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The parallel complexity of exponentiating polynomials over finite fields

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F E Fich,

M TompaAuthors Info & Claims

STOC '85: Proceedings of the seventeenth annual ACM symposium on Theory of computing

Pages 38 - 47

https://doi.org/10.1145/22145.22150

Published: 01 December 1985 Publication History

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Cited By

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Lohrey M(2015)Equality Testing of Compressed StringsCombinatorics on Words10.1007/978-3-319-23660-5_2(14-26)Online publication date: 27-Aug-2015
https://doi.org/10.1007/978-3-319-23660-5_2
Ishai YKushilevitz EPaskin-Cherniavsky AGoldwasser S(2012)From randomizing polynomials to parallel algorithmsProceedings of the 3rd Innovations in Theoretical Computer Science Conference10.1145/2090236.2090244(76-89)Online publication date: 8-Jan-2012
https://dl.acm.org/doi/10.1145/2090236.2090244
von zur Gathen J(2005)Parallel arithmetic computations: A surveyMathematical Foundations of Computer Science 198610.1007/BFb0016236(93-112)Online publication date: 10-Jun-2005
https://doi.org/10.1007/BFb0016236
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The parallel complexity of exponentiating polynomials over finite fields

Modular integer exponentiation (given a, e, and m, compute a^e mod m) is a fundamental problem in algebraic complexity for which no efficient parallel algorithm is known. Two closely related problems are modular polynomial exponentiation (given a(x), e, ...

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STOC '85: Proceedings of the seventeenth annual ACM symposium on Theory of computing

December 1985

484 pages

ISBN:0897911512

DOI:10.1145/22145

Chairman:
Robert Sedgewick

Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

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Association for Computing Machinery

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Published: 01 December 1985

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STOC85: Annual ACM Conference on Theory of Computing

May 6 - 8, 1985

Rhode Island, Providence, USA

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Overall Acceptance Rate 1,469 of 4,586 submissions, 32%

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Cited By

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Lohrey M(2015)Equality Testing of Compressed StringsCombinatorics on Words10.1007/978-3-319-23660-5_2(14-26)Online publication date: 27-Aug-2015
https://doi.org/10.1007/978-3-319-23660-5_2
Ishai YKushilevitz EPaskin-Cherniavsky AGoldwasser S(2012)From randomizing polynomials to parallel algorithmsProceedings of the 3rd Innovations in Theoretical Computer Science Conference10.1145/2090236.2090244(76-89)Online publication date: 8-Jan-2012
https://dl.acm.org/doi/10.1145/2090236.2090244
von zur Gathen J(2005)Parallel arithmetic computations: A surveyMathematical Foundations of Computer Science 198610.1007/BFb0016236(93-112)Online publication date: 10-Jun-2005
https://doi.org/10.1007/BFb0016236
Villard GMacCallum M(1994)Fast parallel computation of the Smith normal form of polynomial matricesProceedings of the international symposium on Symbolic and algebraic computation10.1145/190347.190433(312-317)Online publication date: 1-Aug-1994
https://dl.acm.org/doi/10.1145/190347.190433
Adleman LKompella KSimon J(1988)Using smoothness to achieve parallelismProceedings of the twentieth annual ACM symposium on Theory of computing10.1145/62212.62264(528-538)Online publication date: 1-Jan-1988
https://dl.acm.org/doi/10.1145/62212.62264
Gibson J(1988)A generalisation of Brickell's algorithm for fast modular multiplicationBIT10.1007/BF0195489528:4(755-763)Online publication date: 1-Dec-1988
https://dl.acm.org/doi/10.1007/BF01954895

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Power sums of polynomials over finite fields and applications

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The parallel complexity of exponentiating polynomials over finite fields