Lecture 6: Modular Arithmetic and the RSA public Key Cryptosystem

Background Material

• Any text on elementary number theory.

Reading

• Rivest, R. L., Shamir, A., and Adleman, L., A Method for Obtaining Digital Signatures and Public Key Cryptosystems, CACM, Vol. 21, No. 2, 1978, pp. 120-126.

Topics

1. Go over midterm. See solmid.mws for my solution and an elaboration.
2. RSA Public Key Cryptosystem
   1. Overview of Public Key Cryptosystems.
   2. Overview of the RSA algorithm.
   3. 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
   5. Implementation

Slides

1. rsa.ppt - power point slides containing proofs and background on the necessary number theory.

Maple worksheets and programs

• Worksheet containing an implementation of the RSA algorithm

Assignment

• not determined yet.