

Notes

Instructions, top: Enter numbers in
textfields a:, b:, and
m: then hit return. The results in textfields a*b mod
m: and (a mod m)*(b mod m) mod m: show that you can first take the
mod of two numbers before multiplying them and still get the same
result had you multiplied first, then taken the mod of the result.
This is really great since we plan to exponentiate huge numbers  now
mod exponentiation is merely repeated multiplication of fairly small
(moded) numbers.

Instructions, bottom: Enter numbers in
textfields a:, b: m:, and base:
and hit return. The results in textfields (base^a mod m)^b mod
m: and (base^b mod m)^a mod m: show that the order in
which mod exponentiation is carried out is irrelevant. This is really
great since we plan to use mod exponentiation all over the place.
