## Cryptology ePrint Archive: Report 2019/897

On inverse protocols of Post Quantum Cryptography based on pairs of noncommutative multivariate platforms used in tandem

Vasyl Ustimenko

Abstract: Non-commutative cryptography studies cryptographic primitives and systems which are based on algebraic structures like groups, semigroups and noncommutative rings. We con-tinue to investigate inverse protocols of Non-commutative cryptography defined in terms of subsemigroups of Affine Cremona Semigroups over finite fields or arithmetic rings $Z_m$ and homomorphic images of these semigroups as possible instruments of Post Quantum Cryptography. This approach allows to construct cryptosystems which are not public keys, as outputs of the protocol correspondents receive mutually inverse transformations on affine space $K^n$ or variety $(K^*)^n$, where $K$ is a field or an arithmetic ring. The security of such inverse protocol rests on the complexity of word problem to decompose element of Affine Cremona Semigroup given in its standard form into composition of given generators. We discuss the idea of the usage of combinations of two cryptosystems with cipherspaces $(K^*)^n$ and $K^n$ to form a new cryptosystem with the plainspace $(K^*)^n$, ciphertext $K^n$ and nonbijective highly nonlinear encryption map.

Category / Keywords: cryptographic protocols / Multivariate Cryptography, Noncommutative Cryptography, stable transformation groups and semigroups, semigroups of monomial transformations, word problem for nonlinear multivariate maps , hidden tame homomorphisms, key exchange protocols, cryptosystems, linguistic graphs