References

THE ELLIPTIC CURVES OVER FINITE FIELDS


[1] A. O. L. Atkin and F. Moralin, Elliptic curves and primality proving, Math. Comp. 61 (1993), 29-68.

[2] B. Gezer, H. Özden, A. Tekcan and O. Bizim, The number of rational points on elliptic curves over finite fields, Int. J. Comp. Math. Sci. 1(3) (2007), 178-184.

[3] S. Goldwasser and J. Kilian, Almost all primes can be quickly certified, Proc.18th STOC (Berkeley, May 28-30, 1986), ACM, New York, (1986), 316-329.

[4] N. Koblitz, A elliptic curve cryptosystems, Math. Comp. 177(48) (1987), 203-209.

[5] N. Koblitz, A Course in Number Theory and Cryptography, Springer-Verlag, 1994.

[6] F. Lemmermeyer and R. A. Mollin, On the Tate-Shafarevich groups of Acta Math. Universitatis Comenianae 72(1) (2003), 73-80.

[7] H. W. Jr. Lenstra, Factoring integers with elliptic curves, Ann. Math. 126(3) (1987), 649-673.

[8] V. S. Miller, Use of elliptic curves in cryptography, in advances in cryptology-CRYPTO 85, Lecture Notes in Comp. Sci. 218 (1986), 417-426.

[9] R. A. Mollin, An Introduction to Cryptography, Chapman & Hall/CRC, 2001.

[10] L. J. Mordell, On the rational solutions of the indeterminate equations of the third and fourth degrees, Proc. Cambridge Philos. Soc. 21 (1922), 179-192.

[11] J. H. Silverman, The Arithmetic of Elliptic Curves, Springer-Verlag, 1986.

[12] J. H. Silverman and J. Tate, Rational Points on Elliptic Curves, Undergraduate Texts in Mathematics, Springer, 1992.

[13] A. Tekcan, The elliptic curves over Int. J. Comp. Math. Sci. 1(3) (2007), 165-171.

[14] A. Tekcan, The number of rational points on singular curves over finite fields Int. J. Comp. Math. Sci. 3(1) (2009), 14-17.

[15] A. Tekcan, The elliptic curves Accepted for publication to Ars. Combinatoria.

[16] L. C. Washington, Elliptic Curves, Number Theory and Cryptography, Chapman & Hall /CRC, Boca London, New York, Washington DC, 2003.

[17] A. Wiles, Modular elliptic curves and Fermat’s last theorem, Ann. Math. 141(3) (1995), 443-551.