Ring signature enables the members to sign anonymously without a manager, it has many online applications, such as e-voting, e-money, whistle blowing etc. As a promising post-quantum candidate, lattice-based cryptography attracts much attention recently. Several efficient lattice-based ring signatures have been naturally constructed from lattice basis delegation, but all of them have large verification key sizes. Our observation finds that a new concept called the split- small integer solution(SIS) problem introduced by Nguyen et al. at PKC’15 is excellent in reducing the public key sizes of lattice-based ring signature schemes from basis delegation. In this research, we first define an extended concept called the extended split-SIS problem, and then prove that the hardness of the extended problem is as hard as the approximating shortest independent vectors problem(SIVP) problem within certain polynomial factor. Moreover, we present an improved ring signature and prove that it is anonymous and unforgeable against the insider corruption. Finally, we give two other improved existing ring signature schemes from lattices. In the end, we show the comparison with the original scheme in terms of the verification key sizes. Our research data illustrate that the public key sizes of the proposed schemes are reduced significantly.
Ring signature enables the members to sign anonymously without a manager, it has many online applications, such as e-voting, e-money, whistle blowing etc. As a promising post-quantum candidate, lattice-based cryptography attracts much attention recently. Several efficient lattice-based ring signatures have been naturally constructed from lattice basis delegation, but all of them have large verification key sizes. Our observation finds that a new concept called the split- small integer solution(SIS) problem introduced by Nguyen et al. at PKC’15 is excellent in reducing the public key sizes of lattice-based ring signature schemes from basis delegation. In this research, we first define an extended concept called the extended split-SIS problem, and then prove that the hardness of the extended problem is as hard as the approximating shortest independent vectors problem(SIVP) problem within certain polynomial factor. Moreover, we present an improved ring signature and prove that it is anonymous and unforgeable against the insider corruption. Finally, we give two other improved existing ring signature schemes from lattices. In the end, we show the comparison with the original scheme in terms of the verification key sizes. Our research data illustrate that the public key sizes of the proposed schemes are reduced significantly.
Among post-quantum alternatives, latticebased cryptography is the most promising one, due to its simple operations, reduction from aver-age-case to worstcase hardness, and supporting of rich functionalities. Ring signature enables a user to sign anonymously on behalf of an adaptively chosen group, and has multiple applications in anonymous e-voting, anonymous authentication, whistle blowing etc. However, most lattice-based ring signature schemes were constructed in the random oracle model from lattice basis delegation and they suffer large verification key sizes as a common disadvantage. This work proposes an efficient ring signature scheme from lattice basis delegation without random oracle based on the extended split-SIS problem, whose security is approximately as hard as the worst-case SIVP problem. Our scheme is proved to be anonymous and existentially unforgeable under latticebased assumptions. Finally, the verification key size is significantly reduced to a small constant, instead of increasing linearly with the number of ring members.
Although most existing linkable ring signature schemes on lattice can effectively resist quantum attacks, they still have the disadvantages of excessive time and storage overhead. This paper constructs an identity-based linkable ring signature (LRS) scheme over NTRU lattice by employing the technologies of trapdoor generation and rejection sampling. The security of this scheme relies on the small integer solution (SIS) problem on NTRU lattice. We prove that this scheme has unconditional anonymity, unforgeability, and linkability under the random oracle model (ROM). Through the performance analysis, this scheme has a shorter size of public/private keys, and when the number of ring members is small (such as N ≤ 8 ), this scheme has a shorter signature size compared with other existing latest lattice-based LRS schemes. The computational efficiency of signature has also been further improved since it only involves multiplication in the polynomial ring and modular operations of small integers. Finally, we implemented our scheme and other similar schemes, and it is shown that the time for the signature generation and verification of this scheme decreases roughly by 44.951% and 33.503%, respectively.
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.
Ring signatures, a novel cryptographic primitive, were introduced by Rivest, Shamir, and Tauman at ASIACRYPT 2001. It allows a member of a group to sign a message on behalf of an ad-hoc group of users, known as a ring, without revealing its identity. Ring signatures, initially introduced for applications such as whistle-blowing and confidential disclosures, have since gained significant relevance and widespread adoption across various domains, including blockchain technologies, ad-hoc networks, anonymous transactions, location-based services, cloud computing platforms, and outsourced computation. However, traditional ring signatures are vulnerable if the signers’ keys are compromised. To resolve this vulnerability, Liu and Wong introduced the notion of forward-secure ring signatures at IJNS 2008. Forward-security ensures that even if a signer’s secret key is compromised, signatures generated in prior time periods remain secure. It significantly reduces the damage caused by secret key exposure, making it crucial for long-term security in applications such as whistle-blowing or anonymous authentication. However, most existing forward-secure ring signature schemes are based on number-theoretic assumptions, making them vulnerable to quantum adversaries. Yu and Wang proposed a quantum-safe forward-secure ring signature scheme at ICICS 2023, and Yu et al. further extended this work in Computer Networks (2025), retaining the same ring signature scheme with forward security. But the scheme suffers from large signatures that grow linearly with the ring size. In this paper, we propose a lattice-based forward-secure ring signature scheme in the quantum random oracle model ( QROM ) that simultaneously achieves security against quantum adversaries and compact signature size. Notably, the signature size is logarithmic in the number of members in the ring, enabling significantly better scalability compared to prior constructions.