A New Security Enhancing Solution when Building Digital Signature Schemes
Received: 29 January 2025 | Revised: 25 February 2025 | Accepted: 7 March 2025 | Online: 4 June 2025
Corresponding author: Ha Nguyen Hoang
Abstract
This article introduces a new solution to enhance the security of the digital signature system. First, a new type of hard problem is proposed, which is then used to construct a digital signature scheme. The core difficulty lies in the Discrete Logarithm Problem (DLP) modulo, a composite number which extends the DLP over a finite field by replacing the prime modulus with a composite one. This change leads to a digital signature scheme built on the DLP modulo, a composite number having the same level of security as the schemes constructed simultaneously on two hard problems: the DLP and the Integer Factorization Problem (IFP). This can be seen as a new direction in using two hard problems concurrently to construct a digital signature scheme. The current study also demonstrates that the digital signature scheme built upon a newly proposed problem, achieves a higher security level of 128 bits while minimizing the signature size to 512 bits. That is, although the schemes are built on a single hard problem, a possible attacker must solve two hard problems simultaneously in order to break them. Furthermore, the proposed hard problem can be used to construct both single-signer and multi-signer digital signature schemes, demonstrating the security and applicability of the new hard problem, introduced in this paper.
Keywords:
prime modulus, composite modulus, Schnorr’s digital signature, collective digital signatureDownloads
References
R. L. Rivest, A. Shamir, and L. Adleman, "A method for obtaining digital signatures and public-key cryptosystems," Commun. ACM, vol. 21, no. 2, pp. 120–126, Oct. 1978.
J. Pieprzyk, T. Hardjono, and J. Seberry, Fundamentals of Computer Security. Berlin, New York: Springer, 2003.
D. Wong, Real-World Cryptography. New York: Manning, 2021.
E. S. Ismail, N. M. F. Tahat, and R. R. Ahmad, "A New Digital Signature Scheme Based on Factoring and Discrete Logarithms," Journal of Mathematics and Statistics, vol. 4, no. 4, pp. 222–225, Dec. 2008.
N. M. F. Tahat, E. S. Ismail, and R. R. Ahmad, "A New Blind Signature Scheme Based On Factoring and Discrete Logarithms," International Journal of Cryptology Research, vol. 1, no. 1, pp. 1–9, 2009.
J. He and T. Kiesler, "Enhancing the security of El Gamal’s signature scheme," IEE Proceedings - Computers and Digital Techniques, vol. 141, no. 4, pp. 249–252, Jul. 1994.
L. Harn, "Enhancing the security of El Gamal’s signature scheme," IEE Proceedings - Computers and Digital Techniques, vol. 142, no. 5, pp. 376–376, Sep. 1995.
N. Y. Lee, "Security of Shao’s signature schemes based on factoring and discrete logarithms," IEE Proceedings - Computers and Digital Techniques, vol. 146, no. 2, pp. 119–121, Mar. 1999.
S. Wei, "A New Digital Signature Scheme Based on Factoring and Discrete Logarithms," in Progress on Cryptography: 25 Years of Cryptography in China, K. Chen, Ed. Boston, MA: Springer US, 2004, pp. 107–111.
S. F. Tzeng, Yang ,Cheng Ying, and M. S. and Hwang, "A new digital signature scheme based on factoring and discrete logarithms," International Journal of Computer Mathematics, vol. 81, no. 1, pp. 9–14, Jan. 2004.
J. Pollard and C. Schnorr, "An efficient solution of the congruence x^2 + ky^2 = mpmodn," IEEE Transactions on Information Theory, vol. 33, no. 5, pp. 702–709, Sep. 1987.
S. Vishnoi and V. Shrivastava, "A new Digital Signature Algorithm based on Factorization and Discrete Logarithm problem," International Journal of Computer Trends and Technology, vol. 3, no. 4, pp. 653–657, 2012.
N. Q. Luc, T. T. Nguyen, D. H. Quach, T. T. Dao, and N. T. Pham, "Building Applications and Developing Digital Signature Devices based on the Falcon Post-Quantum Digital Signature Scheme," Engineering, Technology & Applied Science Research, vol. 13, no. 2, pp. 10401–10406, Apr. 2023.
C. P. Schnorr, "Efficient signature generation by smart cards," Journal of Cryptology, vol. 4, no. 3, pp. 161–174, Jan. 1991.
T. T. Nguyen, N. Q. Luc, and T. T. Dao, "Developing Secure Messaging Software using Post-Quantum Cryptography," Engineering, Technology & Applied Science Research, vol. 13, no. 6, pp. 12440–12445, Dec. 2023.
Downloads
How to Cite
License
Copyright (c) 2025 Kim Tuan Nguyen, Ha Nguyen Hoang, Duy Ho Ngoc
This work is licensed under a Creative Commons Attribution 4.0 International License.
Authors who publish with this journal agree to the following terms:
- Authors retain the copyright and grant the journal the right of first publication with the work simultaneously licensed under a Creative Commons Attribution License that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
- Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
- Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) after its publication in ETASR with an acknowledgement of its initial publication in this journal.
