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math.NT2017★ 1 cited
Isogenies for point counting on genus two hyperelliptic curves with maximal real multiplication
Sean Ballentine, Aurore Guillevic, Elisa Lorenzo García +4
Schoof's classic algorithm allows point-counting for elliptic curves over finite fields in polynomial time. This algorithm was subsequently improved by Atkin, using factorizations…
math.NT2014★ 7 cited
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…