Polynomial equivalence problems and applications to multivariate cryptosystems

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

Volumn 2904, Issue , 2003, Pages 235-251

  Levy dit Vehel, Françoise ^a   Perret, Ludovic ^a  

^a ENSTA PARISTECH   (France)

Author keywords

Gr bner Bases; Isomorphism of Polynomials; Multivariate polynomial equations

Indexed keywords

CRYPTOGRAPHY; EQUIVALENCE CLASSES; NUMERICAL METHODS; SET THEORY;

ISOMORPHISM OF POLYNOMIALS; MULTIVARIATE POLYNOMIAL; NUMERICAL RESULTS; POLYNOMIAL EQUIVALENCE;

POLYNOMIALS;

EID: 0346265015     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/978-3-540-24582-7_18     Document Type: Article

References (14)

1. T. Becker and V. Weispfenning: Gröbner Bases, A Computational Approach to Commutative Algebra. In cooperation with Heinz Kredel. Graduate Texts in Mathematics, 141. Springer-Verlag, New York, 1993.
2. N. Courtois, L. Goubin, J. Patarin: Improved Algorithms for Isomorphism of Polynomials. Eurocrypt'98, Springer-Verlag, pp 184-200.
3. D. A. Cox, D. O'Shea, J.B. Little: Ideals, Varieties, and Algorithms: An Introduction to Computational Algebraic Geometry and Commutative Algebra. Undergraduate Texts in Mathematics. Springer-Verlag. New York, 1992.
4. J.-C. Faugère: Algebraic cryptanalysis of HFE using Gröbner bases. INRIA report: RR-4738. Available from http://www.inria.fr/rrrt/rr-4738.html.
5. 4. Journal of pure and applied algebra, vol. 139, 1999, pp. 61-68.
6. 5. Proceedings of ISSAC, pages 75-83. ACM press, July 2002.
7. J.-C. Faugère, Antoine Joux: Algebraic cryptanalysis of hidden field equation (HFE) cryptosystems using Gröbner bases. Crypto 2003, LNCS 2729, Springer-Verlag, August 2003.
8. W. Geiselmann and W. Meier and R. Steinwandt: An Attack on the Isomorphisms of Polynomials Problem with One Secret. Cryptology ePrint Archive: Report 2002/143. Available from http://eprint.iacr.org/2002/143.
9. F. Levy-dit-Vehel and L. Perret: Polynomial equivalence problems and applications to multivariate cryptosystems. Rapport INRIA 2003, to appear.
10. http://magma.maths.usyd.edu.au/magma/
11. T. Matsumoto, H. Imai: Public Quadratic Polynomial-tuples for efficient signature-verification and message-encryption. Eurocrypt'88, Springer-Verlag, pp. 419-453.
12. J. Patarin: Hidden Fields Equations (HFE) and Isomorphisms of Polynomials (IP): two new families of Asymmetric Algorithms. Eurocrypt'96, Springer-Verlag, pp. 33-48.
13. J. Patarin: Hidden Fields Equations (HFE) and Isomorphisms of Polynomials (IP): two new families of Asymmetric Algorithms - Extended version. http://www.cp8.com/sct/uk/partners/page/publi/eurocryptb.ps.
14. T.-T. Moh: A Fast Public Key System With Signature And Master Key Functions. CrypTEC'99, Hong Kong City University Press, pages 63-69, July 1999.