Rabin Cryptosystem - Key Generation

Key Generation

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:

• Choose two large distinct primes p and q. One may choose to simplify the computation of square roots modulo p and q (see below). But the scheme works with any primes.
• Let . Then n is the public key. The primes p and q are the private key.

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 and, then . 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).