Rabin Cryptosystem

The Rabin cryptosystem is a family of public-key encryption schemes based on a trapdoor function whose security, like RSA's, rests on the difficulty of integer factorization. Unlike RSA, inverting the Rabin trapdoor function has been mathematically proven to be as hard as factoring integers, though each output of the function can be generated by any of four possible inputs, which requires extra complexity on decryption to identify the true plaintext among them. Public-key schemes built on the Rabin trapdoor function are used mainly as textbook examples, while RSA remains the basis of the standard schemes used in practice.