A solution for constructing quantum – resistant digital signature schemes
DOI:
https://doi.org/10.54939/1859-1043.j.mst.CSCE8.2024.108-118Keywords:
Digital signature; Digital signature scheme; Discrete logarithm problem; New hard problem; Post-quantum digital signature scheme; Quantum – resistant digital signature scheme.Abstract
In this article, the authors propose a solution for constructing quantum - resistant digital signature schemes based on a new type of hard problem, which belongs to the group of unsolvable problems. Therefore, the algorithms constructed according to the solution proposed here can be resistant to quantum attacks based on the quantum algorithm proposed by P. Shor. In addition to quantum resistance, the signature schemes proposed here can also be used as pre-quantum digital signature schemes (RSA, DSA, etc.) that are widely used in current practical applications.
References
[1]. P. W. Shor. “Algorithms for quantum computation: Discrete logarithms and factoring”. In Proceedings of the 35th Symposium on Foundations of Computer Science, pages 124–134, 1994. DOI: https://doi.org/10.1109/SFCS.1994.365700
[2]. P. W. Shor. “Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer”, in SIAM Journal of Computing, volume 26, no 5, pp. 1484-1509, (1997). DOI: https://doi.org/10.1137/S0097539795293172
[3]. M. Eker. “Modifying Shor's algorithm to compute short discrete logarithms”. In IACR ePrint Archive, report 2016/1128, (2016).
[4]. L. C. Washington. “Elliptic Curves. Number Theory and Cryptography”. Chapman & Hall/CRC, (2008).
[5]. Jeffrey Hoffstein, Jill Pipher and Joseph H. Silverman. “An Introduction to Mathematical Cryptography”. ISBN 978-0-387-77993-5. Springer - Verlag, (2008).
[6]. D. R. Stinson. “Cryptography. Theory and Practice”. Chapman & Hall/CRC, (2006). DOI: https://doi.org/10.1201/9781420057133
[7]. J. Talbot and D. Welsh. “Complexity and Cryptography: An Introduction”. Cambridge University Press, (2006). DOI: https://doi.org/10.1017/CBO9780511755286
[8]. I. Shparlinski. “Cryptographic Applications of Analytic Number Theory”. Complexity Lower Bounds and Pseurandomness. Birkhäuser, (2003). DOI: https://doi.org/10.1007/978-3-0348-8037-4
[9]. S. S. Wagstaff. “Cryptanalysis of Number Theoretic Ciphers”. Chapman & Hall /CRC (2003).
[10]. ISO/IEC 14888-3: Information technology – Security techniques – Digital signatures with appendix. Second edition, (2006).
[11]. National Institute of Standards and Technology, NIST FIPS PUB 186-4. Digital Signature Standard, U.S. Department of Commerce, (2013).
[12]. GOST R 34.10-94. Russian Federation Standard. Information Technology. Cryptographic Data security. Produce and check procedures of Electronic Digital Signature based on Asymmetric Cryptographic Algorithm. Government Committee of the Russia for Standards, 1994 (in Russian).
