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Jisuanji yingyong yanjiu

Proxy blind signature scheme based on braid group

Xiufeng Zhao

Published Jan 1, 2010• 1 citation
OpenAlex

Abstract

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.

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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.
Shor,Boneh,Liptonon et al. present some remarkable quantum algorithms which can solve integer factoring problem, discrete logarithm problem and discrete logarithm problem on elliptic curves in quantum polynomial time. These quantum algorithms are great challenges to classical public key cryptographies based on the above-described hard problems. It seems that braid group is a kind of considerable public key cryptography platform, but current key agreement protocols, such as AAG,AAFG and BDH, all have different degrees of security weaknesses.This paper takes advantage of random braids and non-conjugate transformations to present an improved braid key agreement protocol related to AAG and AAFG, which can make the two communication parties securely share a common key over any insecure channel. This protocol can resists current length-based attacks, linear representation attacks and other conjugacy search attacks.
The rapid development of quantum computing brings great challenges to public key cryptosystems.The braid group,which is non-commutative,provides a new platform of constructing cryptographic protocols.A convertible authenticated encryption scheme over braid group is proposed on the difficulty of conjugacy search problem and multiple conjugacy problem,in which only the designated receiver can recover and authenticate the message,when the sender repudiates the signature,the receiver can prove the dishonesty of the sender by converting the signature to an ordinary one without the cooperating of the sender.As for the resistance against quantum attacks,the proposed scheme has advantage over the schemes based on commutative algebraic structures.
Most of the existing blind proxy re-signature schemes are designed based on the traditional public key cryptosystems, whose security relies on the hardness of big integer factoring, discrete logarithm, elliptic curve discrete logarithm, and so on. However, these problems will be unsecure when facing the attack of quantum computers. Motivated by these concerns, we proposed a blind proxy re-signature scheme based on the problem of isomorphisms of polynomials, which can resist quantum attack, and gave its security proof under the random oracle model. In the proposed scheme, the message can be kept blind by using the hash function, and the delegatee's identity can be kept anonymous by using the problem of isomorphisms of polynomials. Compared with the existing schemes, the new scheme has more secure properties, such as quantum resistance, high efficiency, message blindness, and delegatee anonymity. It is concluded that the proposed scheme has a good application prospect in the future quantum computing environment with low-power hardware.
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.
Introduction: The progress in the development of quantum computing has raised the problem of constructing post-quantum two-key cryptographic algorithms and protocols, i.e. crypto schemes resistant to attacks from quantum computers. Based on the hidden discrete logarithm problem, some practical post-quantum digital signature schemes have been developed. The next step could be the development of post-quantum blind signature protocols. Purpose: To develop blind signature protocols based on the computational difficulty of the hidden discrete logarithm problem. Method: The use of blinding factors introduced by the client during the blind signature protocol when the parameters necessary for the blind signature formation are passed to the signatory. Results: It has been proposed to use blinding multipliers of two different types: left-sided and right-sided ones. With them, you can develop blind signature protocols on the base of schemes with a verification equation defined in non-commutative algebraic structures. New blind signature protocols have been developed, based on the computational difficulty of the hidden discrete logarithm problem. As the algebraic carrier for the developed protocols, finite non-commutative associative algebras of two types are used: 1) those with a global two-sided unit, and 2) those with a large set of global left units. Practical relevance: The proposed protocols have a high performance and can be successfully implemented either in software or in hardware.