Finite algebras in the design of multivariate cryptography algorithms
Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 3 (2023), pp. 80-89.

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A new approach to the design of multivariate public-key cryptalgorithms is introduced. It envisages using non-linear mappings defined as squaring and cubic operations in finite fields represented as finite algebras. The developed approach allows significant reduction of the size of public key and thereby make post-quantum algorithms of multivariate cryptography much more practical. In the developed algorithms, the secret key includes a set of values of structural constants that determine the modifications of the finite fields used and the coefficients in the set of sixth degree polynomials that make up the public key.
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Nikolay A. Moldovyan. Finite algebras in the design of multivariate cryptography algorithms. Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 3 (2023), pp. 80-89. https://geodesic-test.mathdoc.fr/item/BASM_2023_3_a5/

[1] Ding J., Petzoldt A., “Current State of Multivariate Cryptography”, IEEE Security and Privacy Magazine, 15:4 (2017), 28–36 | DOI | MR

[2] Alagic G., Cooper D., Dang Q., Dang T., Kelsey J., Lichtinger J., Liu Y., Miller C., Moody D. Peralta R., Perlner R., Robinson A., Smith-Tone D., Apon D., Status Report on the Third Round of the NIST Post-Quantum Cryptography Standardization Process, NIST Interagency/Internal Report (NISTIR), National Institute of Standards and Technology, Gaithersburg, MD, 2022 (accessed January 2, 2023) | DOI

[3] Post-Quantum Cryptography: Digital Signature Schemes, , 2022 https://csrc.nist.gov/Projects/pqc-dig-sig/standardization/call-for-proposals

[4] Moldovyan N. A., Moldovyanu P. A., “Vector Form of the Finite Fields $GF(p^m)$”, Bulletin of Academy of Sciences of Moldova. Mathematics, 2009, no. 3(61), 57–63 | MR | Zbl

[5] Hashimoto Y., “Recent Developments in Multivariate Public Key Cryptosystems”, International Symposium on Mathematics, Quantum Theory, and Cryptography, Mathematics for Industry, 33, eds. Takagi T., Wakayama M., Tanaka K., Kunihiro N., Kimoto K., Ikematsu Y., Springer, Singapore, 2021, 209–229 | DOI | Zbl

[6] Shuaiting Q., Wenbao H., Yifa Li, Luyao J., “Construction of Extended Multivariate Public Key Cryptosystems”, International Journal of Network Security, 18 (2016), 60–67

[7] Ding J., Petzoldt A., Schmidt D.S., “Oil and Vinegar”, Multivariate Public Key Cryptosystems, Advances in Information Security, 80, Springer, New York, 2020, 89–151 | DOI | MR

[8] Faugére J.-C., “A new efficient algorithm for computing Grőbner basis (F4)”, J. Pure Appl. Algebra, 139:1-3 (1999), 61–88 | DOI | MR | Zbl

[9] Faugére J.-C., “A new efficient algorithm for computing Grőbner basis without reduction to zero (F5)”, Proceedings of the International Symposium on Symbolic and Algebraic Computation, 2002, 75–83 | MR | Zbl