1 Montgomery Modular Multiplication in Hard- ware

FEI KEMT
[81] Lenstra, A. K., and H. W. Lenstra, J., Eds. The Development of the
Number Field Sieve. Lecture Notes in Math. Volume 1554. Springer, 1993.
[82] Lenstra, H. W. Factoring Integers with Elliptic Curves. Annals of Mathe-
matics 126, 2 (1987), 649–673.
[83] Lim, D., Ranasinghe, D. C., Devadas, S., Jamali, B., Abbott, D.,
and Coleb, P. H. Exploiting metastability and thermal noise to build a
re-configurable hardware random number generator. In Noise in Devices and
Circuits III; Proceedings of SPIE (Texas, USA, May 2005), vol. 5844, pp. 294–
309.
[84] MacKay, D. J. C. Introduction to Monte Carlo methods. In Learning in
Graphical Models, M. I. Jordan, Ed., NATO Science Series. Kluwer Academic
Press, 1998, pp. 175–204.
[85] McIvor, C., McLoone, M., McCanny, J., Daly, A., and Marnane,
W. Fast montgomery modular multiplication and rsa cryptographic proces-
sor architectures. In 37th IEEE Computer Society Asilomar Conference on
Signals, Systems and Computers (Monterey, USA, Nov. 2003), pp. 379–384.
[86] Menezes, J. A., Oorschot, P. C., and Vanstone, S. A. Handbook of
Applied Cryptography. CRC Press, New York, Oct. 1996.
[87] Miller, V. S. Use of elliptic curves in cryptography. In Lecture notes
in computer sciences; 218 on Advances in cryptology—CRYPTO 85 (1986),
Springer-Verlag New York, Inc., pp. 417–426.
[88] Montgomery, P. Modular Multiplication without Trial Division. Mathe-
matics of Computation 44, 170 (April 1985), 519–521.
[89] Montgomery, P. Speeding up the Pollard and elliptic curve methods of
factorization. Mathematics of Computation 48 (1987), 243–264.
[90] NEC Corporation. Preliminary User’s Manual System-on-Chip Lite, De-
velopment Board, Hardware, Document No. A15650EE1V0UM00, July 2001.
Available at http://www.ee.nec.de/_pdf/A15650EE1V0UM00.PDF.
[91] organization = Federal Information Processing Standards, Na-
tional Institute of Standards and Technology, U.S. Department
135