Cryptosystems Based on Tropical Congruent Transformation of Symmetric Matrices

Abstract

Recently, public-key cryptography based on tropical semi-rings have been proposed. However, the majority of them are damaged. The main reason is that they use a public matrix to construct commutative matrix semi-rings. New public-key cryptosystems are proposed in this paper. They are based on tropical congruent transformation of symmetric matrix by circular matrix. The NP-hard problem of solving a tropical system of nonlinear equations underlies the cryptosystem’s security. Since a known matrix cannot express the used commutative subsemi-rings of circular matrices and there is no tropical matrix addition operation and power of matrix, the cryptosystems can withstand known attacks, including the KU attack, RM attack, and IK attack. The length of the public key and private key of the new cryptosystems is half that of those described in the literature.