The AGM-X0(N) Heegner Point Lifting Algorithm and Elliptic Curve Point Counting
نویسنده
چکیده
We describe an algorithm, AGM-X0(N), for point counting on elliptic curves of small characteristic p using p-adic lifts of their invariants associated to modular curves X0(N). The algorithm generalizes the contruction of Satoh [10], SST [11], and Mestre [9]. We describe this method and give details of its implementation for characteristics 2, 3, 5, 7, and 13.
منابع مشابه
A General Framework for p–adic Point Counting and Application to Elliptic Curves on Legendre Form
In 2000 T. Satoh gave the first p–adic point counting algorithm for elliptic curves over finite fields. Satoh’s algorithm was followed by the SST algorithm and furthermore by the AGM and MSST algorithms for characteristic two only. All four algorithms are important to Elliptic Curve Cryptography. In this paper we present a general framework for p–adic point counting and we apply it to elliptic ...
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تاریخ انتشار 2003