quadratic residue modulo

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• Quadratic residue — In number theory, an integer q is called a quadratic residue modulo n if it is congruent to a perfect square modulo n; i.e., if there exists an integer x such that: Otherwise, q is called a quadratic nonresidue modulo n. Originally an abstract… …   Wikipedia

• Quadratic residue code — A quadratic residue code is a type of cyclic code.There is a quadratic residue code of length pover the finite field GF(l) whenever pand l are primes, p is odd andl is a quadratic residue modulo p.Its generator polynomial as a cyclic code is… …   Wikipedia

• Quadratic reciprocity — The law of quadratic reciprocity is a theorem from modular arithmetic, a branch of number theory, which shows a remarkable relationship between the solvability of certain quadratic equations modulo different prime moduli.Although it allows us to… …   Wikipedia

• Quadratic sieve — The quadratic sieve algorithm (QS) is a modern integer factorization algorithm and, in practice, the second fastest method known (after the general number field sieve). It is still the fastest for integers under 100 decimal digits or so, and is… …   Wikipedia

• Quadratic residuosity problem — The quadratic residuosity problem in computational number theory is the question of distinguishing by calculation the quadratic residues in modular arithmetic for a modulus N , where N is a composite number. This is an important consideration in… …   Wikipedia

• Quadratic — In mathematics, the term quadratic describes something that pertains to squares, to the operation of squaring, to terms of the second degree, or equations or formulas that involve such terms. Quadratus is Latin for square . Mathematics Algebra… …   Wikipedia

• Quadratic Gauss sum — For the general type of Gauss sums see Gaussian period, Gauss sumIn mathematics, quadratic Gauss sums are certain sums over exponential functions with quadratic argument. They are named after Carl Friedrich Gauss, who studied them… …   Wikipedia

• Proofs of quadratic reciprocity — In the mathematical field of number theory, the law of quadratic reciprocity, like the Pythagorean theorem, has lent itself to an unusual number of proofs. Several hundred proofs of the law of quadratic reciprocity have been found.Proofs that are …   Wikipedia

• Multiplicative group of integers modulo n — In modular arithmetic the set of congruence classes relatively prime to the modulus n form a group under multiplication called the multiplicative group of integers modulo n. It is also called the group of primitive residue classes modulo n. In… …   Wikipedia

• Euler's criterion — In mathematics, Euler s criterion is used in determining in number theory whether a given integer is a quadratic residue modulo a prime. DefinitionEuler s criterion states: Let p be an odd prime and a an integer coprime to p . Then a is a… …   Wikipedia

• Goldwasser-Micali cryptosystem — The Goldwasser Micali cryptosystem (GM) is an asymmetric key encryption algorithm developed by Shafi Goldwasser and Silvio Micali in 1982. GM has the distinction of being the first probabilistic public key encryption scheme which is provably… …   Wikipedia