Rabin cryptosystem

The Rabin cryptosystem is an asymmetric cryptographic technique, whose security, like that of RSA, is related to the difficulty of factorization. However the Rabin cryptosystem has the advantage that the problem on which it relies has been proved to be as hard as integer factorization, which is not currently known to be true of the RSA problem. It has the disadvantage that each output of the Rabin function can be generated by any of four possible inputs; if each output is a ciphertext, extra complexity is required on decryption to identify which of the four possible inputs was the true plaintext.

The process was published in January 1979 by Michael O. Rabin. The Rabin cryptosystem was the first asymmetric cryptosystem where recovering the entire plaintext from the ciphertext could be proven to be as hard as factoring.

As with all asymmetric cryptosystems, the Rabin system uses both a public and a private key. The public key is necessary for later encryption and can be published, while the private key must be possessed only by the recipient of the message.

The precise key-generation process follows:

To encrypt a message only the public key n is needed. To decrypt a ciphertext the factors p and q of n are necessary.

As a (non-real-world) example, if ${\displaystyle p=7}$ and ${\displaystyle q=11}$, then ${\displaystyle n=77}$. The public key, 77, would be released, and the message encoded using this key. And, in order to decode the message, the private keys, 7 and 11, would have to be known (of course, this would be a poor choice of keys, as the factorization of 77 is trivial; in reality much larger numbers would be used).

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