Digital signatures are used to ensure authentication. Blind signature schemes are a special form of digital signatures and important in scenarios which depend on anonymous and secure authentication. (e.g. e-voting) The common digital blind signature schemes are based on asymmetric cryptography with underlying hard problems like integer factorization or discrete logarithm. These hard problems will become weak with the development of quantum computers. To avoid the uselessness of classic cryptography in the post quantum era, it will be important to find alternative methods based on other hard problems. This book deals with the attempt of developing a new blind signature scheme based on lattice signature schemes.
Digital signatures are used to ensure authentication. Blind signature schemes are a special form of digital signatures and important in scenarios which depend on anonymous and secure authentication. (e.g. e-voting) The common digital blind signature schemes are based on asymmetric cryptography with underlying hard problems like integer factorization or discrete logarithm. These hard problems will become weak with the development of quantum computers. To avoid the uselessness of classic cryptography in the post quantum era, it will be important to find alternative methods based on other hard problems. This book deals with the attempt of developing a new blind signature scheme based on lattice 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.
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.
At present, several post-quantum cryptosystems have been proposed, and lattice-based cryptography is the main candidate. Especially in the direction of digital signatures, there are now many practical lattice-based signature schemes. However, there exist few lattice-based signatures with special property such as blind signature. Blind signature was introduced by Chaum for creating untraceable payment system. Then, it is widely used in e-cash and voting, especially in the revolutionary digital cash system based on blockchain. In our paper, we present a method to construct a post-quantum blind signature based on lattice assumptions, and we proved that any existential forger against the security of the resulting scheme can solve theSISq,n,m,βproblem forβ=O(dn). Our main technique is the rejection sampling theory. The expected number of times needed to output a blind signature is at moste2under aborting, and our new scheme has much smaller signature size than those of all the previously proposed blind signature schemes over lattices.
Blind signatures were first introduced by David Chaum. They allow a user to have a message signed by a signer without revealing the message itself. This property is particularly useful in applications such as electronic voting and digital cash, where user anonymity is important. In a blind signature scheme, the user blinds their message before sending it to the signer, who signs the blinded message. The user then unblinds the signed message to obtain a valid signature that can be verified publicly, ensuring that the signer cannot trace the signed message back to the original unblinded version. A good analogy is placing the message inside an envelope and having the envelope signed. Once the envelope is opened, the signature remains valid for the enclosed message, ensuring that the content remains confidential. Such constructions provide anonymity and privacy to the user but given a practical quantum computer, the security of traditional crypto-systems providing such features will be broken. To address this, the development of quantum-resistant cryptographic protocols is essential for maintaining the security of digital transactions and data. Aligning with the same goal, this work aims to thoroughly review the background of lattice-based blind signatures. We start with the foundations of digital signatures in the classical settings and then move on to lattice-based constructions.
Introduction: The progress in the development of quantum computing has raised the problem of constructing post-quantum two-key cryptographic algorithms and protocols, i.e. crypto schemes resistant to attacks from quantum computers. Based on the hidden discrete logarithm problem, some practical post-quantum digital signature schemes have been developed. The next step could be the development of post-quantum blind signature protocols. Purpose: To develop blind signature protocols based on the computational difficulty of the hidden discrete logarithm problem. Method: The use of blinding factors introduced by the client during the blind signature protocol when the parameters necessary for the blind signature formation are passed to the signatory. Results: It has been proposed to use blinding multipliers of two different types: left-sided and right-sided ones. With them, you can develop blind signature protocols on the base of schemes with a verification equation defined in non-commutative algebraic structures. New blind signature protocols have been developed, based on the computational difficulty of the hidden discrete logarithm problem. As the algebraic carrier for the developed protocols, finite non-commutative associative algebras of two types are used: 1) those with a global two-sided unit, and 2) those with a large set of global left units. Practical relevance: The proposed protocols have a high performance and can be successfully implemented either in software or in hardware.
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.