Johannes A Buchmann, Carlos Coronado, Daniel Patrick Martin, Daniela Engelbert, Christoph Ludwig, Raphael Overbeck, Arthur R. Schmidt, Ulrich Vollmer, Ralf-Philipp Weinmann
Digital signatures have become a key technology for making the Internet and other IT infrastructures secure.But in 1994 Peter Shor showed that quantum computers can break all digital signature schemes that are used today and in 2001 Chuang and his coworkers implemented Shor's algorithm for the first time on a 7-qubit NMR quantum computer.This paper studies the question: What kind of digital signature algorithms are still secure in the age of quantum computers?
Digital signatures have become a key technology for making the Internet and other IT infrastructures secure.But in 1994 Peter Shor showed that quantum computers can break all digital signature schemes that are used today and in 2001 Chuang and his coworkers implemented Shor's algorithm for the first time on a 7-qubit NMR quantum computer.This paper studies the question: What kind of digital signature algorithms are still secure in the age of quantum computers?
Quantum computers that can run Shor's algorithm are expected to become available in the next decade. These algorithms can be used to break conventional digital signature schemes (e.g. RSA or ECDSA), which are widely used in embedded systems today. This puts these systems at risk when they are used in safety-relevant long-term applications such as automotive systems or critical infrastructures. To mitigate this risk, classical digital signature schemes used must be replaced by schemes secure against quantum computer based attacks.
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.
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.
This chapter describes the impact of quantum algorithms on the schemes used today, and offers a glimpse of some schemes offering plausible post-quantum security. It introduces one computational problem that has received a lot of attention, and is widely believed to be hard even for quantum algorithms. Quantum cryptography refers to cryptosystems that are implemented using quantum computers, quantum-mechanical phenomena, and quantum communication channels; for this reason, they would be difficult to deploy widely over the existing Internet. Post-quantum cryptosystems, are entirely classical—but are intended to ensure security even if an attacker has access to a quantum computer. The chain-based signature scheme is a stateful signature scheme that is existentially unforgeable under an adaptive chosen-message attack. Quantum computing is covered in the text by Nielsen and Chuang, which also describes Grover’s algorithm and Shor’s algorithm.
One of the most crucial measures to maintain data security is the use of cryptography schemes and digital signatures built upon cryptographic algorithms. The resistance of cryptographic algorithms against conventional attacks is guaranteed by the computational difficulties and the immense amount of computation required to them. In the last decade, with the advances in quantum computing technology and the realization of quantum computers, which have higher computational power compared to conventional computers and can execute special kinds of algorithms (i.e., quantum algorithms), the security of many existing cryptographic algorithms has been questioned. The reason is that by using quantum computers and executing specific quantum algorithms through them, the computational difficulties of conventional cryptographic algorithms can be reduced, which makes it possible to overcome and break them in a relatively short period of time. Therefore, researchers began efforts to find new quantum-resistant cryptographic algorithms that would be impossible to break, even using quantum computers, in a short time. Such algorithms are called post-quantum cryptographic algorithms. In this article, we provide a comprehensive review of the challenges and vulnerabilities of different kinds of conventional cryptographic algorithms against quantum computers. Afterward, we review the latest cryptographic algorithms and standards that have been proposed to confront the threats posed by quantum computers. We present the classification of post-quantum cryptographic algorithms and digital signatures based on their technical specifications, provide examples of each category, and outline the strengths and weaknesses of each category.
Signatures are primarily used as a mark of authenticity, to demonstrate that the sender of a message is who they claim to be. In the current digital age, signatures underpin trust in the vast majority of information that we exchange, particularly on public networks such as the internet. However, schemes for signing digital information, which are based on assumptions of computational complexity, are facing challenges from advances in mathematics, the capability of computers, and the advent of the quantum era. Here, the authors present a review of digital signature schemes, looking at their origins and where they are under threat. Next, the authors introduce post-quantum digital schemes, which are being developed with the specific intent of mitigating against threats from quantum algorithms while still relying on digital processes and infrastructure. Finally, the authors review schemes for signing information carried on quantum channels, which promise provable security metrics. Signatures were invented as a practical means of authenticating communications, and it is important that the practicality of novel signature schemes is considered carefully, which is kept as a common theme of interest throughout this review.