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Recognizing primes in random polynomial time

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M. HuangAuthors Info & Claims

STOC '87: Proceedings of the nineteenth annual ACM symposium on Theory of computing

Pages 462 - 469

https://doi.org/10.1145/28395.28445

Published: 01 January 1987 Publication History

Abstract

This paper is the first in a sequence of papers which will prove the existence of a random polynomial time algorithm for the set of primes. The techniques used are from arithmetic algebraic geometry and to a lesser extent algebraic and analytic number theory. The result complements the well known result of Strassen and Soloway that there exists a random polynomial time algorithm for the set of composites.

References

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L.M. Adleman and M.A. Huang, Recognizhug Primes in Random Polynomial Time, abstract, 1986.

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L.M. Adleman, C. Pomerance, and R.S. Rumely, On Distinguishing Prime Numbers from Composite Numbers, Armals of Math., 117, (1903), 173-206.

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G. Faltings, Endlichkeitssatze fur abelsche Varietaten uber Zahlkorpern, lawat. Math. 73 (1983), 349-366.

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K.F. Gauss, Disquisitiones Arithmeticae, Leipzig, Fleischer, 1801. Translated into English by A.A. Clark, S.J., Yale University Press, New Haven, 1966.

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S. Goldwasser and 2. Kilian, Almost All Primes can be Quickly Certified, Pro~. 18th ACId Syrup. on Theory of Computing, pp. s16-a20,(1086).

Digital Library

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A. Well, Zum Bewels des Torellischen Satzes, Nachr. Akad. Wiss. Gottingen, Math. Phys, K1 (1957) a3-sa.

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Recognizing primes in random polynomial time

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cover image ACM Conferences

STOC '87: Proceedings of the nineteenth annual ACM symposium on Theory of computing

January 1987

471 pages

ISBN:0897912217

DOI:10.1145/28395

Editor:
Alfred V. Aho

Copyright © 1987 ACM.

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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Published: 01 January 1987

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STOC87: 19th Annual ACM Conference on Theory of Computing

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STOC '87 Paper Acceptance Rate 50 of 165 submissions, 30%;

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

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https://doi.org/10.1007/978-3-662-68290-6_3
Mainzer KKahle RMainzer KKahle R(2022)Theoretische GrenzenGrenzen der KI – theoretisch, praktisch, ethisch10.1007/978-3-662-65011-0_3(57-84)Online publication date: 17-Jun-2022
https://doi.org/10.1007/978-3-662-65011-0_3
Nadezhdin EMurphy NDalchau NPhillips ALocke J(2020)Stochastic pulsing of gene expression enables the generation of spatial patterns in Bacillus subtilis biofilmsNature Communications10.1038/s41467-020-14431-911:1Online publication date: 19-Feb-2020
https://doi.org/10.1038/s41467-020-14431-9
Homer SSelman A(2014)Turing and the development of computational complexityTuring's Legacy10.1017/CBO9781107338579.009(299-328)Online publication date: 5-Jun-2014
https://doi.org/10.1017/CBO9781107338579.009
Williams CWilliams C(2011)Quantum Universality, Computability, & ComplexityExplorations in Quantum Computing10.1007/978-1-84628-887-6_4(201-237)Online publication date: 2011
https://doi.org/10.1007/978-1-84628-887-6_4
Itoh TTakeda M(2007)A simple construction for a family of collision‐intractable hash functionsElectronics and Communications in Japan (Part III: Fundamental Electronic Science)10.1002/ecjc.443076120876:12(77-84)Online publication date: 23-Feb-2007
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Itoh THosokawa T(2007)How intractable is the modified chosen discrete logarithm assumption?Electronics and Communications in Japan (Part III: Fundamental Electronic Science)10.1002/ecjc.443075080975:8(108-114)Online publication date: 22-Feb-2007
https://doi.org/10.1002/ecjc.4430750809
Köbler JBeyersdorff O(2006)Von der Turingmaschine zum Quantencomputer — ein Gang durch die Geschichte der KomplexitätstheorieInformatik10.1007/3-540-32743-6_8(165-195)Online publication date: 2006
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Alon NGoldreich OHåstad JPeralta R(2006)Simple Constructions of Almost k‐wise Independent Random VariablesRandom Structures & Algorithms10.1002/rsa.32400303083:3(289-304)Online publication date: 11-Oct-2006
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Cai JZhu H(2005)Progress in computational complexity theoryJournal of Computer Science and Technology10.1007/s11390-005-0735-420:6(735-750)Online publication date: 1-Nov-2005
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