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International Conference on Computational Intelligence and Security (CIS)

Lattice-Based Proxy Signature

Yali Jiang, Fanyu Kong, Xiuling Ju

Published Dec 1, 2010• 15 citations
Publisher

Abstract

Those existing proxy signature schemes are mainly based on the assumed hardness of Big Integer Factoring problem and Discrete Logarithm problem. So they can't resist quantum attacks. This proxy signature scheme is based on the assumed hardness of some lattice problem, which can resist quantum attack. The key pair of proxy signer was generated using basis delegation technology. Combined with GPV basic signature scheme, the proxy signature scheme was constructed. This scheme is satisfied with all the security property of proxy signature schemes. Based on this scheme, variant lattice-based proxy signature schemes will be designed, such as blind proxy signature, multi-grade proxy signature, and identity-based proxy signature etc.

DOI
10.1109/cis.2010.88

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Those existing proxy signature schemes are mainly based on the assumed hardness of Big Integer Factoring problem and Discrete Logarithm problem. So they can't resist quantum attacks. This proxy signature scheme is based on the assumed hardness of some lattice problem, which can resist quantum attack. The key pair of proxy signer was generated using basis delegation technology. Combined with GPV basic signature scheme, the proxy signature scheme was constructed. This scheme is satisfied with all the security property of proxy signature schemes. Based on this scheme, variant lattice-based proxy signature schemes will be designed, such as blind proxy signature, multi-grade proxy signature, and identity-based proxy signature etc.
In a proxy signature scheme, an original signer delegates his/her signing capability to a proxy signer and then the proxy signer can sign messages on behalf of the original signer. The security of many proxy signature schemes that have been proposed depends, either directly or indirectly, on either the difficulty of big integers factoring problem or the difficulty of finding discrete logarithm in a finite group. These types of schemes cannot resist quantum attacks. In this paper, we propose a new lattice-based proxy signature scheme which can resist quantum attacks. The proposed scheme is based on the GGH-signature scheme and also satisfies all the security requirements of proxy signature schemes.
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.
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.
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.
Most of the provably-secure proxy signature schemes rely on the average-case hardness problems such as the integer factorization problems and the discrete logarithm problems. Therefore, those schemes are insecure to quantum analysis algorithms, since there exist quantum algorithms efficiently solving the factorization and logarithm problems. To make secure proxy signature schemes against quantum analysis, some lattice-based proxy signature schemes are suggested. However, none of the suggested lattice-based proxy signature schemes is proxy-protected in the adaptive security model. In the paper, we propose a provably-secure ID-based proxy signature scheme based on the lattice problems. Our scheme is proxy-protected in the adaptive security model.
Proxy signature plays an important role in distributed systems, mobile agent applications, distributed shared object systems, global distribution networks and mobile communications etc., since it allows the original signer to delegate another proxy signer to sign the message instead of himself. However, the proxy signature schemes constructed on the number theory cannot resist quantum computers attack and depend on the public key infrastructure. To mitigate these problems, the alternative schemes are Identity-based proxy signature constructed on lattice. In this paper, an identity-based proxy signature scheme based on Number theorem research unit (NTRU) lattice is proposed and proven secure in the random oracle. Compared with the other existing identity-based proxy signature schemes, the proposed scheme outperforms them in terms of original signer's signature size and signing key size and proxy signer's signing key size.