Project Topics

Here is a listing of possible topics and research questions for the course project. For each topic area, I list a few papers that could serve as the starting point for a survey as well as some open questions that could be the starting point for a research-based project. You are welcome to choose one of the directions listed here or propose your own direction.

Complexity of Lattice Problems

• The Shortest Vector Problem in L₂ is NP-Hard for Randomized Reductions, by Miklós Ajtai

• The Shortest Vector in a Lattice is Hard to Approximate to Within Some Constant, by Daniele Micciancio

• Hardness of Approximating the Shortest Vector Problem in Lattices, by Subhash Khot

• Approximating SVP_∞ to within Almost-Polynomial Factors Is NP-Hard, by Irit Dinur

• On Lattices, Learning with Errors, Random Linear Codes, and Cryptography, by Oded Regev

• Public-Key Cryptosystems from the Worst-Case Shortest Vector Problem, by Chris Peikert

• (Gap/S)ETH Hardness of SVP, by Divesh Aggarwal and Noah Stephens-Davidowitz

Fully Homomorphic Encryption

Constructions

• Fully Homomorphic Encryption without Bootstrapping, by Zvika Brakerski, Craig Gentry, and Vinod Vaikuntanathan

• Fully Homomorphic Encryption without Modulus Switching from Classical GapSVP, by Zvika Brakerski

• Homomorphic Encryption from Learning with Errors: Conceptually-Simpler, Asymptotically-Faster, Attribute-Based, by Craig Gentry, Amit Sahai, and Brent Waters

• Leveled Fully Homomorphic Signatures from Standard Lattices, by Sergey Gorbunov, Vinod Vaikuntanathan, and Daniel Wichs

Applications

• Fast Private Set Intersection from Homomorphic Encryption, by Hao Chen, Kim Laine, and Peter Rindal

• Onion Ring ORAM: Efficient Constant Bandwidth Oblivious RAM from (Leveled) TFHE, by Hao Chen, Ilaria Chillotti, and Ling Ren

Homomorphic Secret Sharing

Foundations

• Function Secret Sharing, by Elette Boyle, Niv Gilboa, and Yuval Ishai

• Foundations of Homomorphic Secret Sharing, by Elette Boyle, Niv Gilboa, Yuval Ishai, Huijia Lin, and Stefano Tessaro

• Spooky Encryption and its Applications, by Yevgeniy Dodis, Shai Halevi, Ron D. Rothblum, and Daniel Wichs

• Homomorphic Secret Sharing from Lattices Without FHE, by Elette Boyle, Lisa Kohl, and Peter Scholl

Applications

• Riposte: An Anonymous Messaging System Handling Millions of Users, by Henry Corrigan-Gibbs, Dan Boneh, and David Mazières

• Splinter: Practical Private Queries on Public Data, by Frank Wang, Catherine Yun, Shafi Goldwasser, Vinod Vaikuntanathan, and Matei Zaharia

Proof Systems

• Succinct Non-Interactive Arguments via Linear Interactive Proofs, by Nir Bitansky, Alessandro Chiesa, Yuval Ishai, Rafail Ostrovsky, and Omer Paneth

• A Non-PCP Approach to Succinct Quantum-Safe Zero-Knowledge, by Jonathan Bootle, Vadim Lyubashevsky, Ngoc Khanh Nguyen, and Gregor Seiler

• Shorter and Faster Post-Quantum Designated-Verifier zkSNARKs from Lattices, by Yuval Ishai, Hang Su, and David J. Wu

Lattice-Based PRFs

• Pseudorandom Functions and Lattices, by Abhishek Banerjee, Chris Peikert, and Alon Rosen

• Key Homomorphic PRFs and Their Applications, by Dan Boneh, Kevin Lewi, Hart Montgomery, and Ananth Raghunathan

• Key-Homomorphic Pseudorandom Functions from LWE with a Small Modulus, by Sam Kim