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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 provided that e, d < #(N ). Our approach is an application of Coppersmith's technique for finding... (Update)
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0.5: Deterministic Polynomial Time Equivalence of Computing the RSA.. - Coron, May (2004) (Correct)
0.2: New Partial Key Exposure Attacks on RSA - Blömer, May (2003) (Correct)
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BibTeX entry: (Update)
@misc{ coron-deterministic,
author = "Jean-Sébastien Coron and Alexander May",
title = "Deterministic Polynomial Time Equivalence of Computing the RSA Secret Key
and Factoring",
url = "citeseer.ist.psu.edu/article/coron04deterministic.html" }
Citations (may not include all citations):1529 A Method for Obtaining Digital Signatures and Public-Key Cry.. - Rivest, Shamir et al. - 1978
103 Factoring polynomials with rational coe#cients (context) - Lenstra, Lenstra et al. - 1982
92 Riemann's hypothesis and tests for primality (context) - Miller - 1975
12 Finding small roots of univariate modular equations revisite.. (context) - Howgrave-Graham - 1997
12 Cryptanalysis of the RSA Schemes with Short Secret Exponent .. - Durfee, Nguyen - 2000
10 Small solutions to polynomial equations and low exponent vul.. (context) - Coppersmith - 1997
4 Computing the RSA Secret Key is Deterministic Polynomial Tim.. - May - 2004
www.shoup.net/ntl/index.html
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