Faster index calculus for the medium prime case. Application to 1175-bit and 1425-bit finite fields.
作者： Antoine Joux
DOI:
关键词: Calculus 、 Discrete logarithm 、 Prime (order theory) 、 Point (geometry) 、 Finite field 、 Computer science 、 Multiplicative function 、 Filter (signal processing) 、 Basis (linear algebra) 、 Index calculus algorithm
摘要: … Unfortunately, we only know how to achieve this for a limited number of index calculus algorithms. More precisely, we show how to use pinpointing for the medium prime case as …
springer.com参考文章(13)
Brian Antony Murphy, Polynomial Selection for the Number Field Sieve Integer Factorisation Algorithm The Australian National University. ,(1999) , 10.25911/5D6272199E44D
Pierrick Gaudry, An algorithm for solving the discrete log problem on hyperelliptic curves theory and application of cryptographic techniques. ,vol. 1807, pp. 19- 34 ,(2000) , 10.1007/3-540-45539-6_2
Antoine Joux, Reynald Lercier, The Function Field Sieve in the Medium Prime Case Advances in Cryptology - EUROCRYPT 2006. ,vol. 4004, pp. 254- 270 ,(2006) , 10.1007/11761679_16
Daniel Panario, Xavier Gourdon, Philippe Flajolet, An Analytic Approach to Smooth Polynominals over Finite Fields algorithmic number theory symposium. pp. 226- 236 ,(1998) , 10.1007/BFB0054865
Daniel M. Gordon, Discrete logarithms in GF(P) using the number field sieve SIAM Journal on Discrete Mathematics. ,vol. 6, pp. 124- 138 ,(1993) , 10.1137/0406010
Emmanuel Thomé, Subquadratic Computation of Vector Generating Polynomials and Improvement of the Block Wiedemann Algorithm Journal of Symbolic Computation. ,vol. 33, pp. 757- 775 ,(2002) , 10.1006/JSCO.2002.0533
Leonard M. Adleman, Ming-Deh A. Huang, Function Field Sieve Method for Discrete Logarithms over Finite Fields Information & Computation. ,vol. 151, pp. 5- 16 ,(1999) , 10.1006/INCO.1998.2761
Pierrick Gaudry, Index calculus for abelian varieties of small dimension and the elliptic curve discrete logarithm problem Journal of Symbolic Computation. ,vol. 44, pp. 1690- 1702 ,(2009) , 10.1016/J.JSC.2008.08.005
P. Gaudry, F. Hess, N. P. Smart, Constructive and destructive facets of Weil descent on elliptic curves Journal of Cryptology. ,vol. 15, pp. 19- 46 ,(2002) , 10.1007/S00145-001-0011-X
Fast evaluation of logarithms in fields of characteristic two IEEE Transactions on Information Theory. ,vol. 30, pp. 587- 594 ,(1984) , 10.1109/TIT.1984.1056941