Comparative Analysis of Zero-Knowledge Proofs Technique using Quadratic Residuosity Problem

Abstract

Zero-knowledge proofs is a type of non-black box security technique and it is stated by the means of quadratic residuosity problem in this paper. We have used quadratic residuosity problem (QRP) for zero-knowledge proofs security system for the comparative analysis of this technique in comparison with discrete logarithm problem in cryptography. The upper bound of QRP with a prime modulus algorithm for quadratic residuosity problem is growing faster in comparison with discrete logarithm problem used by Henry. After that covariance between two different algorithms for different problems are calculated and obtained result is positive, which means random variables used for both functions are growing in same direction which reflect the fact, they are similar in behavior. Both functions are growing in same direction and our functional valued curve converge with Henry (Discrete Logarithm) functional valued curve at a point.