A discrete logarithm implementation of perfect zero-knowledge blobs

1990 ◽  
Vol 2 (2) ◽  
pp. 63-76 ◽  
Author(s):  
Joan F. Boyar ◽  
Stuart A. Kurtz ◽  
Mark W. Krentel
Keyword(s):  
Discrete Logarithm ◽  
Zero Knowledge

scholarly journals A discrete logarithm blob for noninteractive XOR gates

1990 ◽  
Vol 19 (327) ◽  
Author(s):  
Joan Boyar ◽  
Ivan Bjerre Damgård
Keyword(s):  
Building Block ◽  
Discrete Logarithm ◽  
Zero Knowledge ◽  
Discrete Logarithms ◽  
Bit Commitment ◽  
Commitment Scheme

We present a bit commitment scheme based on discrete logarithms. Unlike earlier discrete log based schemes, our system allows non-interactive XORing and negation of bits contained in commitments. When used as a building block in zero-knowledge protocols, our scheme leads to protocols that are statistical (almost perfect) zero-knowledge, and where the prover is unable to break the system, unless he can find a secret discrete logarithm.

A perfect zero-knowledge proof system for a problem equivalent to the discrete logarithm

1993 ◽  
Vol 6 (2) ◽  
pp. 97-116 ◽  
Author(s):  
Oded Goldreich ◽  
Eyal Kushilevitz
Keyword(s):  
Discrete Logarithm ◽  
Proof System ◽  
Zero Knowledge ◽  
Zero Knowledge Proof

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.

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.

Sign in / Sign up

Export Citation Format

Share Document