Typical Algebraic Signature Schemes with Two Hidden Groups
Tác giả
Tài liệu tham khảo
[1] Saarinen, M.-J., Smith-Tone, D.: Post-Quantum Cryptography: 15th International Workshop, PQCrypto 2024, Oxford, UK, 12–14 June 2024, Proceedings, Part I & Part II. International Workshop Post-Quantum Cryptography (2024)
[2] Alamélou, Q., Blazy, O., Cauchie, S., Gaborit, P.: A code-based group signature scheme. Des. Codes Cryptogr. 82(1), 469–493 (2017)
[3] Vedenev, K., Kosolapov, Y.: Theoretical analysis of decoding failure rate of non–binary QC–MDPC codes. In: Esser, A., Santini, P. (eds.) CBCrypto 2023. LNCS, vol. 14311, pp. 35–55. Springer, Cham (2023). https://doi.org/10.1007/978-3-031-46495-9_3
[4] D’Alconzo, G.: On two modifications of the McEliece PKE and the CFS signature scheme. Int. J. Found. Comput. Sci. 35(05), 501–512 (2024)
[5] Battarbee, C., Kahrobaei, D., Perret, L., Shahandashti, S.F.: SPDH-sign: towards efficient, post-quantum group-based signatures. In: Johansson, T., Smith-Tone, D. (eds.) PQCrypto 2023. LNCS, vol. 14154, pp. 113–138. Springer, Cham (2023). https://doi.org/10.1007/978-3-031-40003-2_5
[6] Gärtner, J.: NTWE: a natural combination of NTRU and LWE. In: Johansson, T., Smith-Tone, D. (eds.) PQCrypto 2023. LNCS, vol. 14154, pp. 321–353. Springer, Cham (2023). https://doi.org/10.1007/978-3-031-40003-2_12
[7] Li, L., Lu, X., Wang, K.: Hash-based signature revisited. Cybersecurity 5(1), 13 (2022)
[8] Hamlin, B., Song, F.: Quantum security of hash functions and property-preservation of iterated hashing. In: Ding, J., Steinwandt, R. (eds.) PQCrypto 2019. LNCS, vol. 11505, pp. 329–349. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-25510-7_18
[9] Ding, J., Petzoldt, A., Schmidt, D.S.: Multivariate cryptography. In: Ding, J., Petzoldt, A., Schmidt, D.S. (eds.) Multivariate Public Key Cryptosystems. Advances in Information Security, vol. 80, pp. 7–23. Springer, New York (2020). https://doi.org/10.1007/978-1-0716-0987-3_2
[10] Hashimoto, Y.: Recent developments in multivariate public key cryptosystems. In: Takagi, T., Wakayama, M., Tanaka, K., Kunihiro, N., Kimoto, K., Ikematsu, Y. (eds.) International Symposium on Mathematics, Quantum Theory, and Cryptography. Mathematics for Industry, vol. 33, pp. 209–229. Springer, Singapore (2021). https://doi.org/10.1007/978-981-15-5191-8_16
[11] Moldovyan, D.: New form of the hidden logarithm problem and its algebraic support. Buletinul Academiei de Ştiinţe a Republicii Moldova Matematica 93(2), 3–10 (2020)
[12] Moldovyan, D.: A practical digital signature scheme based on the hidden logarithm problem. Comput. Sci. J. Mold. 86(2), 206–226 (2021)
[13] Ding, J., Petzoldt, A., Schmidt, D.S.: Solving polynomial systems. In: Ding, J., Petzoldt, A., Schmidt, D.S. (eds.) Multivariate Public Key Cryptosystems. Advances in Information Security, vol. 80, pp. 185–248 Springer, New York (2020). https://doi.org/10.1007/978-1-0716-0987-3_8
[14] Moldovyan, N.A.: Finite algebras in the design of multivariate cryptography algorithms. Bul. Acad. Stiinte Repub. Mold. Mat. (3(103)), 80–89 (2024)
[15] Moldovyan, A.A., Moldovyan, N.A.: Vector finite fields of characteristic two as algebraic support of multivariate cryptography. Comput. Sci. J. Mold. 32(1(94)), 46–60 (2024)
[16] Moldovyan, A.A., Moldovyan, D.N.: A new method for developing signature algorithms on finite non-commutative algebras. Bull. Acad. Sci. Mold. Math. (1(98)), 56–65 (2022)
[17] Moldovyan, D.: St. Petersburg Federal Research Center of the Russian Academy of Sciences, A. Moldovyan, and St. Petersburg Federal Research Center of the Russian Academy of Sciences, ‘Algebraic signature algorithms based on difficulty of solving systems of equations’. Vopr. Kiberbezopasnosti (2(48)), 7–17 (2022)
[18] Moldovyan, A.A.: St. Petersburg Federal Research Center of the Russian Academy of Sciences, N. Moldovyan, and St. Petersburg Federal Research Center of the Russian Academy of Sciences, ‘Signature algorithms on finite non-commutative algebras over fields of characteristic two’. Vopr. Kiberbezopasnosti (3(49)), 58–68 (2022)
[19] Zakharov, D.V., Kostina, A.A., Morozova, E.V., Moldovyan, D.N.: A digital signature algorithm on the algebra of 3×3 matrices, which uses two hidden groups. Voprosy kiberbezopasnosti [Cibersecurity questions] (3(67)), 45–54 (2025). https://doi.org/10.21681/2311-3456-2025-3-45-54
[20] Moldovyan, A.A., Moldovyan, D.N., Kostina, A.A.: Algebraic signature algorithms with complete signature randomization. Voprosy kiberbezopasnosti [Cibersecurity questtions] (2(60)), 95–102 (2024). https://doi.org/10.21681/2311-3456-2024-2-95-102
[21] Moldovyan, A.A., Moldovyan, N.A.: A method for strengthening signature randomization in signature algorithms on non-commutative algebras. Vopr. Kiberbezopasnosti (4(62)) (2024)
[22] Moldovyan, D.N., Kostina, A.A.: A method for strengthening signature randomization in algebraic signature algorithms on non-commutative algebras. Voprosy kiberbezopasnosti [Cibersecurity questions] (4(62)), 71–81 (2024). https://doi.org/10.21681/2311-3456-2024-4-71-81
[23] Kuzmin, A., Markov, V., Mikhalev, A., Mikhalev, A., Nechaev, A.: Cryptographic algorithms on groups and algebras. J. Math. Sci. 223, 629–641 (2017)
[24] Roman’kov, V., Ushakov, A., Shpilrain, V.: Algebraic and quantum attacks on two digital signature schemes. J. Math. Cryptol. 17(1), 20220023 (2023)
[25] Ma, Y.: Cryptanalysis of the cryptosystems based on the generalized hidden discrete logarithm problem. Comput. Sci. J. Mold. 32(2(95)), 289–307 (2024). https://doi.org/10.56415/csjm.v32.15
[26] Moldovyan, N.A., Petrenko, A.S.: Algebraic signature algorithm with two hidden groups. Voprosy kiberbezopasnosti [Cibersecurity questions] (6(64)), 98–107 (2024). https://doi.org/10.21681/2311-3456-2024-6-98-107
[27] Duong, M.T., Moldovyan, A.A., Moldovyan, N.A., Nguyen, M.H., Do, B.T.: Structure of 6-dimensional finite non-commutative algebras with many single-sided units. Bull. Electr. Eng. Inform. 14(3), 2017–2030 (2025)
[28] Ding, J., Petzoldt, A.: Current state of multivariate cryptography. IEEE Secur. Priv. Mag. 15(4), 28–36 (2017)