Implementation of the RSA Public - Key Cryptosystem

The history of secret messages, cryptosystems, codes and codecracking is as old as the history of man. In this article, we will deal with the cryptosystem proposed by Rivest, Shamir and Adleman in 1977, see [3]. It has two characteristics which distinguish it from most other encryption methods: The usage of Number Theory and the fact that the process of deciphering is not just opposite to the one of enciphering. As a consequence of the latter feature, the enciphering key is made public, giving the system the attribute "Public-Key". Two applications of this feature will be discussed later, namely a multiuser operation option and an option for authorizing a message by giving a signature. In section 2, we will provide the background from elementary Number Theory, as far as needed for the following. In section 3, we will describe the RSA cryptosystem. A numerical example will be given in section 4. Section 5 contains a discussion about the safety of the system, section 6 describes the extension of the system to multiuser operation. Finally, in section 7, two computer programs are presented. The reader will notice that the problems of finding large prime numbers and factorizing large numbers are closely connected with the concept of the RSA cryptosystem. Roughly speaking, the party that wants to transmit a secret message has to find two large prime numbers and use them in the enciphering and deciphering process, whereas the enemy who wants to crack the code of the message has to find the factorization of the product of these two primes. Up to the present day, it is very hard to find large prime numbers. But it is still much harder to factorize large numbers. Hence, the transmitters of the secret message have an advantage