An Extension of Kedlaya's Algorithm to Hyperelliptic Curves in Characteristic 2
نویسندگان
چکیده
منابع مشابه
Hyperelliptic Curves in Characteristic 2
In this paper we prove that there are no hyperelliptic supersingular curves of genus 2n − 1 in characteristic 2 for any integer n ≥ 2. Let F be an algebraically closed field of characteristic 2, and let g be a positive integer. Write h = blog2(g + 1) + 1c, where b c denotes the greatest integer less than or equal to a given real number. Let X be a hyperelliptic curve over F of genus g ≥ 3 of 2-...
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In this paper we present an extension of Kedlaya’s algorithm for computing the zeta function of an Artin-Schreier curve over a finite field Fq of characteristic 2. The algorithm has running time O(g log q) and needs O(g log q) storage space for a genus g curve. Our first implementation in MAGMA shows that one can now generate hyperelliptic curves suitable for cryptography in reasonable time. We...
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Let ĒΓ be a family of hyperelliptic curves over F cl 2 with general Weierstrass equation given over a very small field F. We describe in this paper an algorithm for computing the zeta function of Ēγ̄, with γ̄ in a degree n extension field of F, which has as time complexity Õ(n3) bit operations and memory requirements O(n2) bits. With a slightly different algorithm we can get time O(n2.667) and me...
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Let α be an automorphism of a hyperelliptic curve C of genus g and let α be the automorphism induced by α on the genus-0 quotient of C by the hyperelliptic involution. Let n be the order of α and let n be the order of α. We show that the characteristic polynomial f of the automorphism α∗ of the Jacobian of C is determined by the values of n, n, and g, unless n = n, n is even, and (2g + 2)/n is ...
متن کاملErrata for “ An Extension of Kedlaya ’ s Algorithm to Hyperelliptic Curves
In this note we correct a gap in the proof of the complexity estimates appearing in our papers [1],[2]. The complexity estimates are correct, but the proof was incomplete at a certain point. The same gap appears in our paper [3], but there the estimate for the space complexity has to be multiplied with a power of log(g), where g is the genus of the curve. First we fill in the gap in [2]. In thi...
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ژورنال
عنوان ژورنال: Journal of Cryptology
سال: 2005
ISSN: 0933-2790,1432-1378
DOI: 10.1007/s00145-004-0231-y