Journal of Cryptology

, Volume 20, Issue 1, pp 39–50 | Cite as

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



We address one of the most fundamental problems concerning the RSA cryptosystem: does the knowledge of the RSA public and secret key pair (e,d) yield the factorization of N = pq in polynomial time? It is well known that there is a probabilistic polynomial-time algorithm that on input (N,e,d) outputs the factors p and q. We present the first deterministic polynomial-time algorithm that factors N given (e,d) provided that e,d < φ(N). Our approach is an application of Coppersmith's technique for finding small roots of univariate modular polynomials.


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Copyright information

© International Association for Cryptologic Research 2006

Authors and Affiliations

  1. 1.University of Luxembourg, 162a avenue de la FaiencerieL-1511Luxembourg
  2. 2.Department of Computer Science, TU Darmstadt, 64289DarmstadtGermany

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