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Jisuanji yingyong yanjiu

Concurrent signature scheme over braid groups

Zhang Xing-kai

Published Jan 1, 2010• 0 citations
OpenAlex

Abstract

To resist the quantum computing,this paper proposed a concurrent signature scheme over braid group on the difficulty of root extraction problem.The initial signer and the matching signer chose two keystones,respectively,which guaranteed the fairness.Analysis shows that before releasing the keystones,both signatures are ambiguous while upon release of the keystones,both signatures become binding to their true signers concurrently.

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To resist the quantum computing,this paper proposed a concurrent signature scheme over braid group on the difficulty of root extraction problem.The initial signer and the matching signer chose two keystones,respectively,which guaranteed the fairness.Analysis shows that before releasing the keystones,both signatures are ambiguous while upon release of the keystones,both signatures become binding to their true signers concurrently.
We propose a fair novel concurrent signature scheme. It resolves the existing problems in traditional concurrent signature schemes, that is initial signer (A) has some advantages over matching signer (B), such as A could show B's ambiguous signature and the keystone to a third party in private to demonstrate B's binding signature but B can not, or A could keep the keystone secret and B do not have power to force A to release it. In our scheme, the keystones were produced by both A and B, that is to say, the two participants in our scheme have equal positions, no one has any priority than the other, so our scheme can achieve the fairness of both sides.
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.
The concept of concurrent signatures was introduced by Chen, Kudla and Paterson in their seminal paper in Eurocrypt 2004 which allows two entities to produce two signatures in such a way that, the signer of each signature is ambiguous from any third party's point of view until the release of a secret, known as the keystone. Once the keystone is released, both signatures become binding to their respective signers concurrently. Later, a stronger notion called perfect concurrent signatures with two concrete schemes was proposed by Susilo, Mu and Zhang. In perfect concurrent signatures, although both signers are known to be trustworthy, the two signatures are still ambiguous to any third party. Unfortunately, Susilo et al.'s schemes are unfair. In this paper, we first show that in their schemes the initial signer can cheat the matching signer by carefully choosing some communication value and then propose fair perfect concurrent signature protocol to fix our attacks.
The concept of concurrent signatures was introduced by Chen et al. in Eurocrypt 2004 which allows two entities to produce two signatures in such a way that, the signer of each signature is ambiguous from any third party¿s point of view until the release of a secret, known as the keystone. Once the keystone is released, both signatures become binding to their respective signers concurrently. In the previous concurrent signature schemes, the roles of participants are asymmetrical, one party, which is called initial signer, needs to create the keystone fix and send the first ambiguous signature, the other party, which is called matching signer, responds to this initial signer by creating another ambiguous signature with the same keystone fix. This work mode may cause some unfairness. In this paper, we construct a perfect concurrent signature protocol for symmetric participants and prove its security. In our concept, the roles of participants are symmetrical. The keystone can not be decided by any participant and the two ambiguous signatures can be published in any order.
Three types of traditional hard problem could be resolved by Shor,Boneh and Lipton's quantum algorithms in po-lynomial time.By the braid group constructed a lot of mathematics difficulties were not an effective solution under the conditions of the quantum computer.It seemed that braid group was a kind of considerable considerable cryptography platform in the future.This paper proposed a new proxy blind signature scheme based on conjugate search problem and the p-th root finding problem,and the exchangeable of the group operation between the elements in the left subgroup and the right subgroup of a braid group.Through program analysis shows that the new scheme is effective and feasible.