Some remarks on parallel exponentiation (extended abstract)

Authors:
Michael Nöcker
Affiliations:
Fachbereich 17 Mathematik-Informatik, Universität Paderborn, D-33095 Paderborn, Germany
Venue:
ISSAC '00 Proceedings of the 2000 international symposium on Symbolic and algebraic computation
Year:
2000

Citing 10
Cited 0

Fast exponentiation in GF(2n)

Lecture Notes in Computer Science on Advances in Cryptology-EUROCRYPT'88
A bridging model for parallel computation

Communications of the ACM
Low complexity normal bases

Discrete Applied Mathematics
Some observations on parallel algorithms for fast exponentiation in GF(2n)

SIAM Journal on Computing
The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms

The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
A survey of fast exponentiation methods

Journal of Algorithms
Modern computer algebra

Modern computer algebra
New Algorithms and Lower Bounds for the Parallel Evaluation of Certain Rational Expressions and Recurrences

Journal of the ACM (JACM)
Gauss Periods and Fast Exponentiation in Finite Fields (Extended Abstract)

LATIN '95 Proceedings of the Second Latin American Symposium on Theoretical Informatics
Fast Key Exchange with Elliptic Curve Systems

CRYPTO '95 Proceedings of the 15th Annual International Cryptology Conference on Advances in Cryptology

Quantified Score

Hi-index	0.00

Visualization

Abstract

We present a lower bound on parallel exponentiation in the model of weighted q-addition chains which neglects communication. We derive an algorithm which covers results of Kung [9] and von zur Gathen [13]. For an actual implementation the (fixed) number of processors and the communication delay have to be taken into account. We develop strategies for this scenario—inspired by the results on weighted q-addition chains—for parallel exponentiation using the BSP-model of Valiant [12]. The latter results are illustrated by implementations of different basis representations for finite fields.