Elliptic curves, primality proving and some Titanic primes
Journées arithmétiques de Luminy 17-21 Juillet 1989, Astérisque, no. 198-199-200 (1991), pp. 245-251.
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     author = {Morain, Fran\c{c}ois},
     title = {Elliptic curves, primality proving and some {Titanic} primes},
     booktitle = {Journ\'ees arithm\'etiques de Luminy 17-21 Juillet 1989},
     editor = {Lachaud Gilles},
     series = {Ast\'erisque},
     pages = {245--251},
     publisher = {Soci\'et\'e math\'ematique de France},
     number = {198-199-200},
     year = {1991},
     mrnumber = {1144327},
     zbl = {0760.11041},
     language = {en},
     url = {http://www.numdam.org/item/AST_1991__198-199-200__245_0/}
}
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Morain, François. Elliptic curves, primality proving and some Titanic primes, dans Journées arithmétiques de Luminy 17-21 Juillet 1989, Astérisque, no. 198-199-200 (1991), pp. 245-251. http://www.numdam.org/item/AST_1991__198-199-200__245_0/

[1] L. M. Adleman, M. A. Huang. Recognizing primes in random polynomial time. Proc. CRYPTO 86.

[2] L. M. Adleman, C. Pomerance, R. S. Rumely. On distinguishing prime numbers from composite numbers. Annals of Math., 117, 1983, pp. 173-206. | DOI | MR | Zbl

[3] L. Adleman, R. L. Rivest, A. Shamir. A method for obtaining digital signatures and public-key cryptosystems. Comm. of the ACM, 21, 2, 1978, pp. 120-126. | DOI | MR | Zbl

[4] A. O. L. Atkin, F. Morain. Elliptic curves and primality proving. Submitted. | MR | Zbl

[5] W. Bosma, M.-P. Van Der Hulst. Faster primality testing. To appear in Proc. Eurocrypt'89. | Zbl

[6] J. Brillhart, D. H. Lehmer, J. L. Selfridge. New primality criteria and factorizations of 2 m ± 1 . Math. of Comp., 29, 130, 1975, pp. 620-647. | MR | Zbl

[7] J. W. S. Cassels. Diophantine equations with special references to elliptic curves. J. London Math. Soc, 41, 1966, pp. 193-291. | DOI | MR | Zbl

[8] D. V. Chudnovsky, G. V. Chudnovsky. Sequences of numbers generated by addition in formal groups and new primality and factorization tests. Research report RC 11262, IBM, Yorktown Heights, 1985. Also appeared in Advances in Applied Mathematics, 7, pp. 385-434. | MR | Zbl

[9] H. Cohen, H. W. Lenstra, Jr. Primality testing and Jacobi sums. Math. of Comp., 42, 165, 1984, pp. 297-330. | DOI | MR | Zbl

[10] H. Cohen, A. K. Lenstra. Implementation of a new primality test. Math. of Comp., 48, 177, 1987, pp. 103-121. | DOI | MR | Zbl

[11] S. Goldwasser, J. Kilian. Almost all primes can be quickly certified. Proc. 18th STOC, Berkeley, 1986, pp. 316-329.

[12] J.-C. Hervé, F. Morain, D. Salesin, B. Serpette, J. Vuillemin, P. Zimmermann. BigNum : A Portable and Efficient Package for Arbitrary-Precision Arithmetic. Rapport Technique INRIA, to appear, 1989.

[13] D. Husemöller. Elliptic curves. GTM 111, Springer, 1987. | MR | Zbl

[14] E. Kaltofen, N. Yui. Explicit construction of the Hilbert class fields of imaginary quadratic fields with class numbers 7 and 11. Proc. EUROSAM '84, Cambridge, England, 1984, pp. 310-320. | DOI | MR | Zbl

[15] E. Kaltofen, N. Yui. Explicit construction of the Hilbert class fields of imaginary quadratic fields by integer lattice reduction. Renseelaer Polytechnic Institute Research Report 89-13, May 1989. | Zbl

[16] H. W. Lenstra, Jr.Elliptic curves and number theoretic algorithms. Report 86-19, Math. Inst., Univ. Amsterdam 1986. | Zbl

[17] H. W. Lenstra, Jr. Factoring integers with elliptic curves. Annals of Math., 126, 1987, pp. 649-673. | DOI | MR | Zbl

[18] F. Morain. Implementation of the Atkin-Goldwasser-Kilian primality testing algorithm. Rapport de Recherche INRIA, 911, Octobre 1988.

[19] F. Morain. Construction of Hilbert class fields of imaginary quadratic fields and dihedral equations modulo p. Rapport de Recherche INRIA, 1087, Septembre 1989.

[20] F. Morain. Atkin's test : news from the front. To appear in Proc. Eurocrypt '89. | MR | Zbl

[21] P. Ribenboim. The book of prime number records. Springer, 1988. | DOI | MR | Zbl

[22] R. Schoof. Elliptic curves over finite fields and the computation of square roots mod p. Math. of Comp., 44, 1985, pp. 483-494. | MR | Zbl

[23] J. T. Tate. The arithmetic of elliptic curves. Inventiones Math., 23, 1974, pp. 179-206. | DOI | EuDML | MR | Zbl

[24] M. C. Wunderlich. A performance analysis of a simple prime-testing algorithm. Math. of Comp., 40, 162, 1983, pp. 709-714. | DOI | MR | Zbl

[25] S. Yates. Titanic primes. J. Recr. Math., 16, 1983/84, pp. 250-260. | MR | Zbl