A public-key cryptosystem based on squaring modulo the product of two primes, introduced in 1979 by Michael O. Rabin and proven to have security reducible to the hardness of integer factorization. It is similar to RSA but uses e=2.
The Rabin cryptosystem was the first asymmetric cryptosystem where recovering the plaintext from the ciphertext could be proven to be as hard as factoring.
The Rabin cryptosystem does not provide indistinguishability against chosen plaintext attacks since the process of encryption is deterministic. An adversary, given a ciphertext and a candidate message, can easily determine whether or not the ciphertext encodes the candidate message (by simply checking whether encrypting the candidate message yields the given ciphertext).
The Rabin cryptosystem is insecure against a chosen ciphertext attack (even when challenge messages are chosen uniformly at random from the message space)
The Rabin cryptosystem can be used to create and verify digital signatures.