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The Montgomery and Joye Powering Ladders are Dual

Hitherto the duality between left-to-right and right-to-left exponentiation algorithms has been a loosely defined concept. Recently, the author made the definition precise by adding requirements on space usage and operation types. Here it is shown that the Montgomery and Joye powering ladders are dual in this sense. Several versions of these algorithms are derived naturally with a cost-free, natural, built-in blinding mechanism as a side channel counter-measure.