Cryptology ePrint Archive: Report 2019/133

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

Vasyl Ustimenko

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.

Category / Keywords: cryptographic protocols / Postquantum Cryptography, Noncommutative and Multivariate Cryptography, key exchange protocols, inverse protocols, semigroups of transformations, decomposition problem

Date: received 9 Feb 2019

Contact author: vasyl at hektor umcs lublin pl

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Version: 20190213:173200 (All versions of this report)

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