Paper 2019/133 Original: eprint.iacr.org/2019/133 ↗

On semigroups of multiplicative Cremona transformations and new solutions of Post Quantum Cryptography.

Abstract

Noncommutative cryptography is based on the applications of algebraic structures like noncommutative groups, semigroups and noncommutative rings. Its intersection with Multivariate cryptography contains studies of cryptographic applications of subsemigroups and subgroups of affine Cremona semigroups defined over finite commutative ring K. We consider special semigroups of transformations of the variety (K*)^n, K=F_q or K=Z_m defined via multiplications of variables. Efficiently computed homomorphisms between such subsemigroups can be used in Post Quantum protocols schemes and their inverse versions when correspondents elaborate mutually inverse transformations of (K*)n. The security of these schemes is based on a complexity of decomposition problem for element of the semigroup into product of given generators. So the proposed algorithms are strong candidates for their usage in postquantum technologies.