#
CS 355: Topics in Cryptography

## Syllabus

## (Fall 1998)

The course is a seminar on topics in cryptography. Course topics this
year include pseudorandomness, security notions for both encryption
and signatures, random oracle analysis, and a bit of distributed computations.
The course is intended for graduate students interested in
cryptography research.
## Topic by lecture - tentative

- Introduction. Crash course in probability, pair wise independence, large deviation bounds.

### Part I: Pseudorandomness

- A bit of complexity theory. Definition of one-way functions.
Amplification of one-wayness.
- Motivation and definition of PRNGs. Next bit test. Proof of universality.
- Hard core bits. Blum-Micali generator. Example: discrete log.
- Goldreich-Levin theorem.
- Left-over-hash Lemma. (HILL)
- Definition of PRFs. Applications.
- The GGM Construction. The NR construction based on DDH.
- Motivation and Definition of PRPs.
The Luby-Rackoff construction a la Naor-Reignold.
- Efficient constructions of PRNG's based on ideal ciphers.

### Part II: Security notions

- Security notions for encryption. Semantic security. Non-malleability.
Attack models.
- Constructions. Probabilistic encryption, Cramer-Shoup.
- Security notions for signatures.
Attack models.
- Constructions. GMR. Dwork-Naor signatures.
- Signatures based on UOWHF.

### Part III: Random oracle analysis

- How to encrypt with a trap door one way function.
- How to sign with a trap door one way function.
- Limits of random oracle analysis a la Canetti-Goldreich-Halevi.

### Part IV: Basic distributed computation.

- Introduction to secure function evaluation. Applications.
- Oblivious transfer. Yao's two party protocol and GMW.
- The BGW multi-party protocol.

Return to course homepage.

Last update: Sep. 21, 1998 by
Dan Boneh.