M. Fouquet, P. Gaudry and R. Harley, \An extension of Satoh's algorithm and its implementation", Journal of the Ramanujan Mathematical Society, 15 (2000), 281-318. Home/Search Document Details and Download
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Computing Zeta Functions of Artin-Schreier Curves over Finite.. - Lauder, Wan (2001) (10 citations) (Correct)
....very practical. As previously mentioned, our algorithm can be extended to arbitrary hyperelliptic curves in characteristic 2, but we focus on the simplest cases in this paper. We refer to the references in [2] for the large literature on point counting, including [7, 19] and the more recent work [8, 9, 10, 11, 12, 17, 18, 22, 23, 25]. Sections 2, 3, 4 and 5 lay the mathematical foundation of our algorithm: it is based mainly upon an extension of the work of Dwork [6] due to Adolphson and Sperber [1] Section 6 contains a statement of the algorithm for what we call Type 1 Artin Schreier curves, and Section 7 describes exactly ....
M. Fouquet, P. Gaudry and R. Harley, An extension of Satoh's algorithm and its implementation, J. Ramanujan Math. Soc. 15, (2000), 281-318.
Hyperelliptic Curves and Cryptography - Jacobson, Jr., Menezes, Stein (2004) (1 citation) (Correct)
....(F q ) are crucial when selecting curves for cryptographic applications. The problem of determining #JC (F q ) for elliptic curves C is now considered to be well solved see Schoof s algorithm [68] and its derivatives when the characteristic of F q is odd, and Satoh s algorithm [65] as modi ed in [22] and [72] when the characteristic of F q is even. Kedlaya s algorithm [42] see also [82] determines #JC (F q ) for hyperelliptic curves C of genus g 2 over nite elds of small characteristic. The AGM method of Mestre and Harley (see [32] is very ecient for genus 1 and 2 curves over ....
M. Fouquet, P. Gaudry and R. Harley, \An extension of Satoh's algorithm and its implementation", Journal of the Ramanujan Mathematical Society, 15 (2000), 281318.
Analysis of the GHS Weil Descent Attack on the ECDLP over .. - Maurer, Menezes, Teske (2001) (3 citations) (Correct)
....curve with given (N; l; m) parameters as follows. First select arbitrary b from the set B = fb 2 F 2 N : m(b) mg; that the elements of B can be eciently enumerated can be seen from Theorem 5(i) Next, compute H = #E b (F 2 N ) where E b : y 2 xy = x 3 b using Satoh s algorithm [31, 8], and test if either H or 2 N 1 2 H (the order of the twist of E b ) is almost a prime. Observe that if b 2 B, then b 2 2 B. Moreover, E b and E b 2 are isogenous over F 2 N . Thus, if b 2 B has already been tested, then one should not select b 2 i for any 1 i N 1. Now, it is known ....
M. Fouquet, P. Gaudry and R. Harley, \An extension of Satoh's algorithm and its implementation", Journal of the Ramanujan Mathematical Society, 15 (2000), 281-318.
Finding Secure Curves with the Satoh-FGH Algorithm and an .. - Fouquet, Gaudry, Harley (2001) (2 citations) Self-citation (Fouquet Gaudry Harley) (Correct)
....recently described this process as a complicated and cumbersome task requiring a few hours on a workstation for 200 bits. Recently, a new algorithm for counting points on curves in small characteristic p 5 was designed by Satoh [Sat00] and we extended it to characteristics two and three in [FGH00]. An independent extension to characteristic two is described by Skjernaa [Skj] Satoh s algorithm is asymptotically superior to SEA for xed p, requiring O(log 3 q) deterministic time, instead of O(log 4 q) under reasonable hypotheses. As demonstrated in [FGH00] the Satoh FGH algorithm ....
....two and three in [FGH00] An independent extension to characteristic two is described by Skjernaa [Skj] Satoh s algorithm is asymptotically superior to SEA for xed p, requiring O(log 3 q) deterministic time, instead of O(log 4 q) under reasonable hypotheses. As demonstrated in [FGH00], the Satoh FGH algorithm is much faster in practice in characteristic two. Indeed we were able to count points over much larger elds (up to 8009 bits) than had previously been possible, and could match the largest size reached with SEA (i.e. 1999 bits) in just three hours. In the following we ....
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M. Fouquet, P. Gaudry, and R. Harley. An extension of Satoh's algorithm and its implementation. J. Ramanujan Math. Soc., 15:281-318, 2000.
Analysis of the GHS Weil Descent Attack on the ECDLP over .. - Maurer, Menezes, Teske (2001) (3 citations) (Correct)
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M. Fouquet, P. Gaudry and R. Harley, \An extension of Satoh's algorithm and its implementation", Journal of the Ramanujan Mathematical Society, 15 (2000), 281-318.
A Survey of Public-Key Cryptosystems - Koblitz, Menezes (Correct)
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M. Fouquet, P. Gaudry and R. Harley, An extension of Satoh's algorithm and its implementation, Journal of the Ramanujan Mathematical Society, 15 (2000), pp. 281-318.
Computing Zeta Functions Of Curves Over Finite Fields - Vercauteren (2003) (1 citation) (Correct)
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M. Fouquet, P. Gaudry, and R. Harley. An extension of Satoh's algorithm and its implementation. J. Ramanujan Math. Soc., 15(4):281-318, 2000.
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