modulo arithmetic V xor

I have been doing some reading on using modulo arithmetic as opposed to
using the xor function, i know that the xor function is modulo 2 arithmetic,
the question is, would breaking the xor function down into N steps decrease
the memory footprint of an algorithm, if so the reduction in time should
vary depending on the size of input 1 and input 2 and how many of them there
are, as part of a stream cipher for example.

the further question arises of how to break it down into steps, i know how
to break down modulo exponentiation but not any of the other forms of modulo
arithmetic.

links to reference material or explenations would be most welcome.


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