92 citations · 1.1k across the 51 of their papers we have counts for
5 papers · 1 filter
Sato-Tate groups of y^2=x^8+c and y^2=x^7-cx
Francesc Fité, Andrew V. Sutherland
We consider the distribution of normalized Frobenius traces for two families of genus 3 hyperelliptic curves over Q that have large automorphism groups: y^2=x^8+c and y^2=x^7-cx wi…
On the distribution of Atkin and Elkies primes for reductions of elliptic curves on average
Igor E. Shparlinski, Andrew V. Sutherland
For an elliptic curve E/Q without complex multiplication we study the distribution of Atkin and Elkies primes l, on average, over all good reductions of E modulo primes p. We show…
A framework for deterministic primality proving using elliptic curves with complex multiplication
Alexander Abatzoglou, Alice Silverberg, Andrew V. Sutherland +1
We provide a framework for using elliptic curves with complex multiplication to determine the primality or compositeness of integers that lie in special sequences, in deterministic…
Finding elliptic curves with a subgroup of prescribed size
Igor E. Shparlinski, Andrew V. Sutherland
Assuming the Generalized Riemann Hypothesis, we design a deterministic algorithm that, given a prime p and positive integer m=o(sqrt(p)/(log p)^4), outputs an elliptic curve E over…
Computing Hasse-Witt matrices of hyperelliptic curves in average polynomial time
David Harvey, Andrew V. Sutherland
We present an efficient algorithm to compute the Hasse-Witt matrix of a hyperelliptic curve C/Q modulo all primes of good reduction up to a given bound N, based on the average poly…