Large superfluous keys in multivariate quadratic asymmetric systems

Lecture Notes in Computer Science

Volumn 3386, Issue , 2005, Pages 275-287

  Wolf, Christopher ^a   Preneel, Bart ^a  

^a UNIVERSITY OF LEUVEN   (Belgium)

Author keywords

Multivariate Quadratic Equations; Public Key Schemes

Indexed keywords

COMPUTATIONAL METHODS; DATA STORAGE EQUIPMENT; MATHEMATICAL TRANSFORMATIONS; QUADRATIC PROGRAMMING;

CRYPTANALYSIS; HIDDEN FIELD EQUATIONS (HFE); MULTIVARIANT QUADRATIC EQUATIONS; PUBLIC KEY SCHEMES;

PUBLIC KEY CRYPTOGRAPHY;

EID: 24144456530     PISSN: 03029743     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1007/978-3-540-30580-4_19     Document Type: Conference Paper

References (16)

1. Alex Biryukov, Christophe De Cannière, An Braeken, and Bart Preneel. A toolbox for cryptanalysis: Linear and affine equivalence algorithms. In Advances in Cryptology - EUROCRYPT 2003, Lecture Notes in Computer Science, pages 33-50. Eli Biham, editor, Springer, 2003.
2. Nicolas Courtois, Louis Goubin, and Jacques Patarin. Quartz: Primitive specification (second revised version), October 2001. https://www.cosic.esat.kuleuven.ac.be/nessie/workshop/submissions/quartzv21-b. zip, 18 pages.
3. th 2003. ePrint Report 2003/211, http://eprint.iacr.org/, 14 pages.
4. Michael R. Garay and David S. Johnson. Computers and Intractability - A Guide to the Theory of NP-Completeness. W.H. Freeman and Company, 1979. ISBN 0-7167-1044-7 or 0-7167-1045-5.
5. W. Geiselmann, R. Steinwandt, and Th. Beth. Attacking the affine parts of SFlash. In Cryptography and Coding - 8th IMA International Conference, volume 2260 of Lecture Notes in Computer Science, pages 355-359. B. Honary, editor, Springer, 2001.
6. Aviad Kipnis, Jacques Patarin, and Louis Goubin. Unbalanced oil and vinegar signature schemes. In Advances in Cryptology - EUROCRYPT 1999, volume 1592 of Lecture Notes in Computer Science, pages 206-222. Jacques Stern, editor, Springer, 1999.
7. Aviad Kipnis and Adi Shamir. Cryptanalysis of the HFE public key cryptosystem. In Advances in Cryptology - CRYPTO 1999, volume 1666 of Lecture Notes in Computer Science, pages 19-30. Michael Wiener, editor, Springer, 1999. http://www.minrank.org/hfesubreg.ps or http://citeseer.nj.nec.com/kipnis99cryptanalysis.html.
8. Tsutomu Matsumoto and Hideki Imai. Public quadratic polynomial-tuples for efficient signature verification and message-encryption. In Advances in Cryptology - EUROCRYPT 1988, volume 330 of Lecture Notes in Computer Science, pages 419-545. Christoph G. Günther, editor, Springer, 1988.
9. Jacques Patarin. Cryptanalysis of the Matsumoto and Imai public key scheme of Eurocrypt'88. In Advances in Cryptology - CRYPTO 1995, volume 963 of Lecture Notes in Computer Science, pages 248-261. Don Coppersmith, editor, Springer, 1995.
10. Jacques Patarin. Asymmetric cryptography with a hidden monomial. In Advances in Cryptology - CRYPTO 1996, volume 1109 of Lecture Notes in Computer Science, pages 45-60. Neal Koblitz, editor, Springer, 1996.
11. Jacques Patarin. Hidden Field Equations (HFE) and Isomorphisms of Polynomials (IP): two new families of asymmetric algorithms. In Advances in Cryptology - EUROCRYPT 1996, volume 1070 of Lecture Notes in Computer Science, pages 33-48. Ueli Maurer, editor, Springer, 1996. Extended Version: http://www.minrank.org/hfe.pdf.
12. Jacques Patarin and Louis Goubin. Trapdoor one-way permutations and multivariate polynomials. In International Conference on Information Security and Cryptology 1997, volume 1334 of Lecture Notes in Computer Science, pages 356-368. International Communications and Information Security Association, Springer, 1997. Extended Version: http://citeseer.nj.nec.com/patarin97trapdoor.html.
13. Peter W. Shor. Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer. SIAM Journal on Computing, 26(5): 1484-1509, October 1997.
14. Ilia Toli. Cryptanalysis of HFE, June 2003. arXiv preprint server, http://arxiv.org/abs/cs.CR/0305034, 7 pages.
15. Christopher Wolf and Bart Preneel. Asymmetric cryptography: Hidden field equations. In European Congress on Computational Methods in Applied Sciences and Engineering 2004- P. Neittaanmäki, T. Rossi, S. Korotov, E. Oñate, J. Périaux, and D. Knörzer, editors, Jyväskylä University, 2004. 20 pages, extended version: http://eprint.iacr.org/2004/072/.
16. rd March 2004. http://eprint.iacr.org/, 21 pages.