Let n be an odd, positive integer and let x be an integer that is relatively prime to n (see modular arithmetic). The integer x is a quadratic residue modulo n if the equation
has an integer solution y. In other words, the integer x is a square modulo n. The integer x is a quadratic non-residue otherwise.
If n is an odd prime number, then exactly half of all integers x relatively prime to n are quadratic residues. If n is the product of two distinct odd primes p and q, then the fraction is one-quarter.
See also Jacobi symbol, Legendre symbol, and Quadratic Residuosity Problem.
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© 2005 International Federation for Information Processing
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Kaliski, B. (2005). Quadratic Residue. In: van Tilborg, H.C.A. (eds) Encyclopedia of Cryptography and Security. Springer, Boston, MA . https://doi.org/10.1007/0-387-23483-7_335
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DOI: https://doi.org/10.1007/0-387-23483-7_335
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