CS 276 &mdash Projects

Here are some suggested topics.

Hard-core predicates

• Every bit of RSA and exponentiation is hard-core
  
  • Johan Hastad, Mats Naslund: The security of all RSA and discrete log bits. J. ACM 51(2): 187-230 (2004)
• The unified framework of Akavia, Goldwasser and Safra
  • Adi Akavia, Shafi Goldwasser, Shmuel Safra: Proving Hard-Core Predicates Using List Decoding. FOCS 2003

One-way Functions and Pseudorandom Generators

• Efficient "hardness amplification" for one-way permutations
  • Oded Goldreich, Russell Impagliazzo, Leonid A. Levin, Ramarathnam Venkatesan, David Zuckerman: Security Preserving Amplification of Hardness FOCS 1990: 318-326
  • See also Goldreich's book
  • A long-standing research question is whether one can do the same for general one-way functions. It's possible that the answer is negative for "black-box reductions."
• Pseudorandom generators from "regular" one-way functions. ("Regular is a technical term, it means all elements of the range have the same number of preimages.)
  • Oded Goldreich, Hugo Krawczyk, Michael Luby: On the Existence of Pseudorandom Generators. SIAM J. Comput. 22(6): 1163-1175 (1993)
  • See also Oded Goldreich's textbook
• The full HILL construction (with Holenstein's simplification). Note that this might be too much to tackle in one month.
  • Johan Hastad, Russell Impagliazzo, Leonid A. Levin, Michael Luby: A Pseudorandom Generator from any One-way Function. SIAM J. Comput. 28(4): 1364-1396 (1999)
  • Thomas Holenstein: Pseudorandom Generators from One-Way Functions: A Simple Construction for Any Hardness. TCC 2006: 443-461
  • Again, it's a long-standing open question whether a more efficient construction (one in which the seed is nearly linear in the input length of the original one-way function) is possible. Maybe no such "black-box" construction is possible. Although, if you are still reading, there is a sort of "doble-negative" result showing that a certain style of "blak-box impossibility" argument will not work here
    • Omer Reingold, Luca Trevisan, Salil P. Vadhan: Notions of Reducibility between Cryptographic Primitives. TCC 2004: 1-20

Impossibility Results

• Key agreement from one-way functions. The work that started it all
  • Russell Impagliazzo, Steven Rudich: Limits on the Provable Consequences of One-Way Permutations STOC 1989: 44-61
  • It might be helpful to read about uniform generation with an NP oracle, for example from
    • Mihir Bellare, Oded Goldreich, Erez Petrank: Uniform Generation of NP-witnesses using an NP-oracle.
    The nature of the impossibility result is clarified in
    • Omer Reingold, Luca Trevisan, Salil P. Vadhan: Notions of Reducibility between Cryptographic Primitives. TCC 2004: 1-20
• One-way permutations from one-way functions
  • Steven Rudich's PhD Thesis
  • Jeff Kahn, Michael E. Saks, Clifford D. Smyth: A Dual Version of Reimer's Inequality and a Proof of Rudich's Conjecture. IEEE Conference on Computational Complexity 2000: 98-103
• Oblivious transfer versus public-key encryption
  • Yael Gertner, Sampath Kannan, Tal Malkin, Omer Reingold, Mahesh Viswanathan: The Relationship between Public Key Encryption and Oblivious Transfer. FOCS 2000: 325-335
• Trapdoor functions from public key encryption
  • Yael Gertner, Tal Malkin, Omer Reingold: On the Impossibility of Basing Trapdoor Functions on Trapdoor Predicates. FOCS 2001: 126-135
• A major open question is whether CCA-secure public-key encryption can be derived in a black-box way (or in any way) from CPA-secure public-key encryption. Currently, the partial evidence is unclear
  • Yael Gertner, Tal Malkin, Steven Myers: Towards a Separation of Semantic and CCA Security for Public Key Encryption. TCC 2007: 434-455
  • Seung Geol Choi, Dana Dachman-Soled, Tal Malkin, Hoeteck Wee: Black-Box Construction of a Non-malleable Encryption Scheme from Any Semantically Secure One. TCC 2008: 427-444
• Collision-resistant hash functions from one-way functions
  • Daniel R. Simon: Finding Collisions on a One-Way Street: Can Secure Hash Functions Be Based on General Assumptions? EUROCRYPT 1998: 334-345

Candidate One-Way Functions and Trapdoor Functions

• Algorithms for Discrete Logarithm
• Discrete Logarithm on Elliptic Curves
• Lattice Problems

Public Key Encryption

• Non-malleable encryption
• The full DNS construction
• Cramer-Shoup
• The unifying framework of Sahai

Obfuscation

• The Barak et al. paper
• Point functions

The Random Oracle Model

• Unimplementable protocols
• Extractable functions

Commitment Schemes

• Stat binding, comp hiding, round lower bound
• Stat binding, comp hiding, construction

Zero Knowledge

• Black-box impossibility results
• Barak's protocols
• Magic functions
• Notions of resettable and concurrent zero knowledge
• Non-interactive zero knowledge