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International Conference on Computer Science and Application Engineering (CSAE)

Lattice-based Concurrent Signatures in the Standard Model

LI Bao-hong, Hongping Zhao, Jiacheng Li

Published Oct 15, 2020• 1 citation
Publisher

Abstract

We present a lattice-based concurrent signature construction as a post-quantum solution to fair exchange of digital signatures. Our construction has the following two desirable features: (1) it is adaptively secure in the standard model, that is, its security does not rely on the random oracle assumption, and (2) it achieves anonymity, a stronger security notion than ambiguity. That is, before the release of the keystone, from a third party's point of view, a signature in our construction could be generated by anyone, not just limited to two parties involved in the exchange. We obtain these results by applying a novel idea to the lattice-based signatures due to Boyen.

DOI
10.1145/3424978.3425018

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We present a lattice-based concurrent signature construction as a post-quantum solution to fair exchange of digital signatures. Our construction has the following two desirable features: (1) it is adaptively secure in the standard model, that is, its security does not rely on the random oracle assumption, and (2) it achieves anonymity, a stronger security notion than ambiguity. That is, before the release of the keystone, from a third party's point of view, a signature in our construction could be generated by anyone, not just limited to two parties involved in the exchange. We obtain these results by applying a novel idea to the lattice-based signatures due to Boyen.
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.
When using digital signatures, we need to deal with the problem of fairness of information exchange. To solve this problem, Chen, etc. introduced a new conception which is named concurrent signatures in Eurocrypt'04. Using concurrent signatures scheme, two entities in the scheme can generate two ambiguous signatures until one of the entities releases additional information which is called keystone. After the keystone is released, the two ambiguous signatures will be bound to their real signers at the same time. In order to provide a method to solve the fairness problem of quantum digital signatures, we propose a new quantum concurrent signature scheme. The scheme we proposed does not use a trusted third party in a quantum computing environment, and has such advantages as no need to conduct complex quantum operations and easy to implement by a quantum circuit. Quantum concurrent signature improves the theory of quantum cryptography, and it also provides broad prospects for the specific applications of quantum cryptography.
Concurrent signatures scheme is an effective way to solve the problem of fair exchange without the help of any trusted third party. Until now, all concurrent signatures are based on traditional cryptosystems, but the emergence of quantum computing poses a severe threat to the security of classic public–key cryptosystems. More and more attentions are being paid to lattice–based cryptosystems, which is one of the candidate cryptosystems against the attacks from quantum computing. In this paper, we present a new formal model of multi–party concurrent signatures scheme and a lattice–based multi–party concurrent signatures scheme. The scheme has comparative advantages in both efficiency and security over the existing concurrent signatures schemes based on traditional cryptosystem. In particular, our scheme is constructed based on constant–size ring signatures, and thus we have solved the open problem: how to construct a multi–party concurrent signatures scheme based on constant–size ring signatures, which was proposed by Tonien et al. (2006).
Traceable signatures (Kiayas et al., 2004) is an anonymous digital signature system that extends the tracing power of opening authority in group signatures. There are many known constructions of traceable signatures but all are based on number-theoretical/pairing assumptions. For such reason, they may not be secure in the presence of quantum computers. This work revisits the notion of traceable signatures and presents a lattice-based construction provably secure in the quantum random oracle model (QROM).
Concurrent Signatures scheme is an effective way to solve the problem of fair exchange without the help of any trusted third party, it has the advantage of efficiency. Until now, all concurrent signatures are based on traditional cryptosystems, but the emergence of quantum computing poses a severe threat to the security of classic public-key cryptosystems. More and more attentions are being paid to lattice-based cryptosystems, which is one of the candidate cryptosystems against the attacks from quantum computing. In this paper we present a new formal model of multi-party concurrent signatures scheme which is constructed based on constant-size ring signatures, and a lattice-based multi-party concurrent signatures scheme. The scheme has comparative advantages in both efficiency and security over the existing concurrent signatures schemes based on traditional cryptosystems. In particular, our scheme is constructed based on constant-size ring signatures, and thus we have solved the open problem: how to construct a multi-party concurrent signatures scheme based on constant-size ring signatures, which was proposed by Dongvu Tonien, Willy Susilo and Reihaneh Safavi-Naini in 2006.
By introducing signcryption technology into concurrent signature,a signcryption-based concurrent signature scheme was presented,which was proven to have the existential unforgeability against adaptive chosen messages attacks under the random oracle model,Based on this scheme,a fair exchange protocol was proposed,which could be used to exchange digital goods.This protocol did not need secure communications channel,in which two parties generate sym-metrical ambiguous signatures and individual keystones were released by themselves,which ensured the properties of confidentiality,ambiguousness and fairness,which made our protocol could be used in e-commerce payment,e-contract signing,mail authentication,etc.