Some properties of vectorial addition chains^†

^*To whom all correspondence should be sent.

Abstract

The concept of the shortest vectorial addition chains is considered to be an optimal approach for computing a monomial inimum number of multiplications. In this paper, some properties of the shortest vectorial addition chain are presented. Furthermore, an approach to achieve the shortest chains in some special cases is proposed. The correctness of these properties and the optimality of this approach are also shown.

Keywords:

• Cascade exponentiation
• monomial evaluation
• addition chain
• addition sequence
• vectorial addition chain
• the shortest vectorial addition chain

C.R. Categories:

• E.3.
• F.2.1.
• G.2.0.
• K.6.5.

^† This research was supported by the Nationl Science Council, Taiwan, R.O.C. under contact:NSC82-0408-E009(1993).

^*To whom all correspondence should be sent.

^† This research was supported by the Nationl Science Council, Taiwan, R.O.C. under contact:NSC82-0408-E009(1993).

^*To whom all correspondence should be sent.

Notes

^† This research was supported by the Nationl Science Council, Taiwan, R.O.C. under contact:NSC82-0408-E009(1993).

^*To whom all correspondence should be sent.