Improvement of digital signature with message recovery and its variants based on elliptic curve discrete logarithm problem

2004 ◽  
Vol 27 (1) ◽  
pp. 61-69 ◽  
Author(s):  
Zuhua Shao
Keyword(s):  
Elliptic Curve ◽  
Digital Signature ◽  
Discrete Logarithm ◽  
Discrete Logarithm Problem ◽  
Message Recovery

A Protocol for Digital Signature Based on the Elliptic Curve Discrete Logarithm Problem

2008 ◽  
Vol 8 (10) ◽  
pp. 1919-1925 ◽  
Author(s):  
Morteza Nikooghada ◽  
Mohammad Reza Bonyadi ◽  
Ehsan Malekian ◽  
Ali Zakerolhos
Keyword(s):  
Elliptic Curve ◽  
Digital Signature ◽  
Discrete Logarithm ◽  
Discrete Logarithm Problem

scholarly journals Collective Signature Protocols for Signing Groups based on Problem of Finding Roots Modulo Large Prime Number

2021 ◽  
Vol 13 (04) ◽  
pp. 59-69
Author(s):  
Tuan Nguyen Kim ◽  
Duy Ho Ngoc ◽  
Nikolay A. Moldovyan
Keyword(s):  
Elliptic Curve ◽  
Prime Number ◽  
Digital Signature ◽  
Discrete Logarithm ◽  
Discrete Logarithm Problem ◽  
Public Key ◽  
Prime Factorization ◽  
Factorization Problem ◽  
Hybrid Combination ◽  
Different Types

Generally, digital signature algorithms are based on a single difficult computational problem like prime factorization problem, discrete logarithm problem, elliptic curve problem. There are also many other algorithms which are based on the hybrid combination of prime factorization problem and discrete logarithm problem. Both are true for different types of digital signatures like single digital signature, group digital signature, collective digital signature etc. In this paper we propose collective signature protocols for signing groups based on difficulty of problem of finding roots modulo large prime number. The proposed collective signatures protocols have significant merits one of which is connected with possibility of their practical using on the base of the existing public key infrastructures.

PERSPECTIVES OF ELLIPTICAL CRYPTOGRAPHY TO ENSURE THE INTEGRITY AND CONFIDENTIALITY OF INFORMATION

2019 ◽  
Author(s):  
Anna ILYENKO ◽  
Sergii ILYENKO ◽  
Yana MASUR
Keyword(s):  
Information Systems ◽  
Elliptic Curve ◽  
Elliptic Curves ◽  
Finite Fields ◽  
Computational Efficiency ◽  
Digital Signature ◽  
Discrete Logarithm ◽  
Algebraic Groups ◽  
Schnorr Signature ◽  
Stability Of Algorithms

In this article, the main problems underlying the current asymmetric crypto algorithms for the formation and verification of electronic-digital signature are considered: problems of factorization of large integers and problems of discrete logarithm. It is noted that for the second problem, it is possible to use algebraic groups of points other than finite fields. The group of points of the elliptical curve, which satisfies all set requirements, looked attractive on this side. Aspects of the application of elliptic curves in cryptography and the possibilities offered by these algebraic groups in terms of computational efficiency and crypto-stability of algorithms were also considered. Information systems using elliptic curves, the keys have a shorter length than the algorithms above the finite fields. Theoretical directions of improvement of procedure of formation and verification of electronic-digital signature with the possibility of ensuring the integrity and confidentiality of information were considered. The proposed method is based on the Schnorr signature algorithm, which allows data to be recovered directly from the signature itself, similarly to RSA-like signature systems, and the amount of recoverable information is variable depending on the information message. As a result, the length of the signature itself, which is equal to the sum of the length of the end field over which the elliptic curve is determined, and the artificial excess redundancy provided to the hidden message was achieved.

scholarly journals On the first fall degree of summation polynomials

2019 ◽  
Vol 13 (3-4) ◽  
pp. 229-237
Author(s):  
Stavros Kousidis ◽  
Andreas Wiemers
Keyword(s):  
Elliptic Curve ◽  
Gröbner Basis ◽  
Discrete Logarithm ◽  
Polynomial Systems ◽  
Discrete Logarithm Problem ◽  
Grobner Basis ◽  
Weil Descent ◽  
Degree Bound

Abstract We improve on the first fall degree bound of polynomial systems that arise from a Weil descent along Semaev’s summation polynomials relevant to the solution of the Elliptic Curve Discrete Logarithm Problem via Gröbner basis algorithms.

scholarly journals Partial Lifting and the Elliptic Curve Discrete Logarithm Problem

Algorithmica ◽  
2006 ◽  
Vol 46 (1) ◽  
pp. 59-68 ◽  
Author(s):  
Qi Cheng ◽  
Ming-Deh Huang
Keyword(s):  
Elliptic Curve ◽  
Discrete Logarithm ◽  
Discrete Logarithm Problem

Digital signature with message recovery based on factoring and discrete logarithm

2015 ◽  
Vol 62 (3) ◽  
pp. 415-423 ◽  
Author(s):  
Min-Shiang Hwang ◽  
Shih-Ming Chen ◽  
Chi-Yu Liu
Keyword(s):  
Digital Signature ◽  
Discrete Logarithm ◽  
Message Recovery
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