$ is more secure than $\\rm HFE$, $\\rm HFEv$ and $\\rm Quartz$ (when $n \\ge 81$ and $D_{HFE} \\ge 129$, $\\rm HFE$ is still secure), and it can reach almost the same speed of computing the secret map by $\\rm C^\\ast$ and $\\rm Sflash^{v2}$ (even though $\\rm C^\\ast$ was broken, its high speed has been affirmed).