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Definition :
O(kM(n)) : – computational complexity of modular exponentiation
where k is number of exponent bits , n is number of digits , and M(n) is computational complexity of the Newton’s division algorithm.
How can I determine is this computational complexity polynomial complexity ?
In fact notation M(n) is that what confusing me most .
Think about the division algorithm.
Does the division algorithm have complexity O(n)? If so, then modular exponentiation is O(k n).
Does the division algorithm have complexity O(n^c) for some constant c? If so, then modular exponentiation is O(k n^c).
Does the division algorithm have complexity O(log n)? If so, then modular exponentiation is O(k log n).
Etc.