Mathematics of Computation

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New frameworks for Montgomery's modular multiplication method

Author(s): Philip B. McLaughlin Jr..
Journal: Math. Comp. 73 (2004), 899-906.
MSC (2000): Primary 11-04, 11Y16; Secondary 11A07, 11T55
Posted: May 7, 2003
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Abstract | References | Similar articles | Additional information

Abstract: We present frameworks for fast modular multiplication based on a modification of Montgomery's original method. For (fixed) large integers, our algorithms may be significantly faster than conventional methods. Our techniques may also be extended to modular polynomial arithmetic.

References:

1.: Richard Crandall and Barry Fagin, Discrete weighted transforms and large-integer arithmetic, Math. Comp. 62 (1994), 305-324. MR 94c:11123
2.: Donald E. Knuth, The Art of Computer Programming, Volume 2: Seminumerical Algorithms (3rd ed.), Addison-Wesley, Boston, MA, 1998. MR 83i:68003
3.: Peter L. Montgomery, Modular multiplication without trial division, Math. Comp. 44 (1985), 519-521. MR 86e:11121
4.: Peter L. Montgomery, Speeding the Pollard and elliptic curve methods of factorization, Math. Comp. 48 (1987), 243-264. MR 88e:11130
5.: H. J. Nussbaumer, Fast Fourier Transform and Convolution Algorithms, (2nd ed.), Springer-Verlag, New York, 1982. MR 83e:65219


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