CS 355: Topics in Cryptography
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
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.
- Constructions. Probabilistic encryption, Cramer-Shoup.
- Security notions for signatures.
- 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.
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Last update: Sep. 21, 1998 by