In mathematics, exponentiation is an operation involving two numbers: the base and the exponent or power. Exponentiation is written as bn, where b is the...

are commonly referred to as square-and-multiply algorithms or binary exponentiation. These can be of quite general use, for example in modular arithmetic...

Modular exponentiation is exponentiation performed over a modulus. It is useful in computer science, especially in the field of public-key cryptography...

tetration (or hyper-4) is an operation based on iterated, or repeated, exponentiation. There is no standard notation for tetration, though Knuth's up arrow...

In exponentiation, the base is the number b in an expression of the form bn. The number n is called the exponent and the expression is known formally as...

a property of exponentiation that (ab)c = abc, so it's unnecessary to use serial exponentiation for this. However, when exponentiation is represented...

mathematics and computer science, optimal addition-chain exponentiation is a method of exponentiation by a positive integer power that requires a minimal number...

multiplication, hence also exponentiation, of diagonal matrices is equivalent to element-wise addition and multiplication, and hence exponentiation; in particular...

usual operations on ordinal numbers: addition, multiplication, and exponentiation. Each can be defined in essentially two different ways: either by constructing...

if μ ≤ π. It will be unique (and equal to π) if and only if μ < π. Exponentiation is given by | X | | Y | = | X Y | , {\displaystyle |X|^{|Y|}=\left|X^{Y}\right|...

The use of the caret for exponentiation can be traced back to ALGOL 60,[citation needed] which expressed the exponentiation operator as an upward-pointing...

in exponentiation, such as in square and cubic forms, any multiplier prefix is considered part of the unit, and thus included in the exponentiation. 1 km2...

multiplication (n = 2), and exponentiation (n = 3). After that, the sequence proceeds with further binary operations extending beyond exponentiation, using right-associativity...

names tetration, pentation, etc., for the extended operations beyond exponentiation. The sequence starts with a unary operation (the successor function...

operations are non-associative; some examples include subtraction, exponentiation, and the vector cross product. In contrast to the theoretical properties...

freshman's dream is a valid identity. This result demonstrates that exponentiation by p produces an endomorphism, known as the Frobenius endomorphism of...

logarithm problem. The computation of ga mod p is known as modular exponentiation and can be done efficiently even for large numbers. Note that g need...

in exponentiation, such as in square and cubic forms, any multiples-prefix is considered part of the unit, and thus included in the exponentiation. 1 Mm2...

A double exponential function is a constant raised to the power of an exponential function. The general formula is f ( x ) = a b x = a ( b x ) {\displaystyle...

** may refer to: **, to express exponentiation in some programming languages **, a pointer to a pointer (or double pointer) in C syntax **, interpolation...

function is used for studying the continuum function and the cardinal exponentiation function. The symbol ℷ {\displaystyle \gimel } is a serif form of the...

subtraction, multiplication, and division. In a wider sense, it also includes exponentiation, extraction of roots, and taking logarithms. Arithmetic systems can...

In mathematics, a rational number is a number that can be expressed as the quotient or fraction ⁠ p q {\displaystyle {\tfrac {p}{q}}} ⁠ of two integers...

Regardless of the specific algorithm used, this operation is called modular exponentiation. For example, consider Z17×. To compute 34 in this group, compute 34...

arithmetic operations (addition, subtraction, multiplication, and division), exponentiation to a real exponent (which includes extraction of the nth root), logarithms...

In general, exponentiation fails to be commutative. However, the equation x y = y x {\displaystyle x^{y}=y^{x}} has solutions, such as x = 2 ,   y = 4...

j {\displaystyle U^{2^{j}}} . This can be accomplished via modular exponentiation, which is the slowest part of the algorithm. The gate thus defined satisfies...

ak ≡ bk (mod m) for any non-negative integer k (compatibility with exponentiation) p(a) ≡ p(b) (mod m), for any polynomial p(x) with integer coefficients...

A compound Poisson process is a continuous-time stochastic process with jumps. The jumps arrive randomly according to a Poisson process and the size of...

step 2, the first exponentiation. This is one reason why this algorithm is well suited for the normal basis, since squaring and exponentiation are relatively...