On Addition Chains¹

¹This research was supported by National Science Council of Republic of China with grant number NSC80-0408-E007-07.

Abstract

This paper presents some mathematical properties of the shortest-length addition chain for a certain set of integers whose binary patterns meet a set of special forms; and the correctness of these properties is proved.

Keywords:

• Addition chain
• the shortest-length addition chain
• big step
• double step
• small step
• star step
• special four
• short-five
• long-five
• RSA public key method
• NP-complete

C.R.Categories:

• E.3.
• F.2.1
• G.2.0
• K.6.5

¹This research was supported by National Science Council of Republic of China with grant number NSC80-0408-E007-07.

²To whom all correspondence should be addressed.

¹This research was supported by National Science Council of Republic of China with grant number NSC80-0408-E007-07.

²To whom all correspondence should be addressed.

Notes

¹This research was supported by National Science Council of Republic of China with grant number NSC80-0408-E007-07.

²To whom all correspondence should be addressed.