Quadratic residuosity problem

The Quadratic Residuosity Problem (QRP) is a fundamental problem in number theory and has important implications in cryptography, particularly in the context of certain cryptographic protocols and security mechanisms. ### Definition The Quadratic Residuosity Problem can be defined as follows: Let \( p \) be a prime number, and let \( a \) be an integer such that \( 1 \leq a < p \).