Abstract
We suggest new applications of protocols of Non-commutative cryptography defined in terms of subsemigroups of Affine Cremona Semigroups over finite commutative rings and their homomorphic images to the constructions of possible instruments of Post Quantum Cryptography. This approach allows to define cryptosystems which are not public keys.
Highlights
Introduction sional affine space RSo the family of large subgroups of cubical transformations of Kn, n > 2 over arbitraryInvestigations of continuous nonlinear transformation commutative ring is an interesting mathematical object.of vector spaces Rn and Cn in term of dynamic sys- We believe that studies of corresponding infinite algetems theory and other method of Chaos Studies have braic graphs of large girth defined over commutative application to Cryptography
Of vector spaces Rn and Cn in term of dynamic sys- We believe that studies of corresponding infinite algetems theory and other method of Chaos Studies have braic graphs of large girth defined over commutative application to Cryptography
As in previous L formed by two copies of Cartesian power KN, where algorithm Alice and Bob use plainspace (K*)m and K is the commutative ring and N is the set of positive ciphertext Km
Summary
Supporting procedure is algorithm of kind of this protocol Alice and Bob have common maps u 2.1 with the same commutative ring K and parameter acting on the variety (K*)m. As in previous L formed by two copies of Cartesian power KN , where algorithm Alice and Bob use plainspace (K*)m and K is the commutative ring and N is the set of positive ciphertext Km. To encrypt Alice maps her message integer numbers. Graphs A(n, q) St′(K) stands for the semigroup of strings of even length are not vertex transitive They form a family of graphs from St(K) and Σ(K) be subsemigroups of strings of with large cycle indicator, which is q-regular family of even length with coordinates of kind x + c, c ∈ K. small world graphs [32]. PROPOSITION 2.Homomorphisms σ of D(n, K) onto A(m, K), n > m described in section 2 induces homomorphism ind(σ) of GD(n, K) onto GA(m, K), n > m
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