منابع مشابه
Modular Isogeny Complexes
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We present a new algorithm to compute the classical modular polynomial Φl in the rings Z[X,Y ] and (Z/mZ)[X, Y ], for a prime l and any positive integer m. Our approach uses the graph of l-isogenies to efficiently compute Φl mod p for many primes p of a suitable form, and then applies the Chinese Remainder Theorem (CRT). Under the Generalized Riemann Hypothesis (GRH), we achieve an expected run...
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The remarkable structure and computationally explicit form of isogeny graphs of elliptic curves over a finite field has made them an important tool for computational number theorists and practitioners of elliptic curve cryptography. This expository paper recounts the theory behind these graphs and examines several recently developed algorithms that realize substantial (often dramatic) performan...
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ژورنال
عنوان ژورنال: Algebraic & Geometric Topology
سال: 2012
ISSN: 1472-2739,1472-2747
DOI: 10.2140/agt.2012.12.1373