88 citations · 270 across the 33 of their papers we have counts for
22 papers · 1 filter
Faster enumeration of primes
David Harvey
We describe several new algorithms for finding all prime numbers up to a given bound , achieving the first ever speedup by a positive power of over the ancient sieve of…
Deterministic methods for finding elements of large multiplicative order
David Harvey, Markus Hittmeir
We revisit the problem of rigorously and deterministically finding elements of large order in the multiplicative group of integers modulo a natural number . Solving this problem…
Counting points on smooth plane quartics
Edgar Costa, David Harvey, Andrew V. Sutherland
We present efficient algorithms for counting points on a smooth plane quartic curve modulo a prime . We address both the case where is defined over and the…
A deterministic algorithm for finding -power divisors
David Harvey, Markus Hittmeir
Building on work of Boneh, Durfee and Howgrave-Graham, we present a deterministic algorithm that provably finds all integers such that in time …
A log-log speedup for exponent one-fifth deterministic integer factorisation
David Harvey, Markus Hittmeir
Building on techniques recently introduced by the second author, and further developed by the first author, we show that a positive integer may be rigorously and deterministica…
An exponent one-fifth algorithm for deterministic integer factorisation
David Harvey
Hittmeir recently presented a deterministic algorithm that provably computes the prime factorisation of a positive integer in bit operations. Prior to this break…