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

  • Authors:
  • Jean-Sebastien Coron;Alexander May

  • Affiliations:
  • University of Luxembourg, 162a avenue de la Faiencerie, L-1511, Luxembourg;Department of Computer Science, TU Darmstadt, 64289, Darmstadt, Germany

  • Venue:
  • Journal of Cryptology
  • Year:
  • 2007

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Abstract

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