Revisiting the Polynomial-Time Equivalence of Computing the CRT-RSA Secret Key and Factoring

The Rivest–Shamir–Adleman (RSA) cryptosystem is currently the most influential and commonly used algorithm in public-key cryptography. Whether security of RSA equivalent to intractability integer factorization problem an interesting issue mathematics Coron May solved above fundamental proved polynomial-time equivalence computing secret key factoring. They demonstrated that modulus N=pq can be factored polynomial time when given information (N,e,d). CRT-RSA variant a fast technical implementation using Chinese Remainder Theorem (CRT), which aims speed up decryption process. We focus on factoring this paper. With help latest partial exposure attack CRT-RSA, we demonstrate there exists outputting for edp,edq<N3/2 (N,e,dp,dq). apply Coppersmith’s lattice-based method as basic mathematical tool finding small root solutions modular equations. Furthermore, provide validation experiments illustrate correctness algorithm, show its by concrete numerical examples.