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Ideal Lattice Based Justifiable Secure Digital Signature Scheme

FENG Chaoyi,ZHAO Yiming

Published May 1, 2017• 0 citations
Publisher

Abstract

In order to guarantee the security of signature scheme under quantum attack,most of the existing lattice-based signature schemes are based on the difficulty hypothesis under general lattice rather than ideal lattice,and it caused lower efficiency of these schemes.To overcome the problem,a new digital signature scheme based on ideal lattice is proposed.By reducing the problem to the PLWE,it is proved that an attacker can not forge a legitimate signature for a new message even if he gets multiple existing messages and the corresponding signature.Analysis result shows that the signature length and the key length of the scheme are reduced by O(n),compared with the existing digital signature scheme based on general lattice.

DOI
10.3969/j.issn.1000-3428.2017.05.017

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In order to guarantee the security of signature scheme under quantum attack,most of the existing lattice-based signature schemes are based on the difficulty hypothesis under general lattice rather than ideal lattice,and it caused lower efficiency of these schemes.To overcome the problem,a new digital signature scheme based on ideal lattice is proposed.By reducing the problem to the PLWE,it is proved that an attacker can not forge a legitimate signature for a new message even if he gets multiple existing messages and the corresponding signature.Analysis result shows that the signature length and the key length of the scheme are reduced by O(n),compared with the existing digital signature scheme based on general lattice.
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.
We propose a variant version of ring learning with errors (R-LWE) assumption. Under the modified slightly assumption which is reducible to the worst-case problems on ideal lattice, we present a construction of digital signatures. So the scheme is provably secure based on the hardness of lattice problems (such as approximating the length of the shortest vector within a fixed poly(n) factor). Compared with some existing typical lattice-based signature schemes, the construction enjoys many advantages, including simple and efficient key generation algorithm, signing algorithm and verification algorithm to improve the efficiency of the scheme as well as to reduce the overhead. The sizes of the secret and public keys and the signature are almost linear O(n log n) (up to poly-logarithmic factors) in the dimension n of the lattice.
Traditional digital signatures are often publicly verifiable, and in certain applications with privacy preservation requirements, the signer does not want the sensitive information it signed to be redelivered by a dishonest verifier.Aiming at the problem that traditional chameleon signatures (CS) cannot resist quantum computer attacks, this paper proposes a lattice-based authentication CS scheme.Based on the analysis of the lattice difficulty problem and the security vulnerability of the CS scheme, it is pointed out that it does not satisfy the third-party unforgeability and the signer rejectability, and a new lattice-based identity CS scheme is established, which is verified under the stochastic predicate machine model, and the storage and transmission efficiency of the scheme is analyzed.The results show that the newly designed identity-based CS scheme on the lattice can effectively resist quantum computer attacks, can sign messages of arbitrary length, and possesses more lightweight storage and transmission efficiency.The optimized chameleon signature scheme has better security and also provides a new solution for digital signatures to resist quantum computer attacks.
Fair exchange is essential in E-commerce, and concurrent signature realizes the fair exchange of digital signatures with removing the requirement of a trusted third party. Multi-party concurrent signature is an extension to the multi-user scenario. The security of existing multi-party concurrent signatures is mostly based on traditional hard problems that could be solved efficiently with quantum algorithms in a post-quantum world. Meanwhile, the lattice-based cryptography is considered to be resistant to quantum attack. Wang et al. proposed a lattice-based multi-party concurrent signature. We give the analysis of their proposed signature scheme and find that it is not secure since an inside adversary can forge the signature. Moreover, the initial signer can produce any signatures, instead of a signature on the original messages, if he is malicious.
The security of digital signatures depends significantly on the signature key. Therefore, to reduce the impact of leaked keys upon existing signatures and subsequent ones, a digital signature scheme with strong forward security could be an effective solution. Most existing strong forward-secure digital signature schemes rely on traditional cryptosystems, which cannot effectively resist quantum attacks. By introducing lattice-based delegation technology into the key-iteration process, a two-direction and lattice-based key-iteration algorithm with strong forward security is proposed. In the proposed algorithm, a unique key pair is assigned to the signer in every period. Based on the proposed algorithm, a strong forward-secure signature scheme is further put forward, which achieves resistance to quantum attacks. Performance analysis shows that under the security assumption of the SIS problem on the lattice, the proposed strong forward-secure signature scheme is existentially unforgeable under the random oracle model. Ultimately, based on the proposed strong forward-secure signature scheme, a remote identity-authentication scheme that is resistant to quantum attacks is proposed, ensuring post-quantum security in the user-authentication process.
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.