Exponentiation Algorithms

Right-to-left exponentiation methods read the exponent from the least significant bit (or other digit) up to the most significant one.

Many exponentiation methods have two variants: one that examines exponents starting at the most significant digit and going down to the least significant one, that is, in left-to-right direction (assuming big-endian notation); and a related one that examines exponents in the opposite direction, that is, right-to-left. For specific methods, see the entries on  binary exponentiation,  2^k-ary exponentiation, and  sliding window exponentiation.

There is a general duality between left-to-right and right-to-left exponentiation: this is explained by representing addition chains ( fixed-exponent exponentiation) as directed multi-graphs such that reversing all arcs turns left-to-right exponentiation into right-to-left exponentiation, or the other way around [ 1].