Joint Sparse Form of Window Three for Koblitz Curve

The joint sparse form (JSF) for the non-adjacent form (NAF) representation of two large integers a and b, was proposed by Solinas. Then Ciet extended it to the -JSF for the -NAF representations of a and b using the endomorphism when computing aP +bQ , where P and Q are two points on the elliptic curve, in elliptic curve cryptography (ECC). It can be observed that -JSF is a special case of -JSF. In this paper, we will extend the -JSF idea to window 3 (RTNAF3), referred to as window three - joint sparse form (WTT-JSF). Mathematical analysis shows that a number of additions can be eliminated with this representation. Moreover, a detail derivation of the length and density of this form is given. The density is 11/27 which is lower than 7/16 when RTNAF3 is applied directly.

• Type: Journal
• Year: 2006
• Where: IJNSEC
• Authors: Yong Ding, Kwok-Wo Wong, Yu-Min Wang
• Keywords: Elliptic Curve, Elliptic Curve Cryptography, IJNSEC 2006, Joint Sparse Form