91.561 Project 1 (Due March 31 midnight)

Write a client-server program using socket API to implement RSA as follows:

1. Let n = 3407 x 6917. The server uses it to create an RSA system (i.e., e and d) upon requests from clients.
2. The client asks the server for his RSA parameter (n, e) and generates a pseudo random number r < n, encrypts n, and sends the encrypted number to the server.
3. The server decrypts the cipher and obtains r.

In this project, you will need to implement the followings:

1. Euclid’s algorithm, to find e such that e is relatively prime to φ(n).
2. Fast exponentiation algorithm
3. Euler’s theorem to find d such that d is an inverse of e mod n.
4. BBS to generate a pseudo random number. Since a random sequence generated using BBS may not be an integer, you need to make it to an integer. A simple way to do so is to add 1 at the beginning if the first digit in the sequence generated by BBS is 0. That is, if BBS generates 011001, then use 1011001 as the random number. For convenience, let p = 1223 and q = 5003.
5. Master-slave concurrent server program on the server program to handle multiple requests.

The C language is preferred, although Java is acceptable.