G. L. Miller, "Riemann's hypothesis and tests for primality", Seventh Annual ACM Symposium on the Theory of Computing, pp. 234--239, 1975 Home/Search Document Not in Database Summary Related Articles Check |
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PRIMES is in P - Agrawal, Kayal, Saxena (2002) (11 citations) (Correct)
....for any prime number p, and any number a not divisible by p, a p 1 = 1 (mod p) Although the converse of this theorem does not hold (and in fact fails spectacularly for Carmichael numbers) this result has been the starting point for several e#cient primality testing algorithms. In 1976, Miller [Mil76] used this property to obtain a deterministic polynomial time algorithm for primality testing assuming Extended Riemann Hypothesis (ERH) His test was modified by Rabin [Rab80] to yield an unconditional but randomized polynomial time algorithm. Solovay and Strassen [SS77] obtained another ....
G. L. Miller. Riemann's hypothesis and tests for primality. J. Comput. Sys. Sci., 13:300--317, 1976.
Dynamic Logic - Harel, Kozen, Tiuryn (1984) (356 citations) (Correct)
.... There is wide interest recently in programs that employ probabilistic moves such as coin tossing or random number draws and whose behavior is described probabilistically (for example, is correct if it does what it is meant to do with probability 1) To give one well known example taken from [Miller, 1976] and [Rabin, 1980] there are fast probabilistic algorithms for checking primality of numbers but no known fast nonprobabilistic ones. Many synchronization problems including digital contract signing, guaranteeing mutual exclusion, etc. are often solved by probabilistic means. This interest has ....
G. L. Miller. Riemann's hypothesis and tests for primality. J. Comput. Syst. Sci., 13:300--317, 1976.
Simple Backdoors for RSA Key Generation - Crepeau, Slakmon (2002) (Correct)
....verification procedure of messages m, c, 1 n 1. Wiener [13] demonstrated that small private exponents may be e#ciently recovered if d .25 3 and this result was recently improved by Boneh and Durfee [1] who showed a similar result for d n .292 . Moreover, it is a well known fact [8] that given a multiple of #(n) such as 1 satisfying de 1 (mod #(n) it is easy to factor n. Boneh, Durfee and Frankel [2] recently demonstrated two interesting results allowing to recover the whole of d given a small e, n and parts of d. Let n = pq such that p q 4 be an RSA moduli. We use ....
G. L. Miller, Riemann's hypothesis and tests for primality, J. Comput. System Sci., 13 (1976), pp. 300--317.
Computing the RSA Secret Key is Deterministic Polynomial Time.. - May (2004) (2 citations) (Correct)
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G. L. Miller, "Riemann's hypothesis and tests for primality", Seventh Annual ACM Symposium on the Theory of Computing, pp. 234--239, 1975
How to Copyright a Function? - Published In Imai (Correct)
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G. Miller, Riemann's hypothesis and tests for primality, Journal of computer and system sciences, vol. 13, pp. 300--317, 1976.
How to Copyright a Function? - Published In Imai (Correct)
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G. Miller, Riemann's hypothesis and tests for primality, Journal of computer and system sciences, vol. 13, pp. 300--317, 1976.
Deterministic Polynomial Time Equivalence of Computing the RSA.. - Coron, May (2004) (Correct)
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G. L. Miller, "Riemann's hypothesis and tests for primality", Seventh Annual ACM Symposium on the Theory of Computing, pp. 234--239, 1975
A Note on Shor's Quantum Algorithm for Prime Factorization - Cao (2005) (Correct)
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G.L. Miller. Riemann's hypothesis and tests for primality. J. Comput. System Sci., 13, pp. 300-317. 1976.
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G.L. Miller. Riemann's hypothesis and tests for primality. Journal of Compter and System Sciences, 13:300--317, 1976.
How to Copyright a Function? - Published In Imai (Correct)
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G. Miller, Riemann's hypothesis and tests for primality, Journal of computer and system sciences, vol. 13, pp. 300--317, 1976.
Deterministic Polynomial Time Equivalence of Computing the RSA.. - Coron, May (2004) (Correct)
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G. L. Miller, "Riemann's hypothesis and tests for primality", Seventh Annual ACM Symposium on the Theory of Computing, pp. 234--239, 1975
Primality and Identity Testing via Chinese Remaindering - Agrawal, Biswas (2003) (1 citation) (Correct)
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G. L. Miller. Riemann's hypothesis and tests for primality. J. Comput. Sys. Sci., 13:300-317, 1976.
PRIMES is in P - Agrawal, Kayal, Saxena (2002) (11 citations) (Correct)
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G. L. Miller. Riemann's hypothesis and tests for primality. J. Comput. Sys. Sci., 13:300-317, 1976.
PRIMES is in P - Agrawal, Kayal, Saxena (2002) (11 citations) (Correct)
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G. L. Miller. Riemann's hypothesis and tests for primality. J. Comput. Sys. Sci., 13:300--317, 1976.
RSA Problem - Rivest (2003) (Correct)
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Gary L. Miller. Riemann's hypothesis and tests for primality. Journal of Computer and Systems Sciences, 13(3):300--317, 1976. 9
A Lower Bound for Primality - Eric Allender Dept (1999) (2 citations) (Correct)
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G. Miller, Riemann's hypothesis and tests for primality, J. Comput. System Sci. 13 (1976), 300--317.
How to Copyright a Function? - Naccache, Shamir, Stern (1999) (1 citation) (Correct)
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G. Miller, Riemann's hypothesis and tests for primality, Journal of computer and system sciences, vol. 13, pp. 300--317, 1976.
Derandomization That is Rarely Wrong From Short Advice.. - Goldreich, Wigderson (2002) (Correct)
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G.L. Miller. Riemann's Hypothesis and Tests for Primality. JCSS, Vol. 13, pages 300--317, 1976.
Are `Strong' Primes Needed for RSA? - Rivest, Silverman (1999) (1 citation) (Correct)
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Gary L. Miller. Riemann's hypothesis and tests for primality. JCSS, 13(3):300--317, 1976.
How to Copyright a Function? - Published In Imai (Correct)
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G. Miller, Riemann's hypothesis and tests for primality, Journal of computer and system sciences, vol. 13, pp. 300--317, 1976.
Distributed Cooperation during the Absence of Communication - Malewicz, Russell.. (2001) (3 citations) (Correct)
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Miller, G.L.: Riemann's Hypothesis and Tests for Primality. Journal of Computer and Systems Sciences, Vol. 13 (1976) 300--317
PKCS #1: RSA Encryption - Version 1.5 - Kaliski (1998) (Correct)
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G.L. Miller. Riemann's hypothesis and tests for primality. Journal of Computer and Systems Sciences, 13(3):300-307, 1976.
A Note on Monte Carlo Primality Tests and Algorithmic.. - Chaitin, Schwartz (1978) (3 citations) (Correct)
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Miller, G. L., Riemann's hypothesis and tests for primality, J. Comput. Syst. Sci. 13, 1976, pp. 300--317.
Unknown - (Correct)
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Miller, Gary L., \Riemann's Hypothesis and Tests for Primality," J. Comput. System Sci. 13 (1976), no. 3, 300-317.
A Signature Scheme with Efficient Protocols - Camenisch, Lysyanskaya (2002) (2 citations) (Correct)
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G. L. Miller. Riemann's hypothesis and tests for primality. Journal of Computer and System Sciences, 13:300--317, 1976.
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