REFERENCES for the Atkin Morain method, Hilbert class polynomials, elliptic curves and Number Theory :-


[1] 'Elliptic Curves in Cryptography' by Blake, Seroussi, Smart.
London Mathematical Society Lecture Note Series #265.
ISBN 0-521-65374-6.

[2] 'Guide to Elliptic Curve Cryptography' by Hankerson, Menezes, Vanstone.
Springer-Verlag ISBN 0-387-95273-X.

[3] 'Prime Numbers A Computational Perspective' by Crandall, Pomerance.
Springer-Verlag ISBN 0-387-94777-9.

[4] 'Software Implementation of the NIST Elliptic Curves over Prime Fields'
by M.Brown, D.Hankerson, J.Lopez and A.Menezes [LNCS 2020]

[5] 'Elliptic Curves and Primality Proving.'
by A.O.L. Atkin and F. Morain [Mathematics of Computation, Vol. 61, No 203, July 1993]

[6] 'Elliptic Curve Public Key Cryptosystems.' by A.J. Menezes
Kluwer Academic Publishers ISBN 0-7923-9368-6.

Speed/Tuning References :-

[7] 'The Software Optimization Cookbook' by Gerber, Bik, Smith & Tian.
Intel Press, ISBN 0-9764832-1-1.
[A later version of this book has appeared, but I do not have it.]

[8] 'Software Optimization Guide for AMD64 Processors'
AMD publication 25112, Revision 3.06, Sept 2005. (Downloadable)
[Similar documents for all AMD & Intel  processors are available free - check their websites.]

General Number Theory References :-

[9] 'Algorithmic Number Theory - Vol 1' by Bach and Shallit.
MIT Press, ISBN 0-262-02405-5.

[10] 'A Course in Computational Algebraic Number Theory' by Cohen
Springer; Graduate Texts in Mathematics, GTM 138
ISBN 3-540-55640-0

[11] 'The Art of Computer Programming, Vol 2, Seminumerical Algorithms'
Donald Knuth, Addison Wesley, ISBN 0-201-89684-2

[12] 'A Course in Number Theory and Cryptography' 2nd Edition
Neal Koblitz, Springer, Graduate Texts in Mathematics GTM 114 ISBN 0-201-89684-2

[13] 'The Design and Analysis of Computer Algorithm's'
A. Aho, J. Hopcroft, and J. Ullman. Addison Wesley (1974)

[14] "Groups, Rings and Fields" by D.A.R.Wallace
Springer Undergraduate Mathematics Series. ISBN 3-540-76177-2

[15] "Prime Numbers - a Computational Perspective" by Crandall and Pomerance
Springer Verlag. ISBN 0-387-94777-9

[16] "Handbook of Applied Cryptography" by A.J. Menezes, P.C. van Oorschot, S.A. Vanstone;
CRC Press, ISBN 0-8493-8523-7

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