Finding small roots of bivariate integer polynomial equations revisited

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

Volumn 3027, Issue , 2004, Pages 492-505

  Coron, Jean Sébastien ^a  

^a GEMPLUS   (France)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS;

BIVARIATE; HIGH-ORDER; LATTICE REDUCTION; MODULAR POLYNOMIAL; POLYNOMIAL EQUATION; S-ALGORITHMS; SIMPLER ALGORITHMS; UNIVARIATE;

POLYNOMIALS;

EID: 24944529717     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/978-3-540-24676-3_29     Document Type: Article

References (14)

1. 0.292, proceedings of Eurocrypt '99, vol. 1592, Lecture Notes in Computer Science.
2. rq for large r, proceedings of Crypto '99, vol. 1666, Lecture Notes in Computer Science.
3. D. Coppersmith, Finding a Small Root of a Uhivariate Modular Equation, proceedings of Eurocrypt '96, vol. 1070, Lecture Notes in Computer Science.
4. D. Coppersmith, Finding a Small Root of a Bivariate Integer Equation; Factoring with High Bits Known, proceedings of Eurocrypt' 96, vol. 1070, Lecture Notes in Computer Science.
5. D. Coppersmith, Small solutions to polynomial equations, and low exponent vulnerabilities. J. of Cryptology, 10(4)233-260, 1997. Revised version of two articles of Eurocrypt '96.
6. D. Coppersmith, Finding small solutions to small degree polynomials. In Proc. of CALC '01, LNCS, Sptinger-Verlag, 2001.
7. N.A. Howgrave-Graham, Finding small roots of univariate modular equations revisited. In Cryptography and Coding, volume 1355 of LNCS, pp. 131-142. Springer Verlag, 1997.
8. C.S. Jutla, On finding small solutions of modular multivariate polynomial equations. Proceedings of Eurocrypt '98, Lecture Notes in Computer Science, vol. 1402.
9. A.K. Lenstra, H.W. Lenstra, Jr., and L. Lovász, Factoring polynomials with rational coefficients. Mathematische Ann., 261:513-534, 1982.
10. U. Maurer, Fast Generation of Prime Numbers and Secure Public-Key Cryptographic Parameters, Journal of Cryptology, vol. 8, no. 3, pp. 123-155, 1995.
11. M. Mignotte, An inequality about factors of polynomials. Math Comp. 28, 11531157, 1974.
12. P.Q. Nguyen and J. Stern, The two faces of lattices in cryptology. Proceedings of CALC '01, LNCS vol. 2146.
13. V. Shoup, OAEP reconsidered. Proceedings of Crypto '01, vol. 2139, Lecture Notes in Computer Science.
14. V. Shoup, Number Theory C++ Library (NTL) version 5.3.1. Available at www.shoup.net.