89 citations · 134 across the 7 of their papers we have counts for
6 papers · 1 filter
Deterministic factoring with oracles
Fran{\c c}ois Morain, Gu{é}na{ë}l Renault, Benjamin Smith
We revisit the problem of integer factorization with number-theoretic oracles, including a well-known problem: can we factor an integer unconditionally, in deterministic polyno…
Computing cardinalities of Q-curve reductions over finite fields
François Morain, Charlotte Scribot, Benjamin Smith
We present a specialized point-counting algorithm for a class of elliptic curves over F\_{p^2} that includes reductions of quadratic Q-curves modulo inert primes and, more generall…
Improvements to the number field sieve for non-prime finite fields
Razvan Barbulescu, Pierrick Gaudry, Aurore Guillevic +1
We propose various strategies for improving the computation of discrete logarithms in non-prime fields of medium to large characteristic using the Number Field Sieve. This includes…
Discrete logarithm computations over finite fields using Reed-Solomon codes
Daniel Augot, François Morain
Cheng and Wan have related the decoding of Reed-Solomon codes to the computation of discrete logarithms over finite fields, with the aim of proving the hardness of their decoding.…
Visualizing elements of Sha[3] in genus 2 jacobians
Nils Bruin, Sander R. Dahmen
Mazur proved that any element xi of order three in the Shafarevich-Tate group of an elliptic curve E over a number field k can be made visible in an abelian surface A in the sense…
Implementing the asymptotically fast version of the elliptic curve primality proving algorithm
François Morain
The elliptic curve primality proving (ECPP) algorithm is one of the current fastest practical algorithms for proving the primality of large numbers. Its running time cannot be prov…