Universal designated verifier signatures can be used to resolve the conflict between authenticity and privacy in some applications. However, all of existing constructions for this primitive are based on hard problems in number theory, and will be ultimately broken in quantum era. To address this issue, we construct the first lattice-based universal designated verifier signatures as a post-quantum candidate for this primitive. Our construction is obtained by directly extending a ring-based variant of the Gentry-Peikert-Vaikuntanathan signature scheme with some additional algorithms, thus the existing key generation and signing implementation can be used without modification. We also show that our construction is provably secure under the Small Integer Solution problem over rings, in the random oracle model.
Universal designated verifier signatures can be used to resolve the conflict between authenticity and privacy in some applications. However, all of existing constructions for this primitive are based on hard problems in number theory, and will be ultimately broken in quantum era. To address this issue, we construct the first lattice-based universal designated verifier signatures as a post-quantum candidate for this primitive. Our construction is obtained by directly extending a ring-based variant of the Gentry-Peikert-Vaikuntanathan signature scheme with some additional algorithms, thus the existing key generation and signing implementation can be used without modification. We also show that our construction is provably secure under the Small Integer Solution problem over rings, in the random oracle model.
Motivated by the need to have secure strong designate verifier signatures (SDVS) even in the presence of quantum computers, a post-quantum lattice-based SDVS scheme is proposed based on the hardness of the short integer solution problem (SIS) and the learning with errors problem (LWE). The proposed SDVS scheme utilizes the Bonsai trees and pre-image sample-able function primitives to generate the designate verifier signature (DVS). In this construction, the un- forge-ability is based on the hardness of the SIS problem which is proven in the random oracle model and the non-transferability is based on the hardness of the LWE problem. As an application of the proposed SDVS scheme, we design a strong designate verifier ring signature scheme (SDVRS) which satisfies non-transferability. It is proven that the identity of the signer is unconditionally protected not only for any third-party but also for the designate verifier. Under the hardness of the SIS problem, the proposed SDVRS scheme is proven to be existentially un-forgeable in the random oracle model.
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.
Building cryptographic schemes upon as many fundamentally different hard problems as possible, seems to be the best way to hedge against future threats such as quantum computers. Being mainly based on the hardness of factoring and computing discrete logarithms, the present security landscape is at risk. In contrast, problems in lattices, such as finding short non-zero vectors, seem to withstand quantum computer attacks and the best known algorithms run in exponential time. In sharp contrast to other fields of cryptography, lattices admit a worst-case to average-case reduction (Ajtai 1996). Instead of assuming that a problem is hard for randomly chosen instances, lattice-based cryptosystems merely require the existence of a single hard instance, i.e., hardness in the worst case. With such an additional "trust anchor", the resulting security guarantees are much more plausible. Quite recently, we have seen an increased interest in lattice-based cryptography with many striking results. In this thesis, we are particularly interested in signature schemes, which provide a supporting pillar for today's economy. While we have seen basic signature schemes from lattices, e.g., (Gentry, Peikert, Vaikuntanathan 2008), (Lyubashevsky, Micciancio 2008), (Lyubashevsky 2009), or (Cash, Hofheinz, Kiltz, Peikert 2009), there are hardly any results dealing with the specific needs of applications, where ordinary signatures often fall too short. In this thesis, we build upon the above results and equip them with additional features, motivated by an exemplary selection of application scenarios. Hence, we demonstrate the great versatility of lattices in cryptography. In particular, we facilitate privacy-friendly electronic elections, fair online contract signing, signature compression, secure signatures in the strongest sense, as well as identity-based primitives. As far as possible, we avoid simplifying assumptions, such as the random oracle model. We believe that our techniques can be transferred to other application scenarios as well. Independently of the these results, we discuss the practical hardness of lattice problems and provide a framework for estimating the security of essentially all modern lattice-based cryptography.
Abstract. We provide an alternative method for constructing lattice-based digital signatures which does not use the “hash-and-sign ” methodology of Gentry, Peikert, and Vaikuntanathan (STOC 2008). Our resulting signature scheme is secure, in the random oracle model, based on the worst-case hardness of the Õ(n1.5)-SIVP problem in general lattices. The secret key, public key, and the signature size of our scheme are smaller than in all previous instantiations of the hash-and-sign signature, and our signing algorithm is also quite simple, requiring just a few matrix-vector multiplications and rejection samplings. We then also show that by slightly changing the parameters, one can get even more efficient signatures that are based on the hardness of the Learning With Errors problem. Our construction naturally transfers to the ring setting, where the size of the public and secret keys can be significantly shrunk, which results in the most practical to-date provably secure signature scheme based on lattices. 1
Digital signatures are fundamental cryptographic primitives that ensure the authenticity and integrity of digital communication. However, in scenarios involving sensitive interactions -- such as e-voting or e-cash -- there is a growing need for more controlled signing mechanisms. Strong-Designated Verifier Signature (SDVS) offers such control by allowing the signer to specify and restrict the verifier of a signature. The existing state-of-the-art SDVS are mostly based on number-theoretic hardness assumptions. Thus, they are not secure against quantum attacks. Moreover, Post-Quantum Cryptography (PQC)-based SDVS are inefficient and have large key and signature sizes. In this work, we address these challenges and propose an efficient post-quantum SDVS (namely, LaSDVS) based on ideal lattices under the hardness assumptions of the Ring-SIS and Ring-LWE problems. LaSDVS achieves advanced security properties including strong unforgeability under chosen-message attacks, non-transferability, non-delegatability, and signer anonymity. By employing the algebraic structure of rings and the gadget trapdoor mechanism of Micciancio et al., we design LaSDVS to minimize computational overhead and significantly reduce key and signature sizes. Notably, our scheme achieves a compact signature size of O(nlogq), compared to O(n2) size, where n is the security parameter, in the existing state-of-the-art PQC designs. To the best of our knowledge, LaSDVS offers the \textit{smallest private key and signature size} among the existing PQC-based SDVS schemes.