Elliptic Pseudoprime
Let 
be an Elliptic Curve defined over the Field of Rational Numbers
having equation
with
and 
Integers. Let 
be a point on with integer coordinates and havinginfinite order in the additive group of rational points of , and let 
be a CompositeNatural Number such that 
, where 
is the Jacobi Symbol. Then if
is called an elliptic pseudoprime for 
.See also Atkin-Goldwasser-Kilian-Morain Certificate, Elliptic Curve Primality Proving,Strong Elliptic Pseudoprime
References
Balasubramanian, R. and Murty, M. R. ``Elliptic Pseudoprimes. II.'' In Séminaire de Théorie des Nombres, Paris 1988-1989 (Ed. C. Goldstein). Boston, MA: Birkhäuser, pp. 13-25, 1990. Gordon, D. M. ``The Number of Elliptic Pseudoprimes.'' Math. Comput. 52, 231-245, 1989. Gordon, D. M. ``Pseudoprimes on Elliptic Curves.'' In Théorie des nombres (Ed. J. M. DeKoninck and C. Levesque). Berlin: de Gruyter, pp. 290-305, 1989. Miyamoto, I. and Murty, M. R. ``Elliptic Pseudoprimes.'' Math. Comput. 53, 415-430, 1989. Ribenboim, P. The New Book of Prime Number Records, 3rd ed. New York: Springer-Verlag, pp. 132-134, 1996.
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