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International Conference on Intelligent Information Hiding and Multimedia Signal Processing (IIH-MSP)

An Efficient Lattice-Based Proxy Signature Scheme without Trapdoor

Chunli Yang, Peigang Qiu, Shihui Zheng, Licheng Wang

Published Sep 1, 2015• 9 citations
Publisher

Abstract

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.

DOI
10.1109/iih-msp.2015.90

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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.
With the advancement of quantum computing, the utilization of quantum algorithms such as Shor’s algorithm enables the efficient resolution of problems that are intractable in classical computing paradigms, posing a significant threat to traditional signature schemes. Lattice-based cryptography is considered one of the most promising post-quantum cryptographic algorithms due to its computational advantages and potential resistance to quantum attacks. Proxy signature is an authorization mechanism that allows the original signer to delegate the signing power to a proxy. The security of existing proxy signature schemes is mostly based on classical hard problems, which cannot guarantee security under quantum attacks. Therefore, this paper combines lattice-based cryptography with proxy signatures to propose a new lattice-based proxy signature scheme (NLBPS). NLBPS constructs signatures using lattice-based trapdoor sampling algorithms and preimage sampling algorithms. Comparative analysis shows that the proposed scheme has relatively smaller key and signature sizes compared to some existing lattice-based proxy signature schemes, and it also offers a certain improvement in computational efficiency.
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.
In response to the issues of low security and computational efficiency in current lattice-based proxy blind signature systems, a novel identity-based proxy blind signature scheme utilizing lattices is proposed. This scheme integrates the user's identity information through matrix accumulation operations to serve as the verification public key, simplifying the identity validation process and strengthening both security and privacy measures. The user's private key as well as the proxy signing key are produced through the extended algorithm of the left sampling algorithm, while the rejection sampling algorithm is employed to produce the proxy blind signature. These enhance the space utilisation of keys and signatures. Moreover, the scheme's security is reducible to solving the small integer solution problem, thereby attaining resilience against one-more unforgeability under the adaptive chosen-message attacks within the random oracle model. Compared to other schemes, our scheme features smaller key and signature sizes, resulting in greater efficiency.
The existing lattice-based signcryption schemes are based on trapdoor generation algorithm and preimage sample algorithm. However, both algorithms are complex, require a lot of time to run, and affect the efficiency of latticed-based signcryption schemes deeply. To solve this problem, the first lattice-based signcryption scheme without trapdoor generation algorithm and preimage sample algorithm is proposed, with the help of the technique of lattice signatures without trapdoors and the associated signature compression technique, as well as the encryption method based on the learning with errors assumption. The scheme achieves indistinguishability against adaptive chosen ciphertext attacks under the learning with errors assumption. It also achieves existential unforgeability against adaptive chosen message attacks under the small integer solution assumption. The proposed scheme is not only quantum resistant, but also efficient.
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.