Power-Modulation Mechanics

a1call · 2019-09-10, 16:35

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.

a1call · 2019-09-11, 00:32

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.

2019-09-10, 16:35	#1
a1call "Rashid Naimi" Oct 2015 Remote to Here/There 2⁶·31 Posts	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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2019-09-11, 00:32	#2
a1call "Rashid Naimi" Oct 2015 Remote to Here/There 2⁶×31 Posts	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.