Lecture 6: RSA public Key Encryption

Background Material

• Modular Arithmetic
• Euclidean Algorithm

Reading

• 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.

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

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

Assignment