scholarly journals Constructing the 2-Element AGDS Protocol based on the Discrete Logarithm Problem

2021 ◽  
Vol 13 (04) ◽  
pp. 13-22
Author(s):  
Tuan Nguyen Kim ◽  
Duy Ho Ngoc ◽  
Nikolay A. Moldovyan
Keyword(s):  
Discrete Logarithm ◽  
Discrete Logarithm Problem ◽  
Group Signature ◽  
Signature Scheme ◽  
Fixed Size ◽  
Electronic Documents ◽  
Computational Difficulty

It is considered a group signature scheme in frame of which different sets of signers sign electronic documents with hidden signatures and the head of the signing group generates a group signature of fixed size. A new mechanism for imbedding the information about signers into a group signature is proposed. The method provides possibilities for reducing the signature size and to construct collective signature protocols for signing groups. New group signature and collective signature protocols based on the computational difficulty of discrete logarithm are proposed.

A Proxy Signature Based on the Difficulty of Solving Equations of Higher on Quaternion Ring

2014 ◽  
Vol 513-517 ◽  
pp. 1951-1954
Author(s):  
Hui Shao ◽  
Fan Zhang ◽  
Xiao Zhuan Yuan ◽  
Chuan Da Qi
Keyword(s):  
Digital Signature ◽  
Discrete Logarithm ◽  
Proxy Signature ◽  
Discrete Logarithm Problem ◽  
Signature Scheme ◽  
Multivariate Functions ◽  
Actual Application ◽  
Solving Equations ◽  
Computational Difficulty ◽  
High Degree

At present, all the applied schemes of the digital signature schemes based on the research of the factoring problem, discrete logarithm problem, and discrete logarithm problem on the elliptic curve cant meet the demand of actual application. This paper introduces the knowledge to the digital signature and studies the signature scheme based on the quaternion ring. The scheme introduces the multivariate functions of high degree to non-commutative quaternion ring, and its safety based on the computational difficulty to solve the the multivariate equations of high degree. The article applies this thought to proxy signature and designs a proxy signature scheme. Finally, it gives the safety analysis of the new scheme.

scholarly journals A New Method for Designing Post-Quantum Signature Schemes

2020 ◽  
pp. 747-754
Author(s):  
Minh Nguyen Hieu ◽  
◽  
Moldovyan Alexander Andreevich ◽  
Moldovyan Nikolay Andreevich ◽  
Canh Hoang Ngoc
Keyword(s):  
Digital Signature ◽  
Quantum Computer ◽  
Multiplicative Group ◽  
Discrete Logarithm ◽  
Quantum Signature ◽  
Discrete Logarithm Problem ◽  
New Method ◽  
Signature Scheme ◽  
Signature Schemes ◽  
Computational Difficulty

The current standards of the digital signature algorithms are based on computational difficulty of the discrete logarithm and factorization problems. Expected appearance in near future of the quantum computer that is able to solve in polynomial time each of the said computational puts forward the actual task of the development of the post-quantum signature algorithms that resist the attacks using the quantum computers. Recently, the signature schemes based on the hidden discrete logarithm problem set in finite non-commutative associative algebras had been proposed. The paper is devoted to a further development of this approach and introduces a new practical post-quantum signature scheme possessing small size of public key and signature. The main contribution of the paper is the developed new method for defining the hidden discrete logarithm problem that allows applying the finite commutative groups as algebraic support of the post-quantum digital signature schemes. The method uses idea of applying multipliers that mask the periodicity connected with the value of discrete logarithm of periodic functions set on the base of the public parameters of the signature scheme. The finite 4-dimensional commutative associative algebra the multiplicative group of which possesses 4-dimensional cyclicity is used as algebraic support of the developed signature scheme.

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.

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