scholarly journals POST-QUANTUM BLIND SIGNATURE PROTOCOL ON NON-COMMUTATIVE ALGEBRAS

2021 ◽  
Vol 37 (4) ◽  
pp. 495-509
Author(s):  
Minh N.H ◽  
Moldovyan D.N, et al.
Keyword(s):  
Finite Field ◽  
Discrete Logarithm ◽  
Blind Signature ◽  
Discrete Logarithm Problem ◽  
Signature Scheme ◽  
Associative Algebras ◽  
Basic Properties ◽  
Commutative Algebras ◽  
Quantum Blind Signature

A method for constructing a blind signature scheme based on a hidden discrete logarithm problem defined in finite non-commutative associative algebras is proposed. Blind signature protocols are constructed using four-dimensional and six-dimensional algebras defined over a ground finite field GF(p) and containing a global two-sided unit as an algebraic support. The basic properties of the used algebra, which determine the choice of protocol parameters, are described.

Structure and Analysis of Certificateless Proxy Blind Signature Scheme without Bilinear Pairing

2013 ◽  
Vol 734-737 ◽  
pp. 3194-3198
Author(s):  
Yi Wang
Keyword(s):  
Finite Field ◽  
Discrete Logarithm ◽  
Public Key Cryptography ◽  
Bilinear Pairing ◽  
Blind Signature ◽  
Discrete Logarithm Problem ◽  
Public Key ◽  
Signature Scheme ◽  
Proxy Blind Signature ◽  
Certificateless Public Key Cryptography

Combined with certificateless public key cryptography and proxy blind signature, an efficient certificateless proxy blind signature scheme is proposed. Its security is based on the discrete logarithm problem. Compared with the existed certificateless proxy blind signature scheme, because without bilinear pairing, it have higher efficiency. According to the different attacker and all kinds of attacks, the scheme is proved to be correct and security under the hardness of discrete logarithm problem in the finite field.

scholarly journals Proposed Developments of Blind Signature Scheme based on The Elliptic Curve Discrete Logarithm Problem

2013 ◽  
Vol 2 (1) ◽  
pp. 151-160
Author(s):  
E.H. El Kinani ◽  
Fatima Amounas
Keyword(s):  
Elliptic Curve ◽  
Elliptic Curve Cryptography ◽  
Discrete Logarithm ◽  
Mathematical Structure ◽  
Blind Signature ◽  
Discrete Logarithm Problem ◽  
Signature Scheme

In recent years, Elliptic Curve Cryptography (ECC) has attracted the attention of researchers due to its robust mathematical structure and highest security compared to other existing algorithm like RSA. Our main objective in this work was to provide a novel blind signature scheme based on ECC. The security of the proposed method results from the infeasibility to solve the discrete logarithm over an elliptic curve. In this paper we introduce a proposed to development the blind signature scheme with more complexity as compared to the existing schemes. Keyword: Cryptography, Blind Signature, Elliptic Curve, Blindness, Untraceability.DOI: 10.18495/comengapp.21.151160

scholarly journals Blind signature protocols based on hidden discrete logarithm problem

2020 ◽  
pp. 71-78
Author(s):  
Dmitry Moldovyan ◽  
Alexander Moldovyan ◽  
Denis Guryanov
Keyword(s):  
High Performance ◽  
Discrete Logarithm ◽  
Blind Signature ◽  
Discrete Logarithm Problem ◽  
Quantum Computers ◽  
Large Set ◽  
Associative Algebras ◽  
Different Types ◽  
Computational Difficulty ◽  
Quantum Digital Signature

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.

scholarly journals Improved lower bound for Diffie–Hellman problem using multiplicative group of a finite field as auxiliary group

2018 ◽  
Vol 12 (2) ◽  
pp. 101-118 ◽  
Author(s):  
Prabhat Kushwaha
Keyword(s):  
Lower Bound ◽  
Finite Field ◽  
Elliptic Curves ◽  
Multiplicative Group ◽  
Discrete Logarithm ◽  
Discrete Logarithm Problem ◽  
Reduction Algorithm ◽  
Practical Applications ◽  
Diffie Hellman ◽  
Estimate Lower

