A New Security Enhancing Solution when Building Digital Signature Schemes - Nguyen, Kim Tuan; Hoang, Ha Nguyen; Ngoc, Duy Ho (Engineering, Technology & Applied Science Research, 2025)
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.