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

Ustymenko Vasyl

Annals of Computer Science and Information Systems

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2021

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Vol. 26

123--130

EN

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.

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Expanding graphs of the Extremal Graph Theory and expanded platforms of post quantum cryptography

Ustimenko Vasyl, Romańczuk-Polubiec Urszula, Wróblewska Aneta

Annals of Computer Science and Information Systems

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2019

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Vol. 19

41--46

EN

Explicit constructions in Extremal Graph Theory give appropriate lower bounds for Turan type problems. In the case of prohibited cycles, the explicit constructions can be used for various problems of Information Security. We observe recent applications of algebraic constructions of regular graphs of large girth and graphs with large cycle indicator to Coding Theory and Cryptography. In particular, we present a new multivariate platforms of postquantum Non-commutative Cryptography defined in graph theoretical terms.

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An Efficient Construction of Quantum Attack Resistant Proxy Re-Encryption Based on (Semi) group Factorization Problems

Wang L., Li J., Gu L., Yan J., Qu Z.

Fundamenta Informaticae

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2018

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Vol. 157, nr 1/2

47--62

EN

Proxy re-encryption (PRE) enables a semi-trusted proxy to transfer Alice's secrets into Bob's secrets but without seeing the secrets. This functionality is very interesting for making balance between the information confidentiality and the mutual accessibility in various scenarios such as public cloud storage systems. During the past decades, many smart PRE schemes were built based on intractability assumptions such as integer factorization problems (IFP) and discrete logarithm problems (DLP). However, Shor's efficient quantum algorithms for IFP and DLP stand great threats towards the security baseline of these schemes. Enlightened by Gu et al.'s recent work on resisting known quantum attacks, we propose an efficient PRE scheme based on the intractability of the (semi)group factorization problems in this paper. The security of the proposed scheme is analyzed according to some heuristic attacks. Moreover, a special instantiation technique is present in detail, and some illustrations are provided for manifesting the effectiveness and efficiency of the proposed methodology.

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Post-Quantum Cryptography: generalized ElGamal cipher over GF(2518)

Hecht P.

Theoretical and Applied Informatics

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2016

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Vol. 28, No. 4

1--14

EN

Post-Quantum Cryptography (PQC) attempts to find cryptographic protocols resistant to attacks by means of for instance Shor's polynomial time algorithm for numerical field problems like integer factorization (IFP) or the discrete logarithm (DLP). Other aspects are the backdoors discovered in deterministic random generators or recent advances in solving some instances of DLP. The use of alternative algebraic structures like non-commutative or non-associative partial groupoids, magmas, monoids, semigroups, quasigroups or groups, are valid choices for these new kinds of protocols. In this paper, we focus in an asymmetric cipher based on a generalized ElGamal non-arbitrated protocol using a non-commutative general linear group. The developed protocol forces a hard subgroup membership search problem into a non-commutative structure. The protocol involves at first a generalized Diffie-Hellman key interchange and further on the private and public parameters are recursively updated each time a new cipher session is launched. Security is based on a hard variation of the Generalized Symmetric Decomposition Problem (GSDP). Working with GF(2518) a 64-bits security is achieved, and if GF(25116) is chosen, the security rises to 127-bits. An appealing feature is that there is no need for big number libraries as all arithmetic if performed in Z251 and therefore the new protocol is particularly useful for computational platforms with very limited capabilities like smartphones or smartcards.