An Application of Sieve Methods to Elliptic Curves

An Application of Sieve Methods to Elliptic Curves

Tác giả: S. Ali Miri, V. Kumar Murty

Nguồn trích: Progress in cryptology-INDOCRYPT 2001-LNCS 22418.7

Năm xuất bản: 1905

Số trang: 98

Tóm tắt:  Let E be an elliptic curve defined over the rationals. Koblitz conjectured that the number of primes p ≤ x such that the number of points |E(F )| on the curve over the finite field of p elements has prime order is asymptotic to p for some constant C E C E x (log x) 2 . We consider curves without complex multiplication. Assuming the GRH (that is, the Riemann Hypothesis for Dedekind zeta functions) we prove that for primes p ≤ x, the group order |E(F x (log x) p 2 )| has at most 16 prime diviso

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