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http://dx.doi.org/10.13089/JKIISC.2002.12.5.75

On the SEA algorithm used in finding secure elliptic curves with an early-abort strategy  

정배은 (한국전자통신연구원 정보보호연구본부)
류희수 (한국전자통신연구원 정보보호연구본부)
Publication Information
Journal of the Korea Institute of Information Security & Cryptology / v.12, no.5, 2002 , pp. 75-85 More about this Journal
Abstract
In using elliptic curves in cryptography, it is important to find a secure elliptic curve. The security of elliptic curve cryptosystem is dependent on the cardinality of the given curve. So, it is necessary to count the number of points of a given elliptic curve to obtain secure curve. It is hewn that when the charateristic is two, the most efficient algorithm finding secure curves is combining the Satoh-FGH algorithm with early-abort strategy$^[1]$. In［1］, the authors wrote that they modified SEA algorithm used in early-abort strategy, but they didn't describe the varaint of SEA algorithm. In this paper, we present some modifications of SEA algorithm and show the result of our implementation.
Keywords
타원곡선 암호;Elkies소수;SEA 알고리즘;early-abort 전략;
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  • Reference
1 ANTS-II: Computing l-isogenies with the p-torsion /
[ J.M. Couveignes ] / Lecture Notes in Comp. Sci.   DOI
2 Advances in Cryptology-Eurocrypt'01: A memory Efficient Version of Satoh's Algorithm /
[ F. Vercauters;B. Preneel;J. Vandewalle ] / LNCS
3 The canonical lift of an ordinary elliptic curve over a finite field and its point counting /
[ T. Satoh ] / J. Ramanujan Math. Soc.
4 ANTS-II: Computing isogenies in GF(2ⁿ) /
[ R. Lecier ] / Lecture Notes in Comp. Sci.   DOI
5 Counting points on elliptic curves over finite fields /
[ R. Schoof ] / J. Theory. Nombres Bordeaux   DOI
6 /
[ I.F. Blake;G. Seroussi;N.P. Smart ] / Elliptic Curves in Cryptography
7 /
[ B. Skjernaa ] / Satoh's algorithm in characteristic 2
8 An extension of Satoh's algorithm and its implementation /
[ M. Fouquet;P. Gaudry;R. Harley ] / J. Ramanujan Math. Soc.
9 Elliptic and modular curves over finite fields and related computational issues /
[ N. Elkies ] / Computational Perspectives on Number Theory
10 Advances in Cryptology-Eurocrypt'01: Finding Secure Curves with the Satoh-FGH Algorithm and an Early-Abort Strategy /
[ M. Fouquet;P. Gaudry;R. Harley ] / LNCS
11 Advances in Cryptology-Eurocrypt'97: Finding good random elliptic curves for cryptosystems defined over F 2ⁿ /
[ R. Lercier ] / LNCS