I read on Wikipedia that modular exponentiation can be done in polynomial time. I've a few questions regarding it (sorry if they seem a bit easy – I'm not a comp sci student).
Is it poly time only for base 2, i.e in binary or will it remain poly time algorithm even if i run it in decimal system i.e base 10?
If I'm calculating $(a^b) \bmod p$, where $1<a<11$, $1 < b \leq (p-1)/2$, and we run this modular exponentiation at most $p/2$ times, all this being done in decimal base 10 system, will it still be poly time?
Even if this is poly time, and this is a big IF, can this process actually be completed in reasonable time in terms of the real worldly time?