# Lecture 8: RSA public Key Encryption

### Background Material

• Chapter 4 of the text.
• Rivest, R. L., Shamir, A., and Adleman, L., A Method for Obtaining Digital Signatures and Public Key Cryptosystems, JACM, Vol. 21, No. 2, 1978, pp. 120-126. (available electronically through the Drexel library - ACM digital library)

### Topics

1. RSA Public Key Cryptosystem
1. Overview of Public Key Cryptosystems.
2. Overview of the RSA algorithm.
3. Review Necessary Number Theory and Number Theoretic Algorithms
1. Modular Arithmetic
2. Greatest Common Divisors and the Euclidean Algorithm
3. Fermat's theorem and the Euler phi function
4. Modular Inverses
5. Modular powers and fast exponentiation
6. Extended Euclidean algorithm
7. Chinese Remainder theorem
4. Proof of correctness

### Slides and Worksheets

1. rsa.ppt (rsa.pdf - power point slides containing proofs and background on the necessary number theory.
2. rsa.mw - Maple implementation of the RSA algorithm.

### Practice Assignment

• Do the exercises in rsa.mw.
Created: April 21, 2008 by jjohnson AT cs DOT drexel DOT edu