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modular exponentiation

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  • 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

  • Modular multiplicative inverse — The modular multiplicative inverse of an integer a modulo m is an integer x such that That is, it is the multiplicative inverse in the ring of integers modulo m. This is equivalent to The multiplicative inverse of a modulo m exists if and only if …   Wikipedia

  • Modular arithmetic — In mathematics, modular arithmetic (sometimes called clock arithmetic) is a system of arithmetic for integers, where numbers wrap around after they reach a certain value the modulus. The Swiss mathematician Leonhard Euler pioneered the modern… …   Wikipedia

  • Exponentiation — Exponent redirects here. For other uses, see Exponent (disambiguation). Exponentiation is a mathematical operation, written as an, involving two numbers, the base a and the exponent (or power) n. When n is a positive integer, exponentiation… …   Wikipedia

  • 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

  • Diskrete Exponentiation — Die diskrete Exponentialfunktion (Synonyme Bezeichnungen sind modulare Exponentiation oder modulares Potenzieren) liefert den Rest bei Division von bx durch m. Die Umkehrung der diskreten Exponentialfunktion heißt diskreter Logarithmus. Die… …   Deutsch Wikipedia

  • Modulare Exponentiation — Die diskrete Exponentialfunktion (Synonyme Bezeichnungen sind modulare Exponentiation oder modulares Potenzieren) liefert den Rest bei Division von bx durch m. Die Umkehrung der diskreten Exponentialfunktion heißt diskreter Logarithmus. Die… …   Deutsch Wikipedia

  • Montgomery reduction — In arithmetic computation, Montgomery reduction is an algorithm introduced in 1985 by Peter Montgomery that allows modular arithmetic to be performed efficiently when the modulus is large (typically several hundred bits). A single application of… …   Wikipedia

  • Discrete logarithm — In mathematics, specifically in abstract algebra and its applications, discrete logarithms are group theoretic analogues of ordinary logarithms. In particular, an ordinary logarithm loga(b) is a solution of the equation ax = b over the… …   Wikipedia

  • RSA — In cryptography, RSA is an algorithm for public key cryptography. It is the first algorithm known to be suitable for signing as well as encryption, and one of the first great advances in public key cryptography. RSA is widely used in electronic… …   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

  • Primitive root modulo n — In modular arithmetic, a branch of number theory, a primitive root modulo n is any number g with the property that any number coprime to n is congruent to a power of g (mod n ). That is, if g is a primitive root (mod n ) and gcd( a , n ) = 1,… …   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

  • Arithmetique modulaire — Arithmétique modulaire Couverture de l’édition originale des Recherches arithmétiques de Gauss, livre fondateur de l’arithmétique modulaire. En mathématiques et plus précisément en théorie algébrique des nombres, l’arithmétique modulaire est un… …   Wikipédia en Français

  • Arithmétique modulaire — Couverture de l’édition originale des Recherches arithmétiques de Gauss, livre fondateur de l’arithmétique modulaire. En mathématiques et plus précisément en théorie algébrique des nombres, l’arithmétique modulaire est un ensemble de méthodes… …   Wikipédia en Français

  • Arithmétique modulaire (synthèse) — Arithmétique modulaire Couverture de l’édition originale des Recherches arithmétiques de Gauss, livre fondateur de l’arithmétique modulaire. En mathématiques et plus précisément en théorie algébrique des nombres, l’arithmétique modulaire est un… …   Wikipédia en Français

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