Robust Comparative Analysis of Zero-Knowledge Proofs using Discrete Logarithm Problem

2020 ◽  
Author(s):  
Chitranjan Prasad Sah ◽  
Preeti Rani Gupta
Keyword(s):  
Comparative Analysis ◽  
Discrete Logarithm ◽  
Discrete Logarithm Problem ◽  
Zero Knowledge

scholarly journals CRYPTOGRAPHIC AUTHENTICATION PROTOCOL ZERO-KNOWLEDGE SECRET ON ELLIPTIC CURVES USING PUBLIC KEYS AND RANDOM MESSAGES

2019 ◽  
Vol 26 ◽  
pp. 22-28
Author(s):  
A.V. ONATSKIY ◽  
Keyword(s):  
Elliptic Curve ◽  
Elliptic Curves ◽  
Information Exchange ◽  
Discrete Logarithm ◽  
Security Protocol ◽  
Discrete Logarithm Problem ◽  
Cryptographic Protocol ◽  
Zero Knowledge ◽  
Public Keys ◽  
Zero Knowledge Proof

We propose a cryptographic protocol with zero-knowledge proof (ZKP) on elliptic curves (EC) using public keys and random messages, allowing to establish the truth of a statement not conveying any additional information about the statement itself. The cryptographic protocols based on zero-knowledge proof allow identification, key exchange and other cryptographic operations to be performed without leakage of sensitive information during the information exchange. The implementation of the cryptographic protocol of the zero-knowledge proof on the basis of the mathematical apparatus of elliptic curves allows to significantly reduce the size of the protocol parameters and increase its cryptographic strength (computational complexity of the breaking). The security of cryptosystems involving elliptic curves is based on the difficulty of solving the elliptic curve discrete logarithm problem. We determine the completeness and correctness of the protocol and give an example of the calculation is given. The cryptographic protocol was modeled in the High-Level Protocol Specification Language, the model validation and verification of the protocol were also performed. The software verification of the cryptographic protocol was performed using the software modules On the Fly Model Checker and Constraint Logic based Attack Searcher. In order to validate the cryptographic protocol resistance to intruder attacks, we used the Security Protocol Animator package for Automated Validation of Internet Security Protocols and Applications. The security of the proposed cryptographic protocol ZKP EC is based on the difficulty of solving the elliptic curve discrete logarithm problem). The recommended elliptical curves according to DSTU 4145-2002 may be used to implement such cryptographic protocol.

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 Cryptographic aspects of real hyperelliptic curves

2010 ◽  
Vol 47 (1) ◽  
pp. 31-65 ◽  
Author(s):  
Michael J. Jacobson ◽  
Renate Scheidler ◽  
Andreas Stein
Keyword(s):  
Hyperelliptic Curve ◽  
Discrete Logarithm ◽  
Mathematical Structure ◽  
Hyperelliptic Curves ◽  
Cryptographic Protocols ◽  
Discrete Logarithm Problem ◽  
Explicit Formulas ◽  
Genus 2

Abstract In this paper, we give an overview of cryptographic applications using real hyperelliptic curves. We review previously proposed cryptographic protocols and discuss the infrastructure of a real hyperelliptic curve, the mathematical structure underlying all these protocols. We then describe recent improvements to infrastructure arithmetic, including explicit formulas for divisor arithmetic in genus 2, and advances in solving the infrastructure discrete logarithm problem, whose presumed intractability is the basis of security for the related cryptographic protocols.

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