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Easy numbers for the elliptic curve primality proving algorithm
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Source International Conference on Symbolic and Algebraic Computation archive
Papers from the international symposium on Symbolic and algebraic computation table of contents
Berkeley, California, United States
Pages: 263 - 268  
Year of Publication: 1992
ISBN:0-89791-489-9
Author
Sponsors
SIGSAM: ACM Special Interest Group on Symbolic and Algebraic Manipulation
SIGNUM: ACM Special Interest Group on Numerical Mathematics
Publisher
ACM  New York, NY, USA
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REFERENCES

Note: OCR errors may be found in this Reference List extracted from the full text article. ACM has opted to expose the complete List rather than only correct and linked references.

 
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L. M. ADLEMAN, C. POMERANCE, AND R. S. RUMELY. On distinguishing prime numbers from composite numbers. Annals of Math. 117 (1983), 173-206.
 
2
A. O. L. ATKIN AND F. MORAIN. Elliptic curves and primality proving. Research Report 1256, INRIA, Juin 1990. Submitted to Math. Comp.
 
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A. O. L. ATKIN AND F. MORAIN. Finding suitable curves for the elliptic curve method of factorization. To appear in Mathematics of Computation. Also available as INRIA Research Report no 1547, M arch 1991.
 
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W. BOSMA. Primality testing using elliptic curves. Tech. Rep. 85-12, Math. Instituut, Universiteit van Amsterdam, 1985.
 
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J. BRILLIIART, D. H. LEHMER, AND J. L. SELFRIDGE. New primality criteria and factorizations of 2m\plusmn1. Math. Comp. 29, 130 (1975), 620-647.
 
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J. BRILLHART, D. H. LEHMER, J. L. SELFRIDGE, B. TUCKERMAN, AND S. S. WAGSTAFF, JR. Factorizations of bn 1, b = 2, 3, 5, 6, 7, 10, 11, 12 up to high powers, 2 ed. No. 22 in Contemporary Mathematics. AMS, 1988.
 
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8
H. COHEN AND A. K. LENSTRA. Implementation of a new primality test. Math. Comp. 48, 177 (1987), 103-121.
 
9
H. COHEN AND H. W. LENSTRA, JR. Primality testing and Jacobi sums. Math. Comp. 42, 165 (1984), 297-330.
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A. K. LENSTRA, H. W. LENSTRA, JR., M. S. MANASSE, AND J. M. POLLARD. The factorization of the ninth Fermat number. To appear, 1991.
 
13
F. MORAIN. Courbes elliptiqu.es et tests de primalitd. PhD thesis, Universit~. Claude Bernard-Lyon I, Septembre 1990.
 
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F. MORAIN. Elliptic curves, primality proving and some Titanic primes. In Journ~es Arthm~tiques I989 (1992), vol. 198-199-200 of Ast~risque, SMF, pp. 245-251.
 
16
F. MORAIN. Prime values of partition numbers and some new large primes, in preparation, Apr. 1992.
 
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J. M. POLLARD. Theorems on factoriza.- tion and prima.lity testing. Proc. Cambr. Philos. Soc. 76 (1974), 521--528.
 
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P. RIBENBOIM. The book of prime number records, 2nd ed. Springer, 1989.
 
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M. C. WUNDERLICH. A performance analysis of a simple prime-testing algorithm. Math. Comp. 40, 162 (1983), 709- 714.


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