On Multivariate Algorithms of Digital Signatures on Secure El Gamal‐Type Mode
Vasyl Ustimenko · 2024
The intersection of noncommutative and multivariate cryptography contains studies of cryptographic applications of subsemigroups and subgroups of affine Cremona semigroups defined over finite commutative ring with the unit. This chapter suggests three such protocols (with a group and with two semigroups as platforms) for their usage with multivariate digital signature systems. Transition of the basic multivariate map to safe El Gamal-type mode does not allow the usage of cryptanalytic algorithms for already broken Imai–Matsumoto cryptosystem or original oil and vinegar signature schemes proposed by J. Patarin. Noncommutative cryptography is an active area of cryptology where the cryptographic primitives and systems are based on algebraic structures like groups, semigroups and noncommutative rings. Semigroup-based cryptography consists of general cryptographical schemes defined in terms of wide classes of semigroups and their implementations for chosen semigroup families.