Zero-knowledge proofs technique using integer factorization for analyzing robustness in cryptography

We have proved that zero-knowledge proofs technique using integer factorization problem has big-oh O(τ1/4)for factoring integers algorithm given by Pollard's rho in comparison with Henry for discrete logarithm problem that is τ+τ/lgτ. Also, we have positively presented covariance between our result and Henry which clearly implies the input variables used for both functions tend to show similar behavior.