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How can I compute an exponential modulo a large integer?

There are techniques to perform a multiplication $a \cdot b \pmod n$ without calculating $a \cdot b$ which could be as large as $(n-1)^2$, the most popular being Montgomery reduction. … Multiplication modulo $n$ can be done in time $O(\ell^2)$ where $\ell$ is the number of digits of $n$; it follows that exponentiation modulo $n$ can be done in time $O(\ell^3)$. …
Gilles 'SO- stop being evil''s user avatar