Recently, lattice signatures based on the Fiat‐Shamir framework have seen a lot of improvements which are efficient in practice. The security of these signature schemes depends mainly on the hardness of solving short integer solutions (SIS) and/or learning with errors problem in the random oracle model. The authors propose an alternative lattice‐based signature scheme on the Fiat‐Shamir framework over the ring . The key generation in the signature scheme is based on the combination of NTRU and Ring SIS like key generation. Both the signature and the verification are done efficiently by doing polynomial convolutions in the ring . The proposed signature scheme is provably secure based on the hardness of the Ring SIS problem in the random oracle model. The scheme is also efficient up to constant factors as the highly practical schemes which have provable secure instantiation.
Recently, lattice signatures based on the Fiat‐Shamir framework have seen a lot of improvements which are efficient in practice. The security of these signature schemes depends mainly on the hardness of solving short integer solutions (SIS) and/or learning with errors problem in the random oracle model. The authors propose an alternative lattice‐based signature scheme on the Fiat‐Shamir framework over the ring . The key generation in the signature scheme is based on the combination of NTRU and Ring SIS like key generation. Both the signature and the verification are done efficiently by doing polynomial convolutions in the ring . The proposed signature scheme is provably secure based on the hardness of the Ring SIS problem in the random oracle model. The scheme is also efficient up to constant factors as the highly practical schemes which have provable secure instantiation.
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
We propose a variant version of ring learning with errors (R-LWE) assumption. Under the modified slightly assumption which is reducible to the worst-case problems on ideal lattice, we present a construction of digital signatures. So the scheme is provably secure based on the hardness of lattice problems (such as approximating the length of the shortest vector within a fixed poly(n) factor). Compared with some existing typical lattice-based signature schemes, the construction enjoys many advantages, including simple and efficient key generation algorithm, signing algorithm and verification algorithm to improve the efficiency of the scheme as well as to reduce the overhead. The sizes of the secret and public keys and the signature are almost linear O(n log n) (up to poly-logarithmic factors) in the dimension n of the lattice.
In this paper, we present a new TRSS (threshold ring signature scheme) which depends on the worst-case hardness of a lattice problem. We apply Fiat-Shamir transform to a lattice-based identification scheme to obtain the proposed scheme. The hardness of the identification scheme which is the hybrid combination of two different designs is based on inhomogeneous short integer solution (ISIS) problem. We give security proof for the proposed TRSS. Comparing the proposed TRSS and the others which are quantum secure, the size of key pairs and the length of the signature are nearly same. Therefore, the proposed scheme is an alternative to the threshold ring signature schemes in post-quantum area.
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.