Cryptanalysis of the tractable rational map cryptosystem

Lecture Notes in Computer Science

Volumn 3386, Issue , 2005, Pages 258-274

  Joux, Antoine ^a   Kunz Jacques, Sébastien ^b   Muller, Frédéric ^b   Ricordel, Pierre Michel ^b  

^a SPOTI   (France)

^b DCSSI Crypto Laboratory   (France)

Author keywords

Gr bner Bases; Isomorphism of Polynomials; Polynomial Systems; Public Key Cryptography; Tractable Rational Map Cryptosystem; XL

Indexed keywords

ALGORITHMS; COMBINATORIAL SWITCHING; FUNCTIONS; POLYNOMIALS; RANDOM PROCESSES;

GRÖBNER BASES; ISOMORPHISM OF POLYNOMIALS; POLYNOMIAL SYSTEMS; TACTABLE RATIONAL MAP CRYPTOSYSTEMS; XL;

PUBLIC KEY CRYPTOGRAPHY;

EID: 24144484756     PISSN: 03029743     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1007/978-3-540-30580-4_18     Document Type: Conference Paper

References (15)

1. W. Adams and P. Loustaunau. An introduction to Gröbner Bases, volume 3 of Graduate Studies in Mathematics. American Mathematical Society, 1994.
2. L. Wang F. Chang. Tractable Rational Map Cryptosystem. Cryptology ePrint archive, Report 2004/046, available at http://eprint.iacr.org.
3. J.-C. Faugère. A New Efficient Algorithm for Computing Gröbner Bases without reduction to zero (F5). In T. Mora, editor, ISSAC 2002, pages 75-83, 2002.
4. J.-C. Faugère. Report on a Successful Attack of HFE Challenge 1 with Gröbner Basis Algorithm F5/2. Announcement on sci.crypt newsgroup, in April 19th 2002.
5. 4). Journal of Pure and Applied Algebra, 139(1-3):61-88, 1999.
6. T. Matsumoto H. Imai. Public Quadratic Polynomial-tuples for Efficient Signature Verification and Message Encryption. In C. G. Günther, editor, Advances in Cryptology - Eurocrypt'88, volume 330 of LNCS, pages 419-453. Springer Verlag, 1988.
7. A. Joux J.-C. Faugère. Algebraic Cryptanalysis of Hidden Field Equation (HFE) Cryptosystems Using Gröbner Bases. In D. Boneh, editor, Advances in Cryptology - Crypto'2003, volume 2729 of LNCS, pages 44-60. Springer Verlag, 2003.
8. A. Kipnis and A. Shamir. Cryptanalysis of the HFE Public-key Cryptosystem. In M. Wiener, editor, Advances in Cryptology - Crypto'99, volume 1666 of LNCS, pages 19-30. Springer Verlag, 1999.
9. D. Lazard. Gröbner Basis, Gaussian Elimination and Resolution of Systems of Algebraic Equations. In J. A. van Hulzen, editor, EUROCAL '83, European Computer Algebra Conference, volume 162 of LNCS, pages 146-156. Springer Verlag, 1983.
10. The magma home page. http://www.maths.usyd.edu.au/u/magma.
11. J. Patarin N. Courtois, A. Klimov and A. Shamir. Efficient Algorithms for Solving Overdefined Systems of Multivariate Polynomial Equations. In B. Preneel, editor, Advances in Cryptology - Eurocrypt'2000, volume 180 of LNCS, pages 392-407. Springer Verlag, 2000.
12. J. Patarin N. Courtois, L. Goubin. Improved Algorithms for Isomorphisms of Polynomials. In K. Nyberg, editor, Advances in Cryptology - Eurocrypt'98, volume 1403 of LNCS, pages 184-200. Springer-Verlag, 1998.
13. J. Patarin N. Courtois, L. Goubin. Flash, a Fast Multivariate Signature Algorithm. In D. Naccache, editor, The Cryptographers' Track at RSA Conference 2001, volume 2020 of LNCS, pages 298-307. Springer-Verlag, 2001.
14. J. Patarin. Cryptanalysis of the Matsumoto and Imai Public Key Scheme of Eurocrypt'88. In D. Coppersmith, editor, Advances in Cryptology - Crypto'95, volume 963 of LNCS, pages 248-261. Springer Verlag, 1995.
15. J. Patarin. Hidden Fields Equations (HFE) and Isomorphisms of Polynomials (IP): Two New Families of Asymmetric Algorithms. In Advances in Cryptology - Eurocrypt'96, volume 1070 of LNCS, pages 33-48. Springer Verlag, 1996.