The intersection of Commutative and 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=Fq or K=Zm defined via multiplications of variables.
Efficiently computed homomorphisms between such subsemigroups can be used in Post Quantum key exchange protocols and in 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. We introduce combination of inverse versions of these schemes with cryptosystems based on stable subsemigroups of Cremona group which use encryption and decryption multivariate maps with the density gap.
MSC 2010: 11T71, 14G50