Journal of Cryptology

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

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

  • Jean-Sebastien CoronEmail author
  • Alexander MayEmail author


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.


Polynomial Time Deterministic Algorithm Small Root Prime Integer Lattice Reduction Algorithm 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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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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