By constructing birational transformation of variables, we derive explicit doubling formulae for all types of defining equations of the curve. For each type of curve, we analyze how many field operations are needed. So far all proposed curves are secure, though they are more special types. Our results allow to choose curves from a large enough variety which have extremely fast doubling needing only one third the time of an addition in the best case. Furthermore, an actual implementation of the new formulae on a Pentium-M processor shows its practical relevance.
Category / Keywords: implementation / Hyperelliptic Curve Cryptosystem Date: received 14 Jul 2005 Contact author: xxfan at mail xidian edu cn Available format(s): Postscript (PS) | Compressed Postscript (PS.GZ) | PDF | BibTeX Citation Version: 20050720:062727 (All versions of this report) Short URL: ia.cr/2005/228