Effect of improved multiplication efficiency on exponentiation algorithms derived from addition chains

Author:

McCarthy D. P.

Abstract

The interaction between the efficiency of the basic multiplication algorithm and the addition chain used to compute x n {x^n} is studied. We conclude that either repeated multiplication by x or repeated squaring should be used and the provenance of each technique is established.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,Computational Mathematics,Algebra and Number Theory

Reference9 articles.

1. On the computation of powers of sparse polynomials;Fateman, Richard J.;Studies in Appl. Math.,1974

2. Polynomial multiplication, powers and asymptotic analysis: some comments;Fateman, Richard J.;SIAM J. Comput.,1974

3. Optimal multiplication chains for computing a power of a symbolic polynomial;Gentleman, W. Morven;Math. Comp.,1972

4. Addition chains with multiplicative cost;Graham, R. L.;Discrete Math.,1978

5. Computation of powers of multivariate polynomials over the integers;Heindel, Lee E.;J. Comput. System Sci.,1972

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