Robustness of Zero-Knowledge Proofs using RSA Problem

Abstract

The Robustness of any cryptographic technique gives us an idea about how that technique is asymptotically secure (asymptotic security), efficient, and can defeat different types of attacks on it. In this research, analysis and study have been done about how non-black-box technique called zero-knowledge proofs, can be used with RSA (Rivest, Shamir, Adleman) problem. One of the better algorithms for factoring needed by the RSA problem is general number field sieve factoring. The efficiency of general number field sieve factoring for RSA problem and discrete logarithm problem is analyzed and compared with each other; covariance between their asymptotic functions is calculated which clearly shows that they are strongly correlated with each other.