Robustness Analysis of Zero-Knowledge Proofs Technique using Subset Sum Problem

Abstract

In this paper, security mechanism called zero knowledge proofs has been defined using subset sum problem. We have used subset sum problem for robustness analysis of zero-knowledge proofs technique in cryptography. The upper bound of subset sum problem given by meet-in-the-middle algorithm is more efficient than Nïve algorithm, so we have used meet-in-the-middle algorithm for analyzing robustness in comparison with discrete logarithm problem used by Henry. Also, we have computed covariance between asymptotic notations of meet-in-the-middle and the discrete logarithm problem is employed in the technique of zero knowledge proofs which is positive. Positive covariance between them shows that relationship between input variants used by both functions is similar in behavior. Both functions are growing in same direction and our used function (meet-in-the-middle) is growing faster than Henry (Discrete Logarithm).