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Forward Secure Proxy Signature Scheme over NTRU Lattice

YE Qing, YANG Xiaomeng, ZHAO Zongqu, ZHANG Jing

Published Nov 1, 2019• 0 citations
Publisher

Abstract

Most existing forward secure proxy signature schemes are constructed based on traditional number theory problems,such as large integer decomposition,discrete logarithm and bilinear pairs,and they are easy to be cracked in a quantum computing environment.In order to deal with the threat of quantum computing environment and reduce the risk of secret key leakage in proxy signature,an identity-based forward secure proxy signature scheme with NTRU lattice is constructed.Introduce forward secure features into the proxy signature over the lattice.Under the random prediction model,the security of the program is converted to the intractability of SIS,and a detailed efficiency analysis is also given.Analysis results show that the scheme realizes forward secrecy and strong non-repudiation,and it is verifiable and strongly identifiable.The computing efficiency is also improved as a result of the shortened signature key of the proxy signer,and shortened signature and signature key of the original signer.

DOI
10.19678/j.issn.1000-3428.0052811

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Most existing forward secure proxy signature schemes are constructed based on traditional number theory problems,such as large integer decomposition,discrete logarithm and bilinear pairs,and they are easy to be cracked in a quantum computing environment.In order to deal with the threat of quantum computing environment and reduce the risk of secret key leakage in proxy signature,an identity-based forward secure proxy signature scheme with NTRU lattice is constructed.Introduce forward secure features into the proxy signature over the lattice.Under the random prediction model,the security of the program is converted to the intractability of SIS,and a detailed efficiency analysis is also given.Analysis results show that the scheme realizes forward secrecy and strong non-repudiation,and it is verifiable and strongly identifiable.The computing efficiency is also improved as a result of the shortened signature key of the proxy signer,and shortened signature and signature key of the original signer.
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.
Summary Proxy signature scheme is an important cryptographic primitive, for an entity can delegate his signing right to another entity. Although identity‐based proxy signature schemes based on conventional number‐theoretic problems have been proposed for a long time, the researchers have paid less attention to lattice‐based proxy signature schemes that can resist quantum attack. In this paper, we first propose an identity‐based proxy signature scheme over Number Theory Research Unit (NTRU)‐lattice. We proved that the proposed paradigm is secure under the hardness of the γ‐shortest vector problem on the NTRU lattice in random oracle model; furthermore, the comparison with some existing schemes shows our scheme is more efficient in terms of proxy signature secret key size, proxy signature size, and computation complexity. As the elemental problem of the proposed scheme is difficult even for quantum computation model, our scheme can work well in quantum age.
With the use of a large number of mobile devices, the problem of key leakage becomes more and more serious. In view of the excellent characteristics of lattice cipher and forward-secure digital signature scheme, the construction of identity-based forward-secure digital signature based on lattice technology has become a research hotspot. However, the identity-based forward secure digital signature scheme on the existing grid has the disadvantage of excessive signature length. This paper uses the technique (without trapdoors) of Lyubashevsky and extended Samplepre, an efficient identity-based forward secure signature scheme from lattice is proposed. Its security is based on the Small Integer Solution (SIS) difficulty assumption, and the strong non-forgery of the signature scheme is achieved. Low computing overhead; The analysis results show that, compared with the existing schemes, the key and signature are smaller in size, more efficient in computing, able to resist quantum attacks, and more practical.
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.
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.
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.