کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
9492929 | 1333907 | 2005 | 18 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
A p-adic point counting algorithm for elliptic curves on legendre form
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موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
اعداد جبر و تئوری
پیش نمایش صفحه اول مقاله
چکیده انگلیسی
In this paper, we present the general framework for p-adic point counting and we apply it to elliptic curves on Legendre form. We show how the λ-modular polynomial can be used for lifting the curve and Frobenius isogeny to characteristic zero and we show how the associated multiplier gives the action of the lifted Frobenius isogeny on the invariant differential. The result is a point counting algorithm for elliptic curves on Legendre form. The algorithm runs in a time complexity of O(n2μ+1/(μ+1)) for fixed p and a space complexity of O(n2) where pn is the field size. We include results from experimeriments in characteristic p=3,5,â¦,19.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Finite Fields and Their Applications - Volume 11, Issue 1, January 2005, Pages 71-88
Journal: Finite Fields and Their Applications - Volume 11, Issue 1, January 2005, Pages 71-88
نویسندگان
Marc Skov Madsen,