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IEEE Access

New Lattice-Based Short Proxy Signature Scheme With Fewer System Parameters in the Standard Model

Zecheng Wang, Huaizhong Bao, Tao Zhao, Faze Du, Xuemin Chen

Published Jan 1, 2022• 6 citations
Publisher

Abstract

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.

DOI
10.1109/access.2022.3178368

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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.
Abstract:The provably secure public-key cryptosystems in the standard model are more practical, but the provably secure lattice-based proxy signature schemes in the standard model have not been constructed up to now. A new lattice-based proxy signature scheme was constructed by using the Boyen’s preimage sampling algorithm.The proposed proxy signature scheme was proved to satisfy the existential unforgeability against adaptive chosen-message attacks based on the hardness of the small integer solution (SIS) problem in the standard model.Finally,the computational performance of the proposed proxy signature scheme was compared with that of the existing lattice-based proxy signature schemes.The comparative results showed that the proposed proxy signature scheme has higher efficiency.
The provably secure public-key cryptosystems in the standard model are more practical,but the provably secure lattice-based proxy signature schemes in the standard model have not been constructed up to now. A new lattice-based proxy signature scheme was constructed by using the Boyen's preimage sampling algorithm. The proposed proxy signature scheme was proved to satisfy the existential unforgeability against adaptive chosen-message attacks based on the hardness of the small integer solution( SIS) problem in the standard model. Finally,the computational performance of the proposed proxy signature scheme was compared with that of the existing lattice-based proxy signature schemes. The comparative results showed that the proposed proxy signature scheme has higher efficiency.
A proxy blind signature scheme is a special form of blind signature which allowed a designated person called proxy signer to sign on behalf of original signers without knowing the content of the message. It combines the advantages of proxy signature and blind signature. Up to date, most proxy blind signature schemes rely on hard number theory problems, discrete logarithm, and bilinear pairings. Unfortunately, the above underlying number theory problems will be solvable in the postquantum era. Lattice‐based cryptography is enjoying great interest these days, due to implementation simplicity and provable security reductions. Moreover, lattice‐based cryptography is believed to be hard even for quantum computers. In this paper, we present a new identity‐based proxy blind signature scheme from lattices without random oracles. The new scheme is proven to be strongly unforgeable under the standard hardness assumption of the short integer solution problem (SIS) and the inhomogeneous small integer solution problem (ISIS). Furthermore, the secret key size and the signature length of our scheme are invariant and much shorter than those of the previous lattice‐based proxy blind signature schemes. To the best of our knowledge, our construction is the first short lattice‐based identity‐based proxy blind signature scheme in the standard model.
By using trapdoor functions with preimage sampling,lattice's growth,and lattice basis randomization in the bonsai tree,a lattice-based proxy signature scheme was proposed.The security of the proxy signature is based on the hardness of average-case SIS(Small Integer Solution) and ISIS(Inhomogeneous Small Integer Solution).It is also existential unforgeability under adaptive chosen-message attack in the random oracle.Compared with the schemes based on factoring or discrete log,the public and secret keys of our scheme are larger,but it requires only linear operation on small integers.
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.
Signcryption is a basic cryptographic primitive that simultaneously captures the functions of encryption and signature. To realize comprehensive information security against quantum computing attacks, lattice-based signcryption schemes have been successively proposed. However, the performance of signcryption schemes should be improved in the lattice setting. An efficient lattice-based signcryption scheme in the standard model is proposed in this paper. Under the ring learning with errors (RLWE) assumption and the ideal short integer solution (ISIS) assumption, the proposed signcryption scheme achieves indistinguishability against adaptive chosen ciphertext attacks (IND-CCA2) and existential unforgeability under an adaptive chosen-message attack (EUF-ACMA). Our scheme not only reduces the communication and computational overhead but also realizes a new design that combines the partitioning technique with the idea of tag-based key encapsulation. The performance analysis results show that our scheme is more efficient than previous lattice-based signcryption schemes in the standard model.