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

Robustness features are essential for any black-box or non-black box security mechanism in cryptography. Zero-knowledge proofs is an example of non-black box security mechanism used in cryptography. In this paper, we have explored and analyzed zero-knowledge proofs using discrete logarithm problem and compared it with integer factoring problem to check its robustness and compatibility for higher security in cryptography. The upper bound of Pollard's rho algorithm for discrete logarithm is growing faster in comparison with Pollard's rho factoring algorithm. The covariance between asymptotic notations of two different algorithms for zero-knowledge proofs are computed and positive covariance result is obtained, which clearly shows that random variants used for both algorithms are growing in same direction and have similar behavior. The functional value line segment of Pollard's rho algorithm for discrete logarithm converges with the functional value line segment of Pollard's rho factoring algorithm at a point.