9 citations · 17 across the 7 of their papers we have counts for
7 papers
The probability that the number of points on the Jacobian of a genus 2 curve is prime
Wouter Castryck, Amanda Folsom, Hendrik Hubrechts +1
In 2000, Galbraith and McKee heuristically derived a formula that estimates the probability that a randomly chosen elliptic curve over a fixed finite prime field has a prime number…
Fast arithmetic in unramified p-adic fields
Hendrik Hubrechts
Let p be prime and Zpn the degree n unramified extension of the ring of p-adic integers Zp. In this paper we give an overview of some very fast algorithms for common operations in…
The distribution of the number of points modulo an integer on elliptic curves over finite fields
Wouter Castryck, Hendrik Hubrechts
Let F be a finite field and let b and N be integers. We prove explicit estimates for the probability that the number of rational points on a randomly chosen elliptic curve E over F…
Quasi-quadratic elliptic curve point counting using rigid cohomology
Hendrik Hubrechts
We present a deterministic algorithm that computes the zeta function of a nonsupersingular elliptic curve E over a finite field with p^n elements in time quasi-quadratic in n. An o…
Memory efficient hyperelliptic curve point counting
Hendrik Hubrechts
In recent algorithms that use deformation in order to compute the number of points on varieties over a finite field, certain differential equations of matrices over p-adic fields e…
Point counting in families of hyperelliptic curves in characteristic 2
Hendrik Hubrechts
Let E_G be a family of hyperelliptic curves over F2^(alg cl) with general Weierstrass equation given over a very small field F. We describe in this paper an algorithm to compute th…