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Old 2019-09-10, 16:35   #1
a1call
 
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"Rashid Naimi"
Oct 2015
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Default Power-Modulation Mechanics

Hi all,

I am starting this thread in the hopes of getting some insights in the mechanics of Power-Modulation.
I did try to decipher below:
https://en.wikipedia.org/wiki/Modular_exponentiation

For the sake of argument suppose that there exists a Black-Box that can perform exponentiation instantly but has limited memory and can not perform Modular arithmetic. In other words it can only raise a base to some power as long as it does not run out of memory. By utilizing such a Black-Box how much faster can a regular computer perform PwerMod of 1M-dd exponent?
Would that be a significant speed-up?

Thanks in advance.
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Old 2019-09-11, 00:32   #2
a1call
 
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"Rashid Naimi"
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To clarify, another way of asking the same question is:
* It would probably take a few hours to Fermat-Primality-Test a 1M-dd candidate.
* Is bulk of the elapsed time spent raising bases to the necessary intermediate powers or else for modular calculations. I assume the answer is the former. Is that correct?
Thanks again in advance.
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