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Journal of Hunan University

Lattice-based Proxy Signature Scheme

Mingwu Zhang

Published Jan 1, 2011• 7 citations
OpenAlex

Abstract

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.

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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.

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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.

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arXiv:1405.3177•International Journal of High Performance Computing and Networking•Jan 1, 2018•15 citations
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.
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.
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.
Lattice-based proxy signature is a kind of signature that can resist the known quantum attack and a special digital signature which has the proxy functionality. So far, as far as I know, all lattice-based proxy signatures that use the "hash-and-sign" method of GPV08 signature are low efficient due to the time-consuming preimage sampleable algorithm. Based on the rejection sampling technique of Lyu12 signature, we proposed an efficient lattice-based proxy signature scheme without trapdoor, and the formal security proof of existentially unforgeable is given in random oracle model. In addition, the length of keys and signature in our scheme are shorter than all existing lattice-based proxy signature schemes, and the computations are also small.
Currently, most of the identity-based proxy signature schemes are based on large integer factorization and discrete logarithm which are insecure in quantum setting. To this problem, we propose a provably-secure identity-based proxy signature scheme over lattice, which uses preimage sampling technology and lattice basis delegation algorithm in fixed dimension. The proposed scheme was proved to satisfy strong unforgeability against selective identity attacks based on the hardness of the small integer solution (SIS) problem in the standard model. And compared with the existing identity-based proxy signature scheme from lattices, our scheme is more secure under the same efficiency.
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.
On the basis of the signatures scheme without trapdoors from lattice, which was proposed by Vadim Lyubashevsky in 2012, we present a new ring signature scheme from lattice. The proposed ring signature scheme is an extension of the signatures scheme without trapdoors. We prove that our scheme is strongly unforgeable against adaptive chosen message in the random oracle model, and prove that the security of our scheme can be reduced to the hardness of the small integer solution (SIS) problem by rejection samplings. Compared with the existing lattice-based ring signature schemes, our new scheme is more efficient and with shorter signature length.