Quasi-optimal algorithms for multiplication in the extensions of image of degree 13, 14 and 15

From an interpolation method on algebraic curves, due to Chudnovsky and Chudnovsky, we construct effective bilinear algorithms for multiplication in the extensions of image of degree 13less-than-or-equals, slantnless-than-or-equals, slant15, with a bilinear complexity equal to 2n+1. These algorithms which are the first hyperelliptic algorithms of multiplication, are obtained from the hyperelliptic curve of genus 2 with plane equation y2+y=x5.