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Chinese Journal of Electronics

An Efficient Post‐quantum Identity‐Based Signature

Yang Zhichao, Dung Hoang Duong, Willy Susilo, Guomin Yang, Chao Li, Chen Rongmao

Published Mar 1, 2021• 7 citations
Publisher

Abstract

Digital signature is one of the most important cryptography primitives. Recently, more and more works have been done to construct signatures over lattice problems to keep them secure in the quantum age. Among them, a ring-based signature scheme named Dilithium is the most efficient one and a candidate in the third round of the National Institute of Standards and Technology's post-quantum cryptography project. To make those schemes work well in large network, we constructed the first ring-based Identity-based signature (IBS) scheme for light-weight authentication. The construction in this paper relies on the transformations introduced by Bellare et al. in Journal of Cryptology (Vol.22, No.1, pp.1–61, 2009) and its security can be proved under the hardness of ring-learning with errors problem in the random oracle model. Due to better trapdoor and polynomial ring setting, our proposed scheme are much better than the previous ones in terms of both computation and communication complexities.

DOI
10.1049/cje.2021.01.006

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Digital signature is one of the most important cryptography primitives. Recently, more and more works have been done to construct signatures over lattice problems to keep them secure in the quantum age. Among them, a ring-based signature scheme named Dilithium is the most efficient one and a candidate in the third round of the National Institute of Standards and Technology's post-quantum cryptography project. To make those schemes work well in large network, we constructed the first ring-based Identity-based signature (IBS) scheme for light-weight authentication. The construction in this paper relies on the transformations introduced by Bellare et al. in Journal of Cryptology (Vol.22, No.1, pp.1–61, 2009) and its security can be proved under the hardness of ring-learning with errors problem in the random oracle model. Due to better trapdoor and polynomial ring setting, our proposed scheme are much better than the previous ones in terms of both computation and communication complexities.
Identity-based signature is an important technique for light-weight authentication. Recently, many efforts have been made to construct identity-based signatures over lattice assumptions since they would remain secure in future quantum age. In this paper we present a new identity-based signature scheme from lattice problems. This scheme is more efficient than other lattice-based identity-based signature schemes in terms of both computation and communication complexities. We prove its security in the random oracle model under short integer solution assumption that is as hard as approximating several worst-case lattice problems. We also extend the scheme to an identity-based message recovery signature scheme that has better performance.
With the rapid development of electronic information technology, digital signature has become an indispensable part of our lives. Traditional public key certificate cryptosystems cannot overcome the limitations of certificate management. Identity-based cryptosystems can avoid the certificate management issues. The development of quantum computers has brought serious challenges to traditional cryptography. Post-quantum cryptography research is imperative. At present, almost all post-quantum identity-based signature (IBS) schemes are constructed using Gaussian sampling or trapdoor technologies. However, these two technologies have a great impact on computational efficiency. To overcome this problem, we construct an IBS scheme on lattices by employing Lyubashevsky’s signature scheme. Based on the shortest vector problem on lattices, our scheme does not use Gaussian sampling or trapdoor technologies. In the random oracle model, it is proved that our scheme is strongly unforgeable against adaptive chosen messages and identity attacks. The security level of our scheme is strongly unforgeable, which is a higher level than the existential unforgeability of other schemes. Compared with other efficient schemes, our scheme has advantages in computation complexity and security.
Identity-based signature (IBS) which is a paradigm built on public key cryptography has played a significant role in light-weight authentication. With the advent of the post quantum era, the lattice has become a main mathematical tool to construct quantum-immune cryptographic schemes. By utilizing an admissible hash function with compatible algorithms and lattice trapdoors as basic building blocks, we propose a new IBS scheme over lattices. The scheme is proved existentially unforgeable against adaptive identity attacks and chosen message attacks in the standard model under inhomogeneous short integer solution assumption via the generalized partitioning proof technique. Moreover, the scheme needs only logarithmic basic matrices as master public key while keeping the same private key size and signature size as those of other standard model lattice-based IBS schemes. This construction is the first adaptive-ID secure standard model IBS scheme over lattice with such space efficiency.
So far, most ring signature schemes rely on hard number theory problems, such as discrete logarithm, bilinear pairings and so on. Unfortunately, the above underlying number theory problems will be solvable in the post quantum era. Lattice-based cryptography is a hotspot of research recently, due to its implementation simplicity and provable security reductions. When the hash-and-sign signature scheme was constructed based on the hardness of worst-case lattice problems, provably secure lattice-based ring signature schemes were finally constructed. However, the hash-and-sign ring signatures were rather inefficient (with megabytes long signatures). In this paper, we propose an alternative method for constructing lattice-based and identity-based ring signature scheme which does not use the hash-and-sign methodology. In the random oracle model, the proposed signature scheme based on the problem in general lattices is unforgeable and holds anonymity. Compared with the previous instantiations of the hash-and-sign ring signature schemes, the lengths of secret key, public key and signatures in the proposed scheme are much shorter. The signing algorithm is quite simple, with matrix-vector multiplications and rejection samplings.
So far, most ring signature schemes rely on hard number theory problems, such as discrete logarithm, bilinear pairings and so on. Unfortunately, the above underlying number theory problems will be solvable in the post quantum era. Lattice-based cryptography is a hotspot of research recently, due to its implementation simplicity and provable security reductions. When the hash-and-sign signature scheme was constructed based on the hardness of worst-case lattice problems, provably secure lattice-based ring signature schemes were finally constructed. However, the hash-and-sign ring signatures were rather inefficient (with megabytes long signatures). In this paper, we propose an alternative method for constructing lattice-based and identity-based ring signature scheme which does not use the hash-and-sign methodology. In the random oracle model, the proposed signature scheme based on the problem in general lattices is unforgeable and holds anonymity. Compared with the previous instantiations of the hash-and-sign ring signature schemes, the lengths of secret key, public key and signatures in the proposed scheme are much shorter. The signing algorithm is quite simple, with matrix-vector multiplications and rejection samplings.
Abstract Hierarchical identity-based signature (HIBS) plays a core role in a large community as it significantly reduces the workload of the root private key generator. To make HIBS still available and secure in post-quantum era, constructing lattice-based schemes is a promising option. In this paper, we present an efficient HIBS scheme in polynomial rings. Although there are many lattice-based signatures proposed in recent years, to the best of our knowledge, our HIBS scheme is the first ring-based construction. In the center of our construction are two new algorithms to extend lattice trapdoors to higher dimensions, which are non-trivial and of independent interest. With these techniques, the security of the new scheme can be proved, assuming the hardness of the Ring-SIS problem. Since operations in the ring setting are much faster than those over integers and the new construction is the first ring-base HIBS scheme, our scheme is more efficient and practical in terms of computation and storage cost when comparing to the previous constructions.