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The Montgomery Modular Inverse-Revisited
July 2000 (vol. 49 no. 7)
pp. 763-766

Abstract—We modify an algorithm given by Kaliski to compute the Montgomery inverse of an integer modulo a prime number. We also give a new definition of the Montgomery inverse, and introduce efficient algorithms for computing the classical modular inverse, the Kaliski-Montgomery inverse, and the new Montgomery inverse. The proposed algorithms are suitable for software implementations on general-purpose microprocessors.

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Index Terms:
Modular arithmetic, modular inverse, almost inverse, Montgomery multiplication, cryptography.
E. Savas, Ç.k. Koç, "The Montgomery Modular Inverse-Revisited," IEEE Transactions on Computers, vol. 49, no. 7, pp. 763-766, July 2000, doi:10.1109/12.863048
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