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Colin D. Walter, "Exponentiation Using Division Chains," IEEE Transactions on Computers, vol. 47, no. 7, pp. 757765, July, 1998.  
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@article{ 10.1109/12.709375, author = {Colin D. Walter}, title = {Exponentiation Using Division Chains}, journal ={IEEE Transactions on Computers}, volume = {47}, number = {7}, issn = {00189340}, year = {1998}, pages = {757765}, doi = {http://doi.ieeecomputersociety.org/10.1109/12.709375}, publisher = {IEEE Computer Society}, address = {Los Alamitos, CA, USA}, }  
RefWorks Procite/RefMan/Endnote  x  
TY  JOUR JO  IEEE Transactions on Computers TI  Exponentiation Using Division Chains IS  7 SN  00189340 SP757 EP765 EPD  757765 A1  Colin D. Walter, PY  1998 KW  Modular exponentiation KW  bit recoding KW  RSA cryptosystem KW  addition chains KW  mary method KW  mixed basis arithmetic KW  radix representation. VL  47 JA  IEEE Transactions on Computers ER   
Abstract—Exponentiation may be performed faster than the traditional square and multiply method by iteratively reducing the exponent modulo numbers which, as exponents themselves, require few multiplications. This mainly includes those with few nonzero bits. For a suitable choice of such divisors, the resulting mixed basis representation of the exponent reduces the expected number of nonsquaring multiplications by over half at the cost of a single extra register. Preprocessing effort depends entirely on the exponent and can be kept down to the work saved in a single exponentiation. Moreover, no precomputed lookup tables are required, so the method is especially applicable where space is at a premium. In particular, it outperforms the instance of the
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