Deterministic polynomial-time equivalence of computing the RSA secret key and factoring

Journal of Cryptology

Volumn 20, Issue 1, 2007, Pages 39-50

  Coron, Jean Sebastien ^a   May, Alexander ^b  

^a UNIVERSITY OF LUXEMBOURG   (Luxembourg)

^b DARMSTADT UNIVERSITY OF TECHNOLOGY   (Germany)

Author keywords

Coppersmith's theorem; RSA

Indexed keywords

PROBABILISTIC POLYNOMIAL TIME ALGORITHM; RSA CRYPTOSYSTEM; UNIVARIATE MODULAR POLYNOMIALS;

ALGORITHMS; CRYPTOGRAPHY; POLYNOMIALS; PROBABILITY;

SECURITY OF DATA;

EID: 33846874546     PISSN: 09332790     EISSN: 14321378     Source Type: Journal    
DOI: 10.1007/s00145-006-0433-6     Document Type: Article

References (12)

1. r q for large r, Proceedings of Crypto '99, pp. 326-337. LNCS, Vol. 1666. Springer-Verlag, Berlin, 1999.
2. D. Coppersmith, Small solutions to polynomial equations and low exponent vulnerabilities, Journal of Cryptology, Vol. 10, No. 4, pp. 223-260, 1997.
3. G. Durfee and P. Nguyen, Cryptanalysis of the RSA schemes with short secret exponent from Asiacrypt '99, Proceedings of Asiacrypt 2000, pp. 14-29. LNCS, Vol. 1976. Springer-Verlag, Berlin, 2000.
4. N. Howgrave-Graham, Finding small roots of univariate modular equations revisited, Proceedings of Cryptography and Coding, pp. 131-142. LNCS, Vol. 1355. Springer-Verlag, Berlin, 1997.
5. N. Howgrave-Graham, Approximate integer common divisors, Proceedings of CALC '01, pp. 51-66. LNCS, Vol. 2146. Springer-Verlag, Berlin, 2001.
6. A. K. Lenstra, H. W. Lenstra and L. Lovász, Factoring polynomials with rational coefficients, Mathematische Annal en, Vol. 261, pp. 513-534, 1982
7. A. May, Computing the RSA secret key is deterministic polynomial time equivalent to factoring, Proceedings of Crypto 2004, pp. 213-219. LNCS, Vol. 3152. Springer-Verlag, Berlin, 2004.
8. G. L. Miller, Riemann's hypothesis and tests for primality, Proceedings of the Seventh Annual ACM Symposium on the Theory of Computing, pp. 234-239, 1975.
9. P. Nguyen and D. Stehlé, Floating-point LLL revisited, Proceedings of Eurocrypt 2005, pp. 215-233. LNCS, Vol. 3494. Springer-Verlag, Berlin, 2005.
10. P.Q. Nguyen and J. Stern, The two faces of lattices in cryptology, Proceedings of CALC '01, pp. 146-180. LNCS, Vol. 2146. Springer-Verlag, Berlin, 2001.
11. R. Rivest, A. Shamir and L. Adleman, A method for obtaining digital signatures and public-key cryptosystems, Communications of the ACM, Vol. 21, No. 2, pp. 120-126, 1978
12. V. Shoup, NTL: A Library for Doing Number Theory, available online at http://www. shoup.net/ntl/index.html