Abstract
This paper presents a k-ary Montgomery modular inverse algorithm over nonbinary computers by using Sedjelmaci's right shift k-ary greatest common divisor scheme. Over traditional binary computers, Kaliski's scheme can output Montgomery modular inverse Q − 12n mod P, where P is coprime to Q and n is the bit length of P. Over k-ary computers, our algorithm can discover the k-ary Montgomery inverse Q − 1km mod P, where P, Q, and k are pairwise relatively prime positive integers and m = log kP. In the worst case, the computational cost of our algorithm is O(m2)k-ary digit operations. Copyright © 2013 John Wiley & Sons, Ltd.
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