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.
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.
Quantum computing represents one of the most disruptive technological advancements of the 21st century, with profound implications for modern cryptographic systems. Traditional digital signature algorithms—such as RSA, DSA, and Elliptic Curve Cryptography (ECC)—derive their security from mathematical problems like integer factorization and discrete logarithms, which are computationally infeasible for classical computers. However, the advent of quantum algorithms, particularly Shor’s and Grover’s algorithms, poses a direct threat to these cryptographic assumptions by drastically reducing the time required to solve such problems. This development renders existing Digital Signature infrastructures potentially obsolete once large-scale quantum computers become operational. To counter this threat, researchers have proposed a range of post-quantum cryptographic (PQC) algorithms, including lattice-based, hash-based, and multivariate polynomial-based signature schemes, which are designed to resist quantum attacks. This paper critically examines the extent of quantum vulnerability in current Digital Signature systems and evaluates the comparative performance, efficiency, and security trade-offs of post-quantum alternatives. The study aims to provide a structured understanding of the ongoing transition toward quantum-resistant digital authentication and to propose a roadmap for secure implementation in future cryptographic environments.
Digital signatures are an important primitive for building secure systems and are used in most real-world security protocols. However, almost all popular signature schemes are either based on the factoring assumption (RSA) or the hardness of the discrete logarithm problem (DSA/ECDSA). In the case of classical cryptanalytic advances or progress on the development of quantum computers, the hardness of these closely related problems might be seriously weakened. A potential alternative approach is the construction of signature schemes based on the hardness of certain lattice problems that are assumed to be intractable by quantum computers. Due to significant research advancements in recent years, lattice-based schemes have now become practical and appear to be a very viable alternative to number-theoretic cryptography. In this article, we focus on recent developments and the current state of the art in lattice-based digital signatures and provide a comprehensive survey discussing signature schemes with respect to practicality. Additionally, we discuss future research areas that are essential for the continued development of lattice-based cryptography.
Asymmetric cryptography plays a critical role in the security, authenticity and sustainability of widely used electronic documents on a level comparable to the security and authenticity of a traditional paper documents in transport and logistics. However, security of the majority of the asymmetric cryptographic techniques currently in use, including those used to confirm the validity of electronic documents, will be compromised due to the forthcoming development of quantum computers. The concept of a quantum computer is no longer just a theory. The race for supremacy in quantum technology is on among countries since it is the most drastic technology in the world. On a large enough quantum computer, an attacker can easily generate fake digital signatures by applying Shor’s algorithm. Digital communications and electronic transactions could be devoid of the guarantee of authenticity and non-repudiation if this vulnerability is not addressed. Post-quantum cryptography strives to provide useful techniques that are resistant to attacks utilizing quantum computers in order to address the threat to existing asymmetric cryptography. In this research, we examine the current post-quantum digital signature algorithms used to confirm the validity of an electronic document in addition to comprehending the utilization of digital signing. Overall, we conclude that in order to define the next generation of electronic documents and to address the quantum threat, it is crucial to standardize a quantum-resistant digital signature scheme.
The advent of quantum computers poses a direct threat to the security of traditional digital signature schemes, which are based on the Rivest–Shamir–Adleman (RSA) and Elliptic Curve Cryptography (ECC) cryptosystems. Shor's algorithm allows solving the Discrete Logarithm Problem (DLP) in polynomial time, whereas Grover's algorithm significantly reduces the effort required for brute-force attacks on symmetric hash functions and ciphers. Although many post-quantum solutions have been proposed, such as lattice-based schemes (e.g., CRYSTALS-Dilithium, Falcon) or hash-based schemes (e.g., SPHINCS+), they still have some limitations to overcome, such as large public keys, bulky signatures, high computational costs, and difficulties in integrating into existing Public Key Infrastructures (PKIs). In this paper, we propose a new type of hard problem, defined over a finite prime field, in which the generator is kept secret to prevent any direct Shor attack and is only subject to a limited influence from Grover. Based on this newly proposed hard problem, we construct a post-quantum digital signature scheme that is both Shor-resistant and Grover-resistant, secure against classical attacks, and fully compatible with current PKI infrastructures. Compared with existing post-quantum digital signature schemes, our solution significantly optimizes the size of public keys and signatures while increasing the speed of signing and verification. The newly proposed hard problem cannot be solved by known classical or quantum algorithms, thus ensuring long-term security. Performance evaluation results show that the scheme provides an optimal balance between performance and security, opening up a cost-effective implementation path for the post-quantum cryptography era.
This article introduces a solution of secure digital archiving in the post-quantum era. The basic tool at secure digital archiving of the electronic documents is the signature schemes, which are used at creation of the certificates and the timestamps. This article deals with the question of security of the signature schemes in the post-quantum era and introduces the post-quantum signature schemes, which will be resistant to the attacks leading by both conventional and quantum computers. The conventional signature schemes, based on factorization or discrete logarithm problem, in case of implementing the Shor algorithm on a quantum computer will be easy to break through. The main point of this article is the proposal of the solution of secure digital archiving with using the secure post-quantum signature schemes.
Abstract Lattice-based digital signature has become one of the widely recognized post-quantum algorithms because of its simple algebraic operation, rich mathematical foundation and worst-case security, and also an important tool for constructing cryptography. This survey explores lattice-based digital signatures, a promising post-quantum resistant alternative to traditional schemes relying on factoring or discrete logarithm problems, which face increasing risks from quantum computing. The study covers conventional paradigms like Hash-and-Sign and Fiat-Shamir, as well as specialized applications including group, ring, blind, and proxy signatures. It analyzes the versatility and security strengths of lattice-based schemes, providing practical insights. Each chapter summarizes advancements in schemes, identifying emerging trends. We also pinpoint future directions to deploy lattice-based digital signatures including quantum cryptography.