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Issue No. 10 - October (2008 vol. 57)
ISSN: 0018-9340
pp: 1435-1438
Hairong Qi , The University of Tennessee, Knoxville
Ortal Arazi , The University of Tennessee, Knoxville
A need to calculate modular multiplicative inverses that involve a power of 2 arises in various number theory and cryptography applications. Known algorithms that perform these calculations involve a number of steps, linearly proportional to the number of characters in a given number. The character can be a single bit or a binary word of any standard size. This letter presents an efficient methodology for a character-based computation of modular multiplicative inverses, efficient at any given base, reducing these calculations to a logarithmic number of steps. Hence, the amount of calculations involved and the computational resources are dramatically decreased from an O(m) complexity to a O(logm) complexity, where m denotes the number of characters in the operand.
Number-theoretic computations, Public key cryptosystems
Hairong Qi, Ortal Arazi, "On Calculating Multiplicative Inverses Modulo $2^{m}$", IEEE Transactions on Computers, vol. 57, no. , pp. 1435-1438, October 2008, doi:10.1109/TC.2008.54
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