Algorithms for Secure Communication

The design of algorithms for sending confidential messages (i.e. messages that no one can read, except the intended receiver) goes back to the beginning of our civilization. However, before the widespread of modern computers, cryptography was practiced by few people: soldiers, or diplomats, or scientists fascinated by the problem of confidential communication. Cryptography algorithms designed in the past were ingenious transformations but were lacking a sound mathematical basis. Recently, the development of computers and of the Internet has opened up new applications of cryptography in business and society. To answer these needs, new algorithms have been developed that use sound mathematical techniques and have produced surprising results, which have opened up impressive possibilities that were considered unrealistic before. We will see examples of algorithms that use modular arithmetic (in which operations are performed modulo an integer) that are based on using functions that are easy to compute but difficult to invert.