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Almost all primes can be quickly certified
Open accessAbstract
This paper presents a new probabilistie primality test.Upon termination the test outputs "composite" or "prime", along with a short proof of correctness, which can be verified in deterministic polynomial time.The test is different from the tests of Miller [M], Solovay-Strassen [SSI, and Rabin [R] in that its assertions of primality are certain, rather than being correct with high probability or dependent on an unproven assumption.Thc test terminates in expected polynomial time on all but at most an exponentially vanishing fraction of the inputs of length k, for every k.This result implies:• There exist an infinite set of primes which can be recognized in expected polynomial time.• Large certified primes can be generated in expected polynomial time.Under a very plausible condition on the distribution of primes in "small" intervals, the proposed algorithm can be shown'to run in expected polynomial time on every input.
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Cites
The Arithmetic of Elliptic Curves
Silverman, J. H. (1986) · Graduate Texts in Mathematics · doi:10.1007/978-1-4757-1920-8 · Cited by 4,044
Cited by
Handbook of applied cryptography
(1997) · Choice Reviews Online · doi:10.5860/choice.34-4512 · Cited by 10,357
The Arithmetic of Elliptic Curves
Silverman, J. H. (1986) · Graduate Texts in Mathematics · doi:10.1007/978-1-4757-1920-8 · Cited by 4,044
Minimum disclosure proofs of knowledge
Brassard, G., Chaum, D., & Crépeau, C. (1988) · Journal of Computer and System Sciences · doi:10.1016/0022-0000(88)90005-0 · Cited by 959
Agrawal, M., Kayal, N., & Saxena, N. (2004) · Annals of Mathematics · doi:10.4007/annals.2004.160.781 · Cited by 931
The State of Elliptic Curve Cryptography
Koblitz, N., Menezes, A., & Vanstone, S. (2000) · Designs, Codes and Cryptography · doi:10.1023/a:1008354106356 · Cited by 685
Metadata
- Authors
- Goldwasser, S., & Kilian, J.
- Venue
- Proceedings of the eighteenth annual ACM symposium on Theory of computing - STOC '86
- Publisher
- ACM Press
- Published
- 1986
- Pages
- 316-329
- OpenAlex
- W2081882878
- Cited by
- 198
- References
- 1
- FWCI
- 7.33
- Type
- conference paper
- Language
- en
- Open access
- gold
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- Goldwasser, S., & Kilian, J. (1986). Almost all primes can be quickly certified. Proceedings of the eighteenth annual ACM symposium on Theory of computing - STOC '86. https://doi.org/10.1145/12130.12162
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