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2011

Group Law Computations on Jacobians of Hyperelliptic Curves

7 years 5 months ago
Group Law Computations on Jacobians of Hyperelliptic Curves
We derive an explicit method of computing the composition step in Cantor’s algorithm for group operations on Jacobians of hyperelliptic curves. Our technique is inspired by the geometric description of the group law and applies to hyperelliptic curves of arbitrary genus. While Cantor’s general composition involves arithmetic in the polynomial ring Fq[x], the algorithm we propose solves a linear system over the base field which can be written down directly from the Mumford coordinates of the group elements. We apply this method to give more efficient formulas for group operations in both affine and projective coordinates for cryptographic systems based on Jacobians of genus 2 hyperelliptic curves in general form.
Craig Costello, Kristin Lauter
Added 23 Dec 2011
Updated 23 Dec 2011
Type Journal
Year 2011
Where IACR
Authors Craig Costello, Kristin Lauter
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