Abstract
If we are going to be able to implement factorization techniques and primality tests using the arithmetic of elliptic curves, we need a fast way of computing (x, y)#i. Actually, the fastest techniques just compute the first coordinate.
“And there he plays extravagant matches In fitless finger-stalls On a cloth untrue With a twisted cue And elliptical billiard balls.”
- William S. Gilbert (The Mikado, Act II)
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References
Kenneth Ireland and Michael Rosen, A Classical Introduction to Modern Number Theory, Springer-Verlag, New York, 1982.
A. K. Lenstra and H. W. Lenstra, Jr., Algorithms in number theory, University of Chicago, Department of Computer Science, Technical Report # 87-008, 1987.
Peter L. Montgomery, “Speeding the Pollard and Elliptic Curve Methods of Factorization,” Math. of Computation, 48(1987), 243–264.
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© 1989 Springer-Verlag New York, Inc.
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Bressoud, D.M. (1989). Applications of Elliptic Curves. In: Factorization and Primality Testing. Undergraduate Texts in Mathematics. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-4544-5_14
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DOI: https://doi.org/10.1007/978-1-4612-4544-5_14
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