I have noticed that in some cases 'polynomial representation' of a number is the preferred method to represent numbers in computer programs, especially those involving modular arithmetic and cryptography.
I have read that it allows to simplify the code required to implement the different arithmetic operations and thus is more comfortable to work with. Also it is claimed that polynomial form is the natural way to represent integers modulo something.
Here are my questions:
Would you please elaborate on the available methods of converting between the traditional little-endian/big-endian representation of integers and their polynomial counter-parts?
Why is the polynomial form a natural way to represent number modulo something ?
Why does it lead to code simplification ?
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