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3 Annals of Computer Science and Information Systems

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On D(n; q) quotients of large girth and hidden homomorphism based cryptographic protocols

Ustymenko Vasyl, Klisowski Michał

Annals of Computer Science and Information Systems

2022

Vol. 32

199--206

Noncommutative cryptography is based on applications of algebraic structures like noncommutative groups,semigroups, and noncommutative rings. Its intersection withMultivariate cryptography contains studies of cryptographicapplications of subsemigroups and subgroups of affine Cremona semigroups defined over finite commutative rings. Efficientlycomputed homomorphisms between stable subsemigroups of affine Cremona semigroups can be used in tame homomorphisms protocols schemes and their inverse versions. The implementationscheme with the sequence of subgroups of affine Cremona group that defines the projective limit was already suggested. We present the implementation of another scheme that uses two projective limits which define two different infinite groups and the homomorphism between them. The security of the corresponding algorithm is based on complexity of the decomposition problem for an element of affine Cremona semigroup into a product of given generators. These algorithms may be used in postquantum technologies.

On new stream algorithms generating sensitive digests of computer files

Ustymenko Vasyl, Pustovit Oleksandr

Annals of Computer Science and Information Systems

2021

Vol. 26

117--121

The paper is dedicated to construction of new fast and flexible hash-based message authentication codes (HMACs) that will provide large files with cryptographically stable digestions in the Postquantum era. These instruments can be used for detecting cyber-terrorist attacks, file audits and checking the integrity of messages during communication, We use algebraic properties of well known extremal graphs D(n, q) and A(n,q) with good expansion property for the construction of HMACS.

On computations with Double Schubert Automaton and stable maps of multivariate cryptography

Ustymenko Vasyl

Annals of Computer Science and Information Systems

2021

Vol. 26

123--130

The families of bijective transformations Gn of affine space Kn over general commutative ring K of increasing order with the property of stability will be constructed. Stability means that maximal degree of elements of cyclic subgroup generated by the transformation of degree d is bounded by d. In the case K-Fq these transformations of Kn can be of an exponential order. We introduce large groups formed by quadratic transformations and numerical encryption algorithm protected by secure protocol of Noncommutative Cryptography. The construction of transformations is presented in terms of walks on Double Schubert Graphs.