POST-QUANTUM BLIND SIGNATURE PROTOCOL ON NON-COMMUTATIVE ALGEBRAS
Keywords:information security, post-quantum cryptography, digital signature, blind signature, finite associative algebra, non-commutative algebra
A method for constructing a blind signature scheme based on a hidden discrete logarithm problem defined in finite non-commutative associative algebras is proposed. Blind signature protocols are constructed using four-dimensional and six-dimensional algebras defined over a ground finite field GF(p) and containing a global two-sided unit as an algebraic support. The basic properties of the used algebra, which determine the choice of protocol parameters, are described.
A.J. Menezes, P.C. Van Oorschot, and S.A. Vanstone, Handbook of Applied Cryptography, Boca Raton, FL: CRC Press (5th printing), 780 p, 2001.
P.W. Shor, “Polynomial-time algorithms for prime factorization and discrete logarithms on quantum computer,” SIAM Journal of Computing, vol. 26, pp. 1484-1509, 1997.
S.Y. Yan, Quantum Attacks on Public-Key Cryptosystems, Springer US. 207 p, 2014.
Federal Register. Announcing Request for Nominations for Public-Key Post-Quantum Cryptographic Algorithms. Available at: https://www.gpo.gov/fdsys/pkg/FR-2016-12-20/pdf/2016-30615.pdf
Post-Quantum Cryptography. 9th International Conference, PQCrypto 2018, Fort Lauderdale, FL, USA, April 9-11, 2018, Proceedings. Lecture Notes in Computer Science series. Springer, vol. 10786, 2018.
D.N. Moldovyan and N.A. Moldovyan, “Cryptoschemes over hidden conjugacy search problem and attacks using homomorphisms,” Quasigroups and Related Systems, vol. 18, pp. 177-186, 2010.
А.А. Молдовян и Н.А. Молдовян, “Новые формы задания скрытой задачи дискретного логарифмирования,” Труды СПИИРАН, № 2 (18). C. 504-529, 2019. (in russia)
D.N. Moldovyan, “Non-Commutative Finite Groups as Primitive of Public-Key Cryptoschemes,” Quasigroups and Related Systems, vol. 18, pp. 165-176, 2010.
D.N. Moldovyan, “Post-quantum public key-agreement scheme based on a new form of the hidden logarithm problem,” Computer Science Journal of Moldova, vol. 27, no.1(79), pp. 56-72, 2019.
D.N. Moldovyan and N.A. Moldovyan, “A New Hard Problem over Non-Commutative Finite Groups for Cryptographic Protocols,” 5th Int. Conference on Mathematical Methods, Models, and Architectures for Computer Network Security, MMM-ANCS 2010 Proceedings. St.Petersburg, vol. 6258, pp. 183−194, September 8−11, 2010.
A.A. Moldovyan and N.A. Moldovyan, “Post-quantum signature algorithms based on the hidden discrete logarithm problem,” Computer Science Journal of Moldova, vol. 26, no.3(78), pp. 301-313, 2018.
N.A. Moldovyan and A.A. Moldovyan, “Finite Non-commutative Associative Algebras as carriers of Hidden Discrete Logarithm Problem,” Вестник ЮУрГУ. Серия “Математическое моделирование и программирование” (Вестник ЮУрГУ ММП), Т. 12, № 1. С. 66–81, 2019.
D. Chaum, “Blind Signatures for Untraceable Payments,” Advances in Cryptology: Proc. of CRYPTO’82. Plenum Press, pp. 199–203, 1983.
J.L. Camenisch, J.-M. Piveteau, and M.A. Stadler, “Blind Signatures Based on the Discrete Logarithm Problem,” In: Advances in Crypology - EUROCRYPT '94, Springer Verlang, vol. 950, pp. 428-432, 1995.
N.A. Moldovyan, “Unified Method for Defining Finite Associative Algebras of Arbitrary Even Dimensions,” Quasigroups and Related Systems, vol. 26, no. 2, pp. 263-270, 2018.
D. Pointcheval and J. Stern, “Security Arguments for Digital Signatures and Blind Signatures,” Journal of Cryptology, vol. 13, no. 3, pp. 361-396, 2000.
C.P. Schnorr, “Efficient signature generation by smart cards,” Journal of Cryptology, vol. 4, pp. 161-174, 1991.
How to Cite
License1. We hereby assign copyright of our article (the Work) in all forms of media, whether now known or hereafter developed, to the Journal of Computer Science and Cybernetics. We understand that the Journal of Computer Science and Cybernetics will act on my/our behalf to publish, reproduce, distribute and transmit the Work.
2. This assignment of copyright to the Journal of Computer Science and Cybernetics is done so on the understanding that permission from the Journal of Computer Science and Cybernetics is not required for me/us to reproduce, republish or distribute copies of the Work in whole or in part. We will ensure that all such copies carry a notice of copyright ownership and reference to the original journal publication.
3. We warrant that the Work is our results and has not been published before in its current or a substantially similar form and is not under consideration for another publication, does not contain any unlawful statements and does not infringe any existing copyright.
4. We also warrant that We have obtained the necessary permission from the copyright holder/s to reproduce in the article any materials including tables, diagrams or photographs not owned by me/us.