Joint Sparse Form of Window Three for Koblitz Curve

10.6633/IJNS.200603.2(2).06

Yong Ding；Kwok-Wo Wong；Yu-Min Wang

Φ-JSF ； JSF ； RTNAFw ； WTT-JSF

International Journal of Network Security

2卷2期（2006 / 03 / 01）

126 - 130

英文

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 ϕ-JSF for the ϕ-NAF representations of a and b using the endomorphism ϕ 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 T-JSF is a special case of T-JSF. In this paper, we will extend the ϕ-JSF idea to window 3 (RTNAF3), referred to as window three T- 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.