Читать книгу Cryptography, Information Theory, and Error-Correction - Aiden A. Bruen - Страница 77

As before, we are given a prime and a generator . Each participant has, as a private key, a secret integer (which can be assumed to lie between 2 and and a public key . Suppose wants to send a secret message , which is in the form of a positive integer less than . Let the integer be the private key for . has, for a public key, . also computes the key , obtained by getting the remainder upon raising the public key of , to the power , and dividing by . (As in the DH key‐exchange, can also find by raising to the power of and dividing by to get the remainder.)

Finally, transmits the cipher text to (as well as . From , can calculate . Since is a prime can calculate , where . Then calculates . This is the El Gamal Cryptosystem.

Remark 3.7 Instead of taking the cipher text , we could also choose the cipher text , where is any keyed symmetric algorithm such as AES.

The RSA digital signature protocol is relatively easy because and are both defined on the same set, namely . For a more complicated digital signature example, we present the El Gamal Digital Signature Scheme.