Analysis of the GHS Weil Descent Attack on the ECDLP over Characteristic Two Finite Fields of Composite Degree

2001 ◽  
pp. 195-213 ◽  
Author(s):  
Markus Maurer ◽  
Alfred Menezes ◽  
Edlyn Teske
Keyword(s):  
Finite Fields ◽  
Characteristic Two ◽  
Weil Descent

scholarly journals Analysis of the GHS Weil Descent Attack on the ECDLP over Characteristic Two Finite Fields of Composite Degree

2002 ◽  
Vol 5 ◽  
pp. 127-174 ◽  
Author(s):  
Markus Maurer ◽  
Alfred Menezes ◽  
Edlyn Teske
Keyword(s):  
Elliptic Curve ◽  
Elliptic Curves ◽  
Finite Fields ◽  
Discrete Logarithm ◽  
Discrete Logarithm Problem ◽  
Signature Scheme ◽  
Extension Degree ◽  
Characteristic Two ◽  
Weil Descent

AbstractIn this paper, the authors analyze the Gaudry-Hess-Smart (GHS) Weil descent attack on the elliptic curve discrete logarithm problem (ECDLP) for elliptic curves defined over characteristic two finite fields of composite extension degree. For each such field F2N, where N is in [100,600], elliptic curve parameters are identified such that: (i) there should exist a cryptographically interesting elliptic curve E over F2N with these parameters; and (ii) the GHS attack is more efficient for solving the ECDLP in E(F2N) than for solving the ECDLP on any other cryptographically interesting elliptic curve over F2N. The feasibility of the GHS attack on the specific elliptic curves is examined over F2176, F2208, F2272, F2304 and F2368, which are provided as examples in the ANSI X9.62 standard for the elliptic curve signature scheme ECDSA. Finally, several concrete instances are provided of the ECDLP over F2N, N composite, of increasing difficulty; these resist all previously known attacks, but are within reach of the GHS attack.

Triple-Cycle Permutations Over Finite Fields of Characteristic Two

2019 ◽  
Vol 30 (02) ◽  
pp. 275-292
Author(s):  
Xianping Liu ◽  
Yuan Chen ◽  
Yunge Xu ◽  
Zhimin Sun
Keyword(s):  
Finite Fields ◽  
Characteristic Two

Triple-cycle permutations over finite fields of characteristic two are studied, and some classes of triple-cycle permutations are proposed in this paper. In addition, new triple-cycle permutations can be constructed by switching construction from known ones.

Computing Logarithms in Finite Fields of Characteristic Two

1984 ◽  
Vol 5 (2) ◽  
pp. 276-285 ◽  
Author(s):  
I. F. Blake ◽  
R. Fuji-Hara ◽  
R. C. Mullin ◽  
S. A. Vanstone
Keyword(s):  
Finite Fields ◽  
Characteristic Two

Low Complexity Normal Elements over Finite Fields of Characteristic Two

2008 ◽  
Vol 57 (7) ◽  
pp. 990-1001 ◽  
Author(s):  
Ariane M. Masuda ◽  
Lucia Moura ◽  
Daniel Panario ◽  
David Thomson
Keyword(s):  
Finite Fields ◽  
Low Complexity ◽  
Characteristic Two
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