Cryptosystems Based on Tropical Congruent Transformation of Symmetric Matrices

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 semi-rings. New cryptosystems proposed in this paper. They congruent transformation symmetric by circular matrix. NP-hard problem solving system nonlinear equations underlies cryptosystem’s security. Since known cannot express used subsemi-rings matrices and there no addition operation power matrix, can withstand attacks, including KU attack, RM IK attack. length key private new half those described literature.