Kipnis-Shamir attack on HFE revisited

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

Volumn 4990 LNCS, Issue , 2008, Pages 399-411

  Jiang, Xin ^a   Ding, Jintai ^b,c   Hu, Lei ^a  

^a INSTITUTE OF GEOLOGY AND GEOPHYSICS   (China)

^b UNIVERSITY OF CINCINNATI   (United States)

^c DARMSTADT UNIVERSITY OF TECHNOLOGY   (Germany)

Author keywords

Gr bner basis; HFE; MinRank; Multivariate public key cryptosystem; Relinearization; XL algorithm

Indexed keywords

BOOLEAN FUNCTIONS; POLYNOMIAL APPROXIMATION; POLYNOMIALS; PUBLIC KEY CRYPTOGRAPHY;

HFE; MINRANK; MULTIVARIATE PUBLIC KEY CRYPTOSYSTEM; RELINEARIZATION; XL ALGORITHM;

CRYPTOGRAPHY;

EID: 54249088990     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/978-3-540-79499-8_31     Document Type: Conference Paper

References (22)

1. Bardet, M., Faugère, J.-C., Salvy, B.: On the complexity of Gröbner basis computation of semi-regular overdetermined algebraic equations. In: Proceedings of the International Conference on Polynomial System Solving, pp. 71-74 (2004) Previously appeared as INRlA report RR-5049.
2. Courtois, N.T.: The Security of Hidden Field Equations (HFE). In: Naccache, D. (ed.) CT-RSA 2001. LNCS, vol. 2020, Springer, Heidelberg (2001)
3. Courtois, N.T.: The Minrank Problem. MinRank, a new Zero-knowledge scheme based on the NP-complete problem Presented at the rump session of Crypto (2000), available at: http://www.minrank.org
4. Courtois, N., Klimov, A., Patarin, J., Shamir, A.: Efficient Algorithms for Solving Overdefined Systems of Multivariate Polynomial Equations. In: Preneel, B. (ed.) EUROCRYPT 2000. LNCS, vol. 1807, pp. 392-407. Springer, Heidelberg (2000)
5. Ding, J., Gower, J., Schmidt, D.: Multivariate Public-Key Cryptosystems. In: Advances in Information Security, Springer, Heidelberg (2006)
6. Ding, J., Schmidt, D.S.: Cryptanalysis of HFEV and Internal Perturbation of HFE. In: Vaudenay, S. (ed.) PKC 2005. LNCS, vol. 3386, pp. 288-301. Springer, Heidelberg (2005)
7. 4). Journal of Plure and Applied Algebra 139, 61-88 (1999)
8. 5). In: Mora, T. (ed.) Proceeding of ISSAC, pp. 75-83. ACM Press, New York (2002)
9. Faugère, J.-C.: Algebraic Cryptanalysis of Hidden Field Equation (HFE) Cryptosystems Using Gröbner Bases. In: Boneh, D. (ed.) CRYPTO 2003. LNCS, vol. 2729, pp. 44-60. Springer, Heidelberg (2003)
10. Garey, M.R., Johnson, D.S.: Computers and Intractability - A Guide to the Theory of NP-Completeness. W.H. Freeman and Company, New York (1979)
11. Granboulan, L., Joux, A., Stern, J.: Inverting HFE Is Quasipolynomial. In: Dwork, C. (ed.) CRYPTO 2006. LNCS, vol. 4117, pp. 345-356. Springer, Heidelberg (2006)
12. Kipnis, A., Shamir, A.: Cryptanalysis of the HFE Public Key Cryptosystem by Relinearization. In: Wiener, M.J. (ed.) CRYPTO 1999. LNCS, vol. 1666, Springer, Heidelberg (1999)
13. Shamir, A., Patarin, J., Courtois, N., Klimov, A.: Efficient Algorithms for Solving Overdefined Systems of Multivariate Polynomial Equations. In: Preneel, B. (ed.) EUROCRYPT 2000. LNCS, vol. 1807, Springer, Heidelberg (2000)
14. Matsumoto, T., Imai, H.: Public Quadratic Polynomial-Tuples for Efficient Signature-Verification and Message-Encryption. In: Günther, C.G. (ed.) EUROCRYPT 1988. LNCS, vol. 330, pp. 419-453. Springer, Heidelberg (1988)
15. Patarin, J.: Hidden Fields Equations (HFE) and Isomorphisms of Polynomials (IP): Two New Families of Asymmetric Algorithms. In: Maurer, U.M. (ed.) EUROCRYPT 1996. LNCS, vol. 1070, pp. 33-48. Springer, Heidelberg (1996)
16. Patarin, J., Courtois, N., Goubin, L.: QUARTZ, 128-Bit Long Digital Signatures. In: Naccache, D. (ed.) CT-RSA 2001. LNCS, vol. 2020, Springer, Heidelberg (2001)
17. Diem, C.: The XL-Algorithm and a Conjecture from Commutative Algebra. In: Lee, P.J. (ed.) ASIACRYPT 2004. LNCS, vol. 3329, pp. 323-337. Springer, Heidelberg (2004)
18. Imai, H., Sugita, M., Faugère, J.-C., Ars, G., Kawazoe, M.: Comparison Between XL and Gröbner Basis Algorithms. In: Lee, P.J. (ed.) ASIACRYPT 2004. LNCS, vol. 3329, pp. 338-353. Springer, Heidelberg (2004)
19. Wolf, C., Preneel, B.:, Taxonomy of public key schemes based on the problem of multivariate quadratic equations. Cryptology ePrint Archive, Report 2005/077, 64 (12th of May, 2005), http://eprint/iacr/org/2005/007/
20. Yang, B.-Y., Chen, J.-M.: All in the XL Family: Theory and Practice. In: Park, C.-s., Chee, S. (eds.) ICISC 2004. LNCS, vol. 3506, pp. 67-86. Springer, Heidelberg (2005)
21. Segers, A.J.M.: Algebraic Attacks from a Groebner Basis Perspective Master's Thesis, 10, 110 (2004) ihttp://www.win.win.tue.nl/~bdeweger/ ReportSegersGB2-11-04.pdf
22. p whose Fourier transforms have constant modulus. In: Proceedings of Alfred Haar Memorial Conference. Colloquia Mathematica Societatis Jnos Bolyai, Budapest, vol. 49 (1985)