Public key cryptography with max-plus matrices and polynomials

Abstract

Employing exotic semirings as platforms for several cryptographic schemes arose several years ago. Exotic semirings are additively idempotent semirings where the elements are certain subsets of numbers (possibly including −∞ and/or +∞) and where the additional and multiplicational operations are min or max, and +, respectively. A revival of non-commutative cryptography may be achieved by means of research in one of the following two directions. The first approach is to stick with the suggested protocols and search for better platform groups. Another approach is to construct new or generalized non-commutative cryptosystems which are based on supposedly harder computational problems. In this paper we follow both approaches using max-plus semirings.