On Inverse Protocols of Post Quantum Cryptography Based on Pairs of Noncommutative Multivariate Platforms Used in Tandem

Abstract

Non-commutative cryptography studies cryptographic primitives and systems which are based on algebraic structures like groups, semigroups and noncommutative rings. We continue to investigate inverse protocols of Non-commutative cryptography defined in terms of subsemigroups of Affine Cremona Semigroups over finite fields or arithmetic rings Zm and homomorphic images of these semigroups as possible instruments of Post Quantum Cryptography. This approach allows to construct cryptosystem which are not public keys, when protocol finish correspondents have mutually inverse transformations on affine space Kn or variety (K*)n where K is the field or 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 usage combinations of two cryptosystems with cipherspaces(K*)n and Kn to form a new cryptosystem with the plainspace(K*)n, ciphertextKn and nonbijective highly nonlinear encryption map.