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The Montgomery Inverse and Its Applications
August 1995 (vol. 44 no. 8)
pp. 1064-1065

Abstract— The Montgomery inverse of b modulo a is b−12n mod a, where n is the number of bits in a. The right-shifting binary algorithm for modular inversion is shown naturally to compute the new inverse in fewer operations than the ordinary modular inverse. The new inverse facilitates recent work by Koç on modular exponentiation and has other applications in cryptography.

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Burton S. Kaliski, "The Montgomery Inverse and Its Applications," IEEE Transactions on Computers, vol. 44, no. 8, pp. 1064-1065, Aug. 1995, doi:10.1109/12.403725
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