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A class of algorithm, abbreviated ECPP, which provides certificates of primality using sophisticated results from the theory of Elliptic Curves. A detailed description and list of references are given by Atkin and Morain (1990, 1993).
Adleman and Huang (1987) designed an independent algorithm using elliptic curves of genus two.
See also Atkin-Goldwasser-Kilian-Morain Certificate, Elliptic Curve Factorization Method, Elliptic Pseudoprime
References
Adleman, L. M. and Huang, M. A. ``Recognizing Primes in Random Polynomial Time.'' In Proc. 19th STOC,
New York City, May 25-27, 1986. New York: ACM Press, pp. 462-469, 1987.
Atkin, A. O. L. Lecture notes of a conference, Boulder, CO, Aug. 1986.
Atkin, A. O. L. and Morain, F. ``Elliptic Curves and Primality Proving.'' Res. Rep. 1256, INRIA, June 1990.
Atkin, A. O. L. and Morain, F. ``Elliptic Curves and Primality Proving.'' Math. Comput. 61, 29-68, 1993.
Bosma, W. ``Primality Testing Using Elliptic Curves.'' Techn. Rep. 85-12, Math. Inst., Univ. Amsterdam, 1985.
Chudnovsky, D. V. and Chudnovsky, G. V. ``Sequences of Numbers Generated by Addition in Formal Groups and
New Primality and Factorization Tests.'' Res. Rep. RC 11262, IBM, Yorktown Heights, NY, 1985.
Cohen, H. Cryptographie, factorisation et primalité: l'utilisation des courbes elliptiques.
Paris: C. R. J. Soc. Math. France, Jan. 1987.
Kaltofen, E.; Valente, R.; and Yui, N. ``An Improved Las Vegas Primality Test.'' Res. Rep. 89-12, Rensselaer
Polytechnic Inst., Troy, NY, May 1989.