CS456/CS656 Cryptography
Spring 2001


Instructor: Christino Tamon
Lecture: Science Center 344 MWF 10am
Office hours: Science Center 373 MW 9-10am, 11-noon F 9-10am
Pre-requisites: MA211 or MA346, good programming skills and/or mathematical curiosity.
Syllabus: Cryptography is the study of secure communication over insecure channels. We will study the basic methods and concepts in theoretical cryptography along with their applications. Concepts such as one-way functions and trapdoor permutations (functions that are easy to compute but computationally hard to invert), pseudorandom sequence generators (devices that produces sequences that are computationally random), public-key cryptosystems (secure systems that require no secret agreement), one-way hash functions (tools to authenticate messages and to verify data integrity), digital signatures (mechanisms for signing documents), and zero-knowledge proofs (convincing a party of a fact without revealing its proof). Most of the topics require background in number theory and probability theory. The first part of the course will be spent on developing the necessary background in these areas, mainly number theory. The second part of the course is spent on the applications of these to building cryptographic tools.
Grading scheme Texts: [main][recommended]

Assignments

  1. Cryptogram. Out: 01/12/01. Due: 01/19/01.

Tentative Outline

  1. General framework of a cryptographic system: Alice, Bob, and Eve. One-time XOR pad (unconditionally secure). Problems with reusing the XOR pad. Types of attacks on cryptosystems: ciphertext-only, known-plaintext, chosen-plaintext, adaptive chosen-plaintext, chosen-ciphertext.
  2. The Rivest-Shamir-Adleman Public-Key CryptoSystem:
  3. A Probabilistic Public-Key CryptoSystem (Goldwasser-Micali):
  4. A Pseudorandom Bit Generator (Blum-Blum-Shub):
  5. More efficient probabilistic PKCS (Blum-Goldwasser):
  6. Recent PKCS (Cramer-Shoup): Citation: Ronald Cramer and Victor Shoup. A practical public-key cryptosystem provably secure against chosen ciphertext attack. Advances in Cryptology: Proceedings of CRYPTO'98.
  7. Zero Knowledge Proofs:
  8. Other topics: