Lecture 6: Overview of Public-Key Cryptography and RSA

In this lecture, we give an overview to the public-key cryptography, which is also referred to as asymmetric cryptography. We will first introduce the background of public-key cryptography. Then we will study the model of public-key cryptosystem, and the requirement to design a practical public-key algorithm. Finally, we will study the design of RSA algorithm. The concept of public-key (asymmetric) cryptography evolved from an attempt to address the following two difficult problems associated with the secret-key (symmetric) cryptosystem. • Key distribution. Symmetric encryption requires a shared secret key. As we have seen in the previous lecture, this leads to the problem of key distribution, which in turn requires secret sharing either between the communicating parties or between the communicating hosts and the KDC. • Non-repudiation. In symmetric encryption, the sending party may deny sending the message, because it is possible for the receiver to forge a message based on the same secret key. Accordingly, the receiving party may claim the receipt of a message from the sender which is actually forged by himself. To address both problems, Diffie and Hellman achieved an important breakthrough in 1976. The proposed scheme was radically different from all previous approaches to cryptography. First, it uses a pair of different keys in contrast to one shared key in symmetric encryption. Second, it is based on mathematical functions instead of substitution and permutation. The proposed scheme is called pubic-key (asymmetric) cryptography, which is one of the greatest revolutions in the history of cryptography. Its use of two keys has profound consequences in facilitating key distribution, and providing digital signature. However, the scheme proposed by Diffie and Hellman is not a general-purpose encryption algorithm. It can only provide secure secret key exchange. Thus it presents a challenge for the cryptologists to design a general-purpose encryption algorithm that satisfies the public-key encryption requirements. One of the first responses to the challenge was developed in 1977 by Rivest, Shamir, Adleman at MIT, so called RSA. Since then, the RSA scheme has become the most widely accepted and implemented general-purpose approach to public-key encryption.