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Title: On the distribution of Atkin and Elkies primes for reductions of elliptic curves on average
Authors: Shparlinski, I 
Sutherland, Andrew V 
Keywords: Atkin primes;Elkies primes;Elliptic curves
Issue Date: 2015
Publisher: LMS Journal of Computation and Mathematics
Source: LMS Journal of Computation and Mathematics, vol. 18, issue 1 (2015) pp. 308-322
Abstract: For an elliptic curve E/QE/Q without complex multiplication we study the distribution of Atkin and Elkies primes ℓℓ, on average, over all good reductions of EE modulo primes pp. We show that, under the generalized Riemann hypothesis, for almost all primes pp there are enough small Elkies primes ℓℓ to ensure that the Schoof–Elkies–Atkin point-counting algorithm runs in (logp)4+o(1)(log⁡p)4+o(1) expected time.
Appears in Collections:Eng - Journal articles (DHET subsidised)

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