Abstract
From an interpolation method on algebraic curves, due to Chudnovsky and Chudnovsky, we construct effective bilinear algorithms for multiplication in the extensions of F 16 of degree 13⩽ n⩽15, with a bilinear complexity equal to 2 n+1. These algorithms which are the first hyperelliptic algorithms of multiplication, are obtained from the hyperelliptic curve of genus 2 with plane equation y 2+ y= x 5.
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