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Issue No.10 - October (2008 vol.57)
pp: 1435-1438
Ortal Arazi , The University of Tennessee, Knoxville
ABSTRACT
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.
INDEX TERMS
Number-theoretic computations, Public key cryptosystems
CITATION
Ortal Arazi, "On Calculating Multiplicative Inverses Modulo $2^{m}$", IEEE Transactions on Computers, vol.57, no. 10, pp. 1435-1438, October 2008, doi:10.1109/TC.2008.54
REFERENCES
[1] P. Montgomery, “Modular Multiplication without Trial Division,” Math. Computation, vol. 44, pp. 519-521, 1985.
[2] J. Tudor, “An Algorithm for Exact Division,” J. Symbolic Computation Archive, vol. 15, pp. 169-180, Feb. 1993.
[3] S.R. Dusse and B.S. Kaliski, “A Cryptographic Library for the Motorola DSP5600,” Advances in Cryptology, Proc. Ann. EuroCrypt Conf., pp. 230-244, 1990.
[4] J.L. Massey, “Cryptography: Fundamentals and Applications,” Advanced Technology Seminars, Feb. 1993.
[5] B.S. Kaliski, “The Montgomery Inverse and Its Applications,” IEEE Trans. Computers, vol. 44, no. 8, pp. 1064-1065, Aug. 1995.
[6] E. Savas and Ç.K. Koç, “The Montgomery Modular Inverse—Revised,” IEEE Trans. Computers, vol. 49, no. 7, pp. 763-766, July 2000.
[7] D. Matula, A. Fit-Florea, and M. Thornton, “Table Lookup Structures for Multiplicative Inverses Modulo 2/Sup k,” Proc. 17th IEEE Symp. Computer Arithmetic, pp. 156-163, June 2005.
19 ms
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