Power analysis and exponentiation by squaring
You can begin by first reading the seminal paper of Paul Kocher. He gave the reference for Timing and Power analysis attacks. The best is to read the papers, and understand the philosophy of Side Chanel Attacks.
The method he described, has been enhanced by many authors, and it become impossible to ignore how to securelly implement algorithm on embedded systems.
After that the most destructive attacks is the one introduced by Dan Boneh known as the "Faults Attack".