On the security of PKC using non-abelian group

Abstract

Security is very important in cryptosystems, and after introducing the notion of provable security, it became the main issue of security. In this paper, we introduce several public key cryptosystems using non-abelian groups, i.e. MOR[22, 23, 24], $MST_1$, and $MST_2$[18]. And, we analyze their security, check whether they are provably secure, and convert them to provably secure cryptosystems against adaptive chosen ciphertext attack in the random oracle model using generic conversion method. We mainly focus on the MOR system.