Public-key encryption

In the previous chapters, we looked at many cipher systems where we spent quite a bit of effort developing techniques (1) to determine what method might have been used to encrypt a given cipher text and, once that was known, (2) to “crack” the cipher and come up with the key. In all these methods, an enemy knowing the encryption key compromises the system as it is an easy step to figure out the decryption key. Likewise, knowing the decryption key allows one to easily recover the encryption key. Such system are sometimes called symmetric ciphers or secret-key ciphers. Furthermore, all these methods are what we might term pencil-and-paper methods, as they can be implemented using only paper and pencil. The methods we are about to examine require the power of computers in order to perform the necessary computations.

In contrast to a secret-key cipher, a public-key cipher is a cipher where the encryption key is made public while the decryption key is kept secret. This allows many people to encrypt a message to the holder of the decryption key. Of course, knowledge of the encryption key in a public-key cipher must not allow someone to recover the decryption key, at least not without a tremendous amount of effort. (Thus all our previous ciphers fail miserably in this regard.) Public-key ciphers are also known as asymmetric ciphers, to distinguish them from symmetric ciphers.