Theory of cryptography | Computational hardness assumptions | Computational number theory

Quadratic residuosity problem

The quadratic residuosity problem (QRP) in computational number theory is to decide, given integers and , whether is a quadratic residue modulo or not.Here for two unknown primes and , and is among the numbers which are not obviously quadratic non-residues (see below). The problem was first described by Gauss in his Disquisitiones Arithmeticae in 1801. This problem is believed to be computationally difficult.Several cryptographic methods rely on its hardness, see . An efficient algorithm for the quadratic residuosity problem immediately implies efficient algorithms for other number theoretic problems, such as deciding whether a composite of unknown factorization is the product of 2 or 3 primes. (Wikipedia).

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On The Complexity of Computing Roots and Residuosity Over Finite Fields - Swastik Kopparty

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From playlist Discriminant of a Quadratic Equation

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From playlist Discriminant of a Quadratic Equation

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From playlist Discriminant of a Quadratic Equation

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From playlist GED Prep Videos

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From playlist Mathematics

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From playlist Algebra

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Related pages

Disquisitiones Arithmeticae | Cocks IBE scheme | Jacobi symbol | Computational hardness assumption | Euclidean algorithm | Legendre symbol | Character (mathematics) | Pseudorandom number generator | Blum Blum Shub | Computational number theory | Computational complexity theory | Higher residuosity problem | Quadratic residue | Goldwasser–Micali cryptosystem