Editing Exponentiation by squaring (section)

{{short description|Algorithm for fast exponentiation}}
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In [[mathematics]] and [[computer programming]], '''exponentiating by squaring''' is a general method for fast computation of large [[positive integer]] powers of a [[number]], or more generally of an element of a [[semigroup]], like a [[polynomial]] or a [[square matrix]]. Some variants are commonly referred to as '''square-and-multiply''' algorithms or '''binary exponentiation'''. These can be of quite general use, for example in [[modular arithmetic]] or powering of matrices. For semigroups for which [[Abelian group#Notation|additive notation]] is commonly used, like [[elliptic curve]]s used in [[cryptography]], this method is also referred to as '''double-and-add'''.