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Journal of Information Security and Applications

A survey of quantum secure group signature schemes: Lattice-based approach

Meryem Soysaldı, Sedat Akleylek

Published Jan 27, 2023• 13 citations
Publisher
DOI
10.1016/j.jisa.2023.103432

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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.
A group signature allows a group member who signs the message on behalf of the other group members. Any recipient also verifies the signature without knowing the signer. However, it is possible to reveal the signer’s identity since the group signatures have the tracing mechanism. In general, the group signature size increases the number of group members. However, the schemes are also proposed with the constant signature size. On the other hand, the security of some schemes are based on the discrete logarithm and factorization problems while some schemes which are secure against quantum attacks are proposed. To the best of our knowledge, the signature scheme in the group concept has not been proposed on lattices in quantum oracles. In this paper, we propose a new constant-size and partially-dynamic group signature scheme on lattice assumptions. We combine the Dilithium signature scheme, a Stern-like zero-knowledge scheme and Regev’s encryption scheme. We give a zero-knowledge argument system for our proposed scheme and security analysis in the quantum random oracle model. According to the comparison results, the proposed scheme has better size complexity in asymptotic concept.
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.