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.
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.
This paper aimed to provide a thorough examination of recent advancements in digital signatures, emphasizing data security, authentication, and information non-repudiation in the digital age. The study is based on a review of scientific literature from the period 2020 to 2025, in which fundamental principles such as cryptography, public key infrastructure (PKI), hash functions, and RSA algorithms were analysed. It was confirmed that the practical principles of digital signatures were analysed in sensitive areas such as blockchain and healthcare, along with emerging technologies like post-quantum systems and artificial intelligence. The research findings showed that traditional algorithms like RSA are gradually being replaced by newer models such as Syrga-1 and HBSS, which provide better protection against quantum attacks. The importance of PKI in identity verification and certificate management within decentralized systems was confirmed. We consider digital signatures to be essential for ensuring integrity and non-repudiation in many applications. This study enhances academic literature by elucidating contemporary difficulties and prospects for continued progress in digital security. Nonetheless, constraints remain concerning the experimental status of post-quantum technologies and the absence of widespread standardization. Recommendations include expediting the standardization of post-quantum algorithms, incorporating them with blockchain technology, formulating lightweight schemes for the Internet of Things, and enhancing awareness about the usage of digital signatures in both public and private sectors.
Signature schemes, proposed in 1976 by Diffie and Hellman, have become ubiquitous across modern communications. They allow for the exchange of messages from one sender to multiple recipients, with the guarantees that messages cannot be forged or tampered with and that messages also can be forwarded from one recipient to another without compromising their validity. Signatures are different from, but no less important than encryption, which ensures the privacy of a message. Commonly used signature protocols—signatures based on the Rivest–Adleman–Shamir (RSA) algorithm, the digital signature algorithm (DSA), and the elliptic curve digital signature algorithm (ECDSA)—are only computationally secure, similar to public key encryption methods. In fact, since these rely on the difficulty of finding discrete logarithms or factoring large primes, it is known that they will become completely insecure with the emergence of quantum computers. We may therefore see a shift towards signature protocols that will remain secure even in a post-quantum world. Ideally, such schemes would provide unconditional or information-theoretic security. In this paper, we aim to provide an accessible and comprehensive review of existing unconditionally securesecure signature schemes for signing classical messages, with a focus on unconditionally secure quantum signature schemes.
Quantum computers are moving closer to reality, and with that comes a serious concern for today’s public-key cryptography. Many of the encryption and digital signature systems we rely on now, such as RSA and ECC, may no longer be secure in the future. Because of this, researchers are actively looking for new methods that can protect digital communication in the post-quantum era. One of the most promising directions is lattice-based cryptography. This paper gives a simple and focused review of lattice-based signature schemes. It brings together the main ideas from the existing literature and explains how these schemes are built, why they are considered secure, and what makes them practical. The review mainly discusses schemes based on hard lattice problems such as SIS and LWE. To make the comparison clearer, a table is also included that compares different signature schemes in terms of key size, signature size, security level, and computational efficiency. Overall, this study shows why lattice-based signature schemes are becoming an important part of modern cryptographic research and why they may play a major role in securing digital systems against future quantum threats.
The protection and security of information have always been and continue to be one of the major challenges we face today. Message encryption, digital signatures, financial and banking transactions, and the emerging cryptocurrency market are all threatened by the advancement of quantum computing and its potential ability to break the keys of current algorithms. Cryptographic environments based on public key encryption and digital signatures could be compromised by a sufficiently powerful quantum computer. Over the last decade, state organizations and companies dedicated to information technologies have made significant progress in the development of quantum and postquantum cryptography. This article aims to provide an overview of the advancements and evolution of quantum and post-quantum cryptography algorithms, highlighting their importance in creating secure encryption to mitigate the potential threats posed by quantum computing.
Quantum computers are moving closer to reality, and with that comes a serious concern for today's public-key cryptography. Many of the encryption and digital signature systems we rely on now, such as RSA and ECC, may no longer be secure in the future. Because of this, researchers are actively looking for new methods that can protect digital communication in the post-quantum era. One of the most promising directions is lattice-based cryptography. This paper gives a simple and focused review of lattice-based signature schemes. It brings together the main ideas from the existing literature and explains how these schemes are built, why they are considered secure, and what makes them practical. The review mainly discusses schemes based on hard lattice problems such as SIS and LWE. To make the comparison clearer, a table is also included that compares different signature schemes in terms of key size, signature size, security level, and computational efficiency. Overall, this study shows why lattice-based signature schemes are becoming an important part of modern cryptographic research and why they may play a major role in securing digital systems against future quantum threats.
Information security is a fundamental and urgent issue in the digital transformation era. Cryptographic techniques and digital signatures have been applied to protect and authenticate relevant information. However, with the advent of quantum computers and quantum algorithms, classical cryptographic techniques have been in danger of collapsing because quantum computers can solve complex problems in polynomial time. Stemming from that risk, researchers worldwide have stepped up research on post-quantum algorithms to resist attack by quantum computers. In this review paper, we survey studies in recent years on post-quantum cryptography (PQC) and provide statistics on the number and content of publications, including a literature overview, detailed explanations of the most common methods so far, current implementation status, implementation comparisons, and discussion on future work. These studies focused on essential public cryptography techniques and digital signature schemes, and the US National Institute of Standards and Technology (NIST) launched a competition to select the best candidate for the expected standard. Recent studies have practically implemented the public key encryption/key encapsulation mechanism (PKE/KEM) and digital signature schemes on different hardware platforms and applied various optimization measures based on other criteria. Along with the increasing number of scientific publications, the recent trend of PQC research is increasingly evident and is the general trend in the cryptography industry. The movement opens up a promising avenue for researchers in public key cryptography and digital signatures, especially on algorithms selected by NIST.