Parallelizing Explicit Formula for Arithmetic in the Jacobian of Hyperelliptic Curves

One of the recent thrust areas in research on hyperelliptic curve cryptography has been to obtain explicit formulae for performing arithmetic in the Jacobian of such curves. We continue this line of research by obtaining parallel versions of such formulae. Our first contribution is to develop a general methodology for obtaining parallel algorithm of any explicit formula. Any parallel algorithm obtained using our methodology is provably optimal in the number of multiplication rounds. We next apply this methodology to Lange's explicit formula for arithmetic in genus 2 hyperelliptic curve

• Type: Conference
• Year: 2003
• Where: ASIACRYPT
• Authors: Pradeep Kumar Mishra, Palash Sarkar
• Keywords: ASIACRYPT 2003, Cryptology, Explicit Formula, Inversion Free Arithmetic, Parallel Algorithm