The optimal algorithm to evaluate ⁿ using elementary multiplication methods
TL;DR: The optimality of the binary algorithm to evaluate xn is established where x is an integer or a completely dense polynomial modulo m, n is a positive integer, and the multiplications are done using a simple improvement on the naive algorithm.
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Abstract: The optimality of the binary algorithm to evaluate xn is established where x is an integer or a completely dense polynomial modulo m, n is a positive integer, and the multiplications are done using a simple improvement on the naive algorithm.
read more
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Citations
Effect of improved multiplication efficiency on exponentiation algorithms derived from addition chains
TL;DR: The interaction between the efficiency of the basic multiplication algorithm and the addition chain used to compute x' is studied in this article, and it is concluded that either repeated multiplication by x or repeated squaring should be used and the provenance of each technique is established.
Bellman's, Knut's, Lupanov's, Pippenger's problems and their variations as generalizations of the addition chain problem
Vadim Kochergin
- 01 Jan 2022
TL;DR: In this article , various generalizations of the effective exponentiation problem, also known as the addition chains problem in additive terminology, are considered and compared and the methods that were used to obtain them are evaluated and consistently compared.
Speeding up the computations on an elliptic curve using addition-subtraction chains
François Morain,Jorge Olivos +1 more
TL;DR: Notre meilleur algorithme est 11,11% plus rapide que la methode binaire ordinaire and cela permet d'accelerer en consequence les algorithmes de primalite and de factorisation qui utilisent les courbes elliptiques.
Speeding up subgroup cryptosystems
M Martijn Stam
- 01 Jan 2003
TL;DR: The final author version and the galley proof are versions of the publication after peer review that features the final layout of the paper including the volume, issue and page numbers.
References
Optimal multiplication chains for computing a power of a symbolic polynomial
TL;DR: This paper shows that in a certain model of symbolic manipulation of algebraic formulae, the simple method of computing a power of a symbolic polynomial by repeated multiplication by the originalPolynomial is, in essence, the optimal method.
5
•Book
The Art of Computer Programming
Donald Ervin Knuth
- 01 Jan 1968
TL;DR: The arrangement of this invention provides a strong vibration free hold-down mechanism while avoiding a large pressure drop to the flow of coolant fluid.
Optimal multiplication chains for computing a power of a symbolic polynomial
TL;DR: In this paper, it was shown that in a certain model of symbolic manipulation of algebraic formulae, the simple method of computing a power of a symbolic polynomial by repeated multiplication by the original polynomial is, in essence, the optimal method.