Читать книгу Cryptography, Information Theory, and Error-Correction - Aiden A. Bruen - Страница 73

This is one of the most mathematically elegant algorithms in cryptography. Communicating parties and end up generating a common secret key, so there is a connection with symmetric encryption. On the other hand, the method of generating the common key is quite similar to the RSA algorithm and indeed is said to have inspired the RSA algorithm. The security of DH, like the security of RSA, is computational.

The DH key exchange may proceed in the following way:

Participants , wish to generate a common secret key. First, a suitable prime is publicly chosen and then a generator for . Here, a generator (which always exists!) has the property that if we take all powers of from 1 to and calculate their remainders when we divide by , we obtain all possible numbers in some order (see Chapter 19). Recall that means the remainder when is divided by . Here, in this section, and in the problems, and will be simply denoted by .

Procedure. , choose secret numbers and transmit to , , respectively.

receives and calculates .

receives and calculates .

Now, and , are in possession of a common secret key , since .