Abstract
A new blind signature scheme is proposed which is characterized in that it is based on a hidden discrete logarithm problem defined in a finite commutative associative algebra. The used algebraic support represents a 4-dimensional commutative associative algebra defined over the ground finite field GF(p), commutative group of which possesses 4-dimensional cyclicity. The public key represents a triple of vectors contained in different cyclic subgroup of the multiplicative group. Correspondingly, three different blinding factors are used to insure the anonymity property of the introduced blind signature protocol.
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References
Rivest RL, Shamir A, Adleman LM (1978) A method for obtaining digital signatures and public key cryptosystems. Commun ACM 21(2):120–126
ElGamal T (1985) A public key cryptosystem and a signature scheme based on discrete logarithms. IEEE Trans Inform Theory 31(4):469–472
Chaum D (1988) Blind Signature Systems. U.S. Patent # 4,759,063
Chaum D (1983) Blind signatures for untraceable payments. advances in cryptology: Proc. of CRYPTO’82. Plenum Press, pp. 199–203
Camenisch JL, Piveteau JM, Stadler MA (1995) Blind Signatures Based on the Discrete Logarithm Problem. Advances in Cryptology - EUROCRYPT '94 volume 950 of LNCS, Springer Verlang, pp 428–432
Yan SY (2014) Quantum attacks on public-key cryptosystems. Springer, US, p 207
Ding J, Steinwandt R (2018) Post-Quantum Cryptography. 10th International Conference, PQCrypto 2019, Chongqing, China, May 8–10, 2019, Proceedings. Lecture Notes in Computer Science series. Springer, vol. 11505
Shor PW (1997) Polynomial-time algorithms for prime factorization and discrete logarithms on quantum computer. SIAM J Comput 26:1484–1509
Smolin JA, Smith G, Vargo A (2013) Oversimplifying quantum factoring. Nature 499(7457):163–165
Jozsa R (1988) Quantum algorithms and the Fourier transform. Proc Royal Soc A 454:323–337
Ekert A, Jozsa R (1996) Quantum computation and Shor’s factoring algorithm. Rev Mod Phys 68:733–752
NIST (2016) 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 (accessed January 10, 2021)
NIST (2020) Post-Quantum Cryptography. Round 3 Submissions. Available at: https://csrc.nist.gov/projects/post-quantum-cryptography/round-3-submissions (accessed January 10, 2021)
Kuzmin AS, Markov VT, Mikhalev AA, Mikhalev AV, Nechaev AA (2017) Cryptographic algorithms on groups and algebras. J Math Sci 223(5):629–641
Moldovyan-Dmitriy N (2019) Post-quantum public key-agreement scheme based on a new form of the hidden logarithm problem. Comput Sci J Moldova 27(79):56–72
Moldovyan-Dmitriy N, Moldovyan-Nikolay A, Moldovyan-Alexander A (2020) Commutative encryption method based on hidden logarithm problem. Bullet South Ural State Univ Ser Math Model Programm Comput Softw 13(2):54–68
Moldovyan-Nikolay A, Moldovyan-Alexander A (2019) Finite non-commutative associative algebras as carriers of hidden discrete logarithm problem. Bullet South Ural State Univ Ser Math Model Programm Comput Softw 12(1):66–81
Moldovyan-Nikolay A, Abrosimov IK (2019) Post-quantum electronic digital signature scheme based on the enhanced form of the hidden discrete logarithm problem. Vestnik Saint Petersburg Univ Appl Math Comput Sci Control Process 15(2):212–220 ((In Russian))
Moldovyan-Nikolay A, Moldovyan-Alexander A (2020) Candidate for practical post-quantum signature scheme. Vestnik Saint Petersburg Univ Appl Math Comput Sci Control Process 16(4):455–461
Moldovyan-Dmitriy N (2010) Non-commutative finite groups as primitive of public-key cryptoschemes. Quasigroups Relat Syst 18:165–176
Moldovyan-Nikolay A (2020) Unified method for defining finite associative algebras of arbitrary even dimensions. Quasigroups Relat Syst 26(2):263–270
Minh NH, Moldovyan-Alexander A, Moldovyan-Nikolay A, Canh HN (2020) A new method for designing post-quantum signature schemes. J Commun 15(10):747–754
Moldovyan-Dmitriy N, Moldovyan-Alexander A, Moldovyan-Nikolay A (2020) Digital signature scheme with doubled verification equation. Comput Sci J Moldova 28(82):80–103
Moldovyan-Nikolay A, Moldovyanu-Peter A (2009) New primitives for digital signature algorithms. Quasigroups Relat Syst 17(2):271–282
Pointcheval D, Stern J (2000) Security arguments for digital signatures and blind signatures. J Cryptol 13:361–396
Koblitz N, Menezes AJ (2007) Another look at “provable security.” J Cryptol 20:3–37
Schnorr CP (1991) Efficient signature generation by smart cards. J Cryptol 4:161–174
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We would like to express our sincere gratitude to the anonymous referee for his/her helpful comments that will help to improve the quality of the manuscript.
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This research is supported by RFBR (project # 21–57-54001-Bьeт_a) and by Vietnam Academy of Science and Technology (project # QTRU01.13/21–22).
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Minh N.H and Moldovyan N.A has directed the conceptualization, formal analysis, writing—original draft preparation, writing—review & editing. Modovyan D.N, Minh L.Q and Giang N.L have directed the conceptualization, formal analysis, writing—review & editing. All authors reviewed and approved the final manuscript.
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Nguyen, M.H., Moldovyan, D.N., Moldovyan, N.A. et al. Blind Signature Protocol Based on Hidden Discrete Logarithm Problem Set in a Commutative Algebra. Iran J Sci Technol Trans Sci 46, 323–332 (2022). https://doi.org/10.1007/s40995-021-01257-3
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DOI: https://doi.org/10.1007/s40995-021-01257-3