Abstract In 2004, Muzereau, Smart and Vercauteren [A. Muzereau, N. P. Smart and F. Vercauteren, The equivalence between the DHP and DLP for elliptic curves used in practical applications, LMS J. Comput. Math. 7 2004, 50–72] showed how to use a reduction algorithm of the discrete logarithm problem to Diffie–Hellman problem in order to estimate lower bound for the Diffie–Hellman problem on elliptic curves. They presented their estimates on various elliptic curves that are used in practical applications. In this paper, we show that a much tighter lower bound for the Diffie–Hellman problem on those curves can be achieved if one uses the multiplicative group of a finite field as auxiliary group. The improved lower bound estimates of the Diffie–Hellman problem on those recommended curves are also presented. Moreover, we have also extended our idea by presenting similar estimates of DHP on some more recommended curves which were not covered before. These estimates of DHP on these curves are currently the tightest which lead us towards the equivalence of the Diffie–Hellman problem and the discrete logarithm problem on these recommended elliptic curves.

scholarly journals Finding roots in with the successive resultants algorithm

2014 ◽  
Vol 17 (A) ◽  
pp. 203-217 ◽  
Author(s):  
Christophe Petit
Keyword(s):  
Finite Field ◽  
Elliptic Curve ◽  
Finite Fields ◽  
Coding Theory ◽  
Discrete Logarithm ◽  
Discrete Logarithm Problem ◽  
Polynomial Equations ◽  
Preliminary Results ◽  
Characteristic Case ◽  
Practical Security

AbstractThe problem of solving polynomial equations over finite fields has many applications in cryptography and coding theory. In this paper, we consider polynomial equations over a ‘large’ finite field with a ‘small’ characteristic. We introduce a new algorithm for solving this type of equations, called the successive resultants algorithm (SRA). SRA is radically different from previous algorithms for this problem, yet it is conceptually simple. A straightforward implementation using Magma was able to beat the built-in Roots function for some parameters. These preliminary results encourage a more detailed study of SRA and its applications. Moreover, we point out that an extension of SRA to the multivariate case would have an important impact on the practical security of the elliptic curve discrete logarithm problem in the small characteristic case.Supplementary materials are available with this article.

Cryptanalysis of a Batch Proxy Quantum Blind Signature Scheme

2014 ◽  
Vol 53 (9) ◽  
pp. 3109-3115 ◽  
Author(s):  
Xiao-Qiu Cai ◽  
Yu-Hui Zheng ◽  
Rui-Ling Zhang
Keyword(s):  
Blind Signature ◽  
Signature Scheme ◽  
Quantum Blind Signature

Batch proxy quantum blind signature scheme

2011 ◽  
Vol 56 (5) ◽  
pp. 1-9 ◽  
Author(s):  
JinJing Shi ◽  
RongHua Shi ◽  
Ying Guo ◽  
XiaoQi Peng ◽  
Ying Tang
Keyword(s):  
Blind Signature ◽  
Signature Scheme ◽  
Quantum Blind Signature

Efficient Convertible User Designating Confirmer Partially Blind Signature with Provable Security

2011 ◽  
Vol 282-283 ◽  
pp. 307-311
Author(s):  
Li Zhen Ma
Keyword(s):  
Provable Security ◽  
Discrete Logarithm ◽  
Random Oracle Model ◽  
Random Oracle ◽  
Blind Signature ◽  
Discrete Logarithm Problem ◽  
Public Key ◽  
Signature Schemes ◽  
Partially Blind Signature ◽  
Provably Secure

Any one who knows the signer’s public key can verify the validity of a given signature in partially blind signature schemes. This verifying universality may be used by cheats if the signed message is sensitive or personal. To solve this problem, a new convertible user designating confirmer partially blind signature, in which only the designated confirmer (designated by the user) and the user can verify and confirm the validity of given signatures and convert given signatures into publicly verifiable ones, is proposed. Compared with Huang et al.’s scheme, the signature size is shortened about 25% and the computation quantity is reduced about 36% in the proposed scheme. Under random oracle model and intractability of Discrete Logarithm Problem the proposed scheme is provably secure.

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