Public-Key Cryptography Based on Tropical Circular Matrices

Abstract

Some public-key cryptosystems based on the tropical semiring have been proposed in recent years because of their increased efficiency, since the multiplication is actually an ordinary addition of numbers and there is no ordinary multiplication of numbers in the tropical semiring. However, most of these tropical cryptosystems have security defects because they adopt a public matrix to construct commutative semirings. This paper proposes new public-key cryptosystems based on tropical circular matrices. The security of the cryptosystems relies on the NP-hard problem of solving tropical nonlinear systems of integers. Since the used commutative semiring of circular matrices cannot be expressed by a known matrix, the cryptosystems can resist KU attacks. There is no tropical matrix addition operation in the cryptosystem, and it can resist RM attacks. The new cryptosystems can be considered as a potential post-quantum cryptosystem.

Keywords

• cryptographic algorithm
• key exchange protocol
• public-key encryption scheme
• tropical algebra
• tropical circular matrices