exponentiation algorithm

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• Exponentiation by squaring — Exponentiating by squaring is an algorithm used for the fast computation of large integer powers of a number. It is also known as the square and multiply algorithm or binary exponentiation. In additive groups the appropriate name is double and… …   Wikipedia

• Algorithm characterizations — The word algorithm does not have a generally accepted definition. Researchers are actively working in formalizing this term. This article will present some of the characterizations of the notion of algorithm in more detail. This article is a… …   Wikipedia

• Algebraic-group factorisation algorithm — Algebraic group factorisation algorithms are algorithms for factoring an integer N by working in an algebraic group defined modulo N whose group structure is the direct sum of the reduced groups obtained by performing the equations defining the… …   Wikipedia

• Nth root algorithm — The principal n th root sqrt [n] {A} of a positive real number A , is the positive real solution of the equation:x^n = A(for integer n there are n distinct complex solutions to this equation if A > 0, but only one is positive and real).There is a …   Wikipedia

• nth root algorithm — The principal nth root of a positive real number A, is the positive real solution of the equation xn = A (for integer n there are n distinct complex solutions to this equation if A > 0, but only one is positive and real). There is a very fast… …   Wikipedia

• Modular exponentiation — is a type of exponentiation performed over a modulus. It is particularly useful in computer science, especially in the field of cryptography. Doing a modular exponentiation means calculating the remainder when dividing by a positive integer m… …   Wikipedia

• Addition-chain exponentiation — In mathematics and computer science, optimal addition chain exponentiation is a method of exponentiation by positive integer powers that requires a minimal number of multiplications. It works by creating a minimal length addition chain that… …   Wikipedia

• Williams' p + 1 algorithm — In computational number theory, Williams p + 1 algorithm is an integer factorization algorithm, one of the family of algebraic group factorisation algorithms. It was invented by Hugh C. Williams in 1982. It works well if the number N to be… …   Wikipedia

• Pollard's p - 1 algorithm — Pollard s p − 1 algorithm is a number theoretic integer factorization algorithm, invented by John Pollard in 1974. It is a special purpose algorithm, meaning that it is only suitable for integers with specific types of factors; it is the simplest …   Wikipedia

• Digital Signature Algorithm — The Digital Signature Algorithm (DSA) is a United States Federal Government standard or FIPS for digital signatures. It was proposed by the National Institute of Standards and Technology (NIST) in August 1991 for use in their Digital Signature… …   Wikipedia

• Itoh-Tsujii inversion algorithm — The Itoh Tsujii inversion algorithm is used to invert elements in a finite field. It was introduced in 1988 and first used over GF(2 m ) using the normal basis representation of elements, however the algorithm is generic and can be used for other …   Wikipedia