First fall degree and Weil descent

Finite Fields and their Applications

Volumn 30, Issue , 2014, Pages 155-177

  Hodges, Timothy J ^a   Petit, Christophe ^b   Schlather, Jacob ^a  

^a UNIVERSITY OF CINCINNATI   (United States)

^b UNIVERSITÉ CATHOLIQUE DE LOUVAIN   (Belgium)

Author keywords

Degree of regularity; Finite field; First fall degree; Weil descent

Indexed keywords

CRYPTOGRAPHY;

DEGREE OF REGULARITY; ELLIPTIC CURVE DISCRETE LOGARITHM PROBLEMS; FINITE FIELDS; FIRST FALL DEGREE; POLYNOMIAL SYSTEMS; WEIL DESCENTS;

POLYNOMIALS;

EID: 84905043097     PISSN: 10715797     EISSN: 10902465     Source Type: Journal    
DOI: 10.1016/j.ffa.2014.07.001     Document Type: Article

References (25)

1. M. Bardet, J.-C. Faugère, B. Salvy, and B.-Y. Yang Asymptotic behaviour of the degree of regularity of semi-regular systems of equations Mega 2005, Eighth International Symposium on Effective Methods in Algebraic Geometry 2005 1 14
2. L. Bettale, J.-C. Faugère, and L. Perret Cryptanalysis of multivariate and odd-characteristic HFE variants D. Catalano, N. Fazio, R. Gennaro, A. Nicolosi, Public Key Cryptography PKC 2011 Lect. Notes Comput. Sci. vol. 6571 2011 Springer Berlin 441 458
3. L. Bettale, J.-C. Faugère, and L. Perret Cryptanalysis of HFE, multi-HFE and variants for odd and even characteristic Des. Codes Cryptogr. 69 2012 1 52
4. J. Buchmann, A. Pyshkin, and R.-P. Weinmann A zero-dimensional Gröbner basis for AES-128 FSE 2006 Lect. Notes Comput. Sci. vol. 4047 2006 78 88
5. L. Carlitz Representations by quadratic forms in a finite field Duke Math. J. 21 1954 123 137
6. J. Ding, and T.J. Hodges Inverting the HFE systems is quasipolynomial for all fields Advances in Cryptology Crypto 2011 Lect. Notes Comput. Sci. vol. 6841 2011 Springer Berlin 724 742
7. V. Dubois, and N. Gama The first fall degree of HFE systems M. Abe, Advances in Cryptology, 16th International Conference on the Theory and Application of Cryptology and Information Security ASIACRYPT 2010 Lect. Notes Comput. Sci. vol. 6477 2010 Springer Berlin 557 576
8. J.-C. Faugère, Mohab Safey El Din, and Pierre-Jean Spaenlehauer Computing loci of rank defects of linear matrices using Gröbner bases and applications to cryptology ISSAC 2010 2010 257 264
9. J.-C. Faugère, and A. Joux Algebraic cryptanalysis of Hidden Field Equation (HFE) cryptosystems using Gröbner bases D. Boneh, Advances in Cryptology CRYPTO 2003 Lect. Notes Comput. Sci. vol. 2729 2003 Springer Berlin 44 60 (Pubitemid 137636934)
10. J.-C. Faugère, A. Joux, L. Perret, and J. Treger Cryptanalysis of the hidden matrix cryptosystem LATINCRYPT 2010 2010 241 254
11. J.-C. Faugère A new efficient algorithm for computing Gröbner bases (F4) J. Pure Appl. Algebra 139 1999 61 89
12. J.-C. Faugère A new efficient algorithm for computing Gröbner bases without reduction to zero (F5) Proc. ISSAC 2002 New York, NY, USA 2002 75 83 (Pubitemid 35023374)
13. J.-C. Faugère, Patrizia M. Gianni, Daniel Lazard, and Teo Mora Efficient computation of zero-dimensional Gröbner bases by change of ordering J. Symb. Comput. 16 1993 329 344
14. n) http://eprint.iacr.org/2011/598 2011
15. J.-C. Faugère, Ludovic Perret, Christophe Petit, and Guenael Renault Improving the complexity of index calculus algorithms in elliptic curves over binary fields EUROCRYPT 2012 Lect. Notes Comput. Sci. vol. 7237 2012 27 44
16. L. Granboulan, A. Joux, and J. Stern Inverting HFE is quasi-polynomial C. Dwork, Advances in Cryptology CRYPTO 2006 Lect. Notes Comput. Sci. vol. 4117 2006 Springer Berlin 345 356
17. T.J. Hodges, and J. Schlather The degree of regularity of a quadratic polynomial J. Pure Appl. Algebra 217 2013 207 217
18. R. Lidl, and H. Niederreiter Finite Fields Encycl. Math. Appl. vol. 20 1997 Cambridge University Press
19. J. Patarin Hidden field equations and isomorphism of polynomials (IP): two new families of asymmetric algorithms U. Maurer, Eurocrypt '96 Lect. Notes Comput. Sci. vol. 1070 1996 Springer Berlin 33 48 (Pubitemid 126071052)
20. J. Patarin, and L. Goubin Asymmetric cryptography with Sboxes Proc. ICICS'97 Beijing, China Lect. Notes Comput. Sci. vol. 1334 1997 369 380
21. J. Patarin, and L. Goubin Trapdoor one-way permutations and multivariate polynomials Proc. ICICS'97 Beijing, China Lect. Notes Comput. Sci. vol. 1334 1997 356 368 (Pubitemid 127148063)
22. Christophe Petit, and Jean-Jacques Quisquater On polynomial systems arising from a Weil descent X. Wang, K. Sako, ASIACRYPT 2012 Lect. Notes Comput. Sci. vol. 7658 2012 451 466
23. J. Riordan An Introduction to Combinatorial Analysis 2002 Dover
24. F 5 for generic MQ with number of equations linear in that of variables Number Theory and Cryptography Workshop TU Darmstadt, Germany, November 21-22, 2013 Lect. Notes Comput. Sci. vol. 8260 2013 19 33
25. X. Zhao, and D. Feng Bypassing the decomposition attacks on two-round multivariate schemes by a practical cubic round IET Inf. Secur. 4 3 September 2010 167 184