CS 355: Topics in Cryptography

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

Part I: Pseudorandomness

• A bit of complexity theory.
  Definition of one-way functions and one-way permutations.
   
• Motivation and definition of PRNGs.
  Next bit test. Proof of universality.
   
• Hard core bits. Blum-Micali generator. Example: discrete log.
  Proof of Yao's XOR lemma (section 3). See also a simple write-up.
   
• Goldreich-Levin theorem. Naslund's theorem. Subset sum PRNG.
  Subset sum pseudorandom generator (section 2)
  Alternate proof of Goldreich-Levin theorem. (section 3.3)
   
• 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. Modes of operation for block-ciphers.
  Luby Rackoff revisited.
   
• Left-over-hash Lemma. Extractors.
  Proof and applications (Section 4).

Part II: Basic distributed computation.

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

Part III: Cryptographic privacy

• Private Information Retrieval. The KO and CMS protocols.
  A Survey on Private Information Retrieval
   
• Private computation of decision trees.
   
• Private computation of set intersection.
   
• Searching on encrypted data.

Part IV: Cryptographic content protection

• Broadcast encryption: FN, NNL.
• Tracing traitors. Combinatorial and algebraic constructions.