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.
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.
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.
In the past, many ID-based signature (IBS) schemes based on the integer factorization or discrete logarithm problems were proposed. With the progress on the development of quantum technology, IBS schemes mentioned above would become vulnerable. Recently, several IBS schemes over lattices were proposed to be secure against attacks in the quantum era. As conventional public-key settings, ID-based public-key settings have to offer a revocation mechanism to revoke misbehaving or malicious users. However, in the past, little work focuses on the revocation problem in the IBS schemes over lattices. In this article, we propose a new revocable IBS (RIBS) scheme with short size over lattices. Based on the short integer solution (SIS) assumption, we prove that the proposed RIBS scheme provides existential unforgeability against adaptive chosen-message attacks. As compared to the existing IBS schemes over lattices, our RIBS scheme has better performance in terms of signature size, signing key size, and the revocation mechanism with public channels.
Hierarchical identity-based signature (HIBS), which plays an important role in large communities, is a generaliza-tion of identity-based signature (IBS). In this paper, we present a new HIBS scheme from lattices without ran-dom oracles. The new scheme is proven to be strongly unforgeable against selective identity attacks under the standard hardness assumption of the short integer so-lution (SIS) problem. Furthermore, the secret key size and the signature length of our scheme are both invariant and much shorter than those of the previous lattice-based HIBS schemes. To the best of our knowledge, our con-struction is the first short lattice-based HIBS scheme in the standard model.
Abstract. We propose a variant of the “bonsai tree ” signature scheme, a lattice-based existentially unforgeable signature scheme in the standard model. Our construction offers the same efficiency as the “bonsai tree” scheme but supports the stronger notion of strong unforgeability. Strong unforgeability demands that the adversary is unable to produce a new message-signature pair (m, s), even if he or she is allowed to see a different signature s ′ for m. In particular, we provide the first treeless signature scheme that supports strong unforgeability for the post-quantum era in the standard model. Moreover, we show how to directly implement identity-based, and even hierarchical identity-based, signatures (IBS) in the same strong security model without random oracles. An additional advantage of this direct approach over the usual generic conversion of hierarchical identity-based encryption to IBS is that we can exploit the efficiency of ideal lattices without significantly harming security. We equip all constructions with strong security proofs based on mild worst-case assumptions on lattices and we also propose concrete security parameters.
Proxy signature schemes safely ensure that an original signer transfers the signing right to a proxy signer, and a variety of these schemes have been developed for secure applications. Constructions of proxy signature schemes vary; recently developed schemes utilize lattices to safeguard against quantum attacks. However, existing lattice-based proxy schemes proved secure in the standard model have many public system parameters, reducing the efficiency of these schemes. To solve this problem, we utilize an admissible hash function with compatible algorithms (AHFwCA) and lattice trapdoors as an initial framework to propose a new lattice-based proxy signature scheme. While maintaining a similar key and signature size as prior schemes, this new proxy signature scheme requires fewer public system parameters. Compared with requiring linear basic matrices as public system parameters found in other standard model schemes, the proposed new scheme depends upon logarithmic basic matrices. Under the standard inhomogeneous short integer solution (ISIS) assumption, we prove that the scheme is existentially unforgeable against chosen message attacks and chosen warrant attacks (EUF-CMA-CWA) in the standard model by using the generalized partitioning proof technique. Thus, this paper partially solves the many parameters problem existed in the standard model lattice-based signature schemes.
Signcryption is a cryptographic primitive that can provide valid solution for authentication and confidentiality.In this paper, an efficient identity-based signcryption scheme from lattice was proposed.Our scheme based on Macciancio and Piekert's trapdoor generation method and delegate algorithm for lattice.Our main idea is that establish the identity-based system master key via trapdoor generation method for lattice, and extract user's key by trapdoor delegate algorithm.With the aid of random oracle, we prove that the proposed scheme has CCA security under the learning with errors (LWE) assumption and unforgeability against adaptive chosen messages attacks under the small integer solution (SIS) assumption.Comparison with signature-then-encryption approach shows that our scheme is efficient.