Two infinite sets of primes with fast primality tests

Janos Pintz, William L. Steiger, E. Szemerédi

Research output: Chapter in Book/Report/Conference proceedingConference contribution

2 Citations (Scopus)

Abstract

Infinite sets P and Q of primes are described, p ⊂ Q. For any natural number n it can be decided if n∈ p in (deterministic) time O((log n 9). This answers affirmatively the question of whether there exists an infinite set of primes whose membership can be tested in polynomial time, and is the main result of the paper. Also, for every n∈Q.we show how to produce at random, in expected time O((log n)3), a certificate of length O(logn) which can be verified in (deterministic) time O((log n) 3); this is less than the time needed for two exponentiations and is much faster than existing methods. Finally it is important that P is relatively dense (at least cn1/3logn elements less than n). Elements of Q in a given range may be generated quickly, but it would be costly for an adversary to search Qin this range; this could be useful in cryptography.

Original languageEnglish
Title of host publicationProceedings of the Annual ACM Symposium on Theory of Computing
PublisherAssociation for Computing Machinery
Pages504-509
Number of pages6
ISBN (Print)0897912640, 9780897912648
DOIs
Publication statusPublished - 1988
Event20th Annual ACM Symposium on Theory of Computing, STOC 1988 - Chicago, IL, United States
Duration: May 2 1988May 4 1988

Other

Other20th Annual ACM Symposium on Theory of Computing, STOC 1988
CountryUnited States
CityChicago, IL
Period5/2/885/4/88

Fingerprint

Cryptography
Polynomials

ASJC Scopus subject areas

  • Software

Cite this

Pintz, J., Steiger, W. L., & Szemerédi, E. (1988). Two infinite sets of primes with fast primality tests. In Proceedings of the Annual ACM Symposium on Theory of Computing (pp. 504-509). Association for Computing Machinery. https://doi.org/10.1145/62212.62261

Two infinite sets of primes with fast primality tests. / Pintz, Janos; Steiger, William L.; Szemerédi, E.

Proceedings of the Annual ACM Symposium on Theory of Computing. Association for Computing Machinery, 1988. p. 504-509.

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Pintz, J, Steiger, WL & Szemerédi, E 1988, Two infinite sets of primes with fast primality tests. in Proceedings of the Annual ACM Symposium on Theory of Computing. Association for Computing Machinery, pp. 504-509, 20th Annual ACM Symposium on Theory of Computing, STOC 1988, Chicago, IL, United States, 5/2/88. https://doi.org/10.1145/62212.62261
Pintz J, Steiger WL, Szemerédi E. Two infinite sets of primes with fast primality tests. In Proceedings of the Annual ACM Symposium on Theory of Computing. Association for Computing Machinery. 1988. p. 504-509 https://doi.org/10.1145/62212.62261
Pintz, Janos ; Steiger, William L. ; Szemerédi, E. / Two infinite sets of primes with fast primality tests. Proceedings of the Annual ACM Symposium on Theory of Computing. Association for Computing Machinery, 1988. pp. 504-509
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