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The Computer Journal

Hierarchical Identity-Based Signature in Polynomial Rings

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

Published Mar 10, 2020• 6 citations
Publisher

Abstract

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.

DOI
10.1093/comjnl/bxaa033

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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.
Lattice-based hierarchical identity-based signature (HIBS) schemes are receiving significant attention due to provable security reductions and potential security for quantum computers. However, most of the existing HIBS schemes based on lattices are less efficient for practical applications. To make lattice-based HIBS schemes become more practical, this paper presents an efficient HIBS scheme from lattices. Both the secret key size and the signature length of our proposal are much shorter than those of other lattice-based HIBS proposals. Our scheme is proven to be strongly unforgeable against adaptive identity attacks in the random oracle model. The security of the construction relies on the standard short integer solution (SIS) assumption.
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.
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.
Identity-based ring signature is the combination of the identity-based cryptography and ring signature.It can be used in many practical applications.Most of the existing identity-based ring signatures are based the bilinear pairing assumption.How ever,bilinear pairing problem is no longer hard in the quantum era.To construct an identity-based ring signature securing in the quantum era,in this paper,we presented an identity-based ring signature scheme based on lattices.The scheme is secure in the standard model.The security of scheme is based on the standard small integer solution(SIS) assumption.Compared with other identity-based ring signature schemes from lattices in the standard model,our scheme enjoys higher 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.