I am a member of Courant's Theoretical Computer Science Group. My work is in the areas of cryptography, quantum computation, and complexity theory. A main focus of my research is on lattice-based cryptography, and specifically the Learning With Errors problem. I am also most interested in questions in biology, specifically in deciphering the pre-mRNA splicing code.

Research

lattice Theoretical computer science and cryptography: A main focus of our research is on lattice-based cryptography, and specifically, the Learning With Errors (LWE) problem. Lattice-based cryptography offers many advantages over traditional number-theoretic cryptography, including its conjectured security against quantum computers, making it one of the leading candidates for post-quantum (or quantum-resistant) cryptography. It is also incredibly versatile, allowing the construction of advanced cryptographic protocols like fully homomorphic encryption.

splicing Splicing code: Genes in our genome contain long "comments", known as introns, that are removed in a process called splicing shortly after the DNA gets transcribed into RNA. The sequence features that demarcate those introns are highly intricate and are known as the splicing code. In our lab, we are combining wet lab high-throughput experiments with machine learning analysis to gain insight into this remarkable process. We expect our results to have implications for diagnosis of genetic disorders and for RNA therapeutics.

Students

Ph.D.

MS

Postdocs

  • Young Kun Ko, joint with Subhash Khot (Ph.D. 2018, Princeton)
  • Euiwoong Lee, joint with Subhash Khot (Ph.D. 2017, CMU)
  • Omri Weinstein (Ph.D. 2015, Princeton; assistant professor, Columbia)
  • Aravindan Vijayaraghavan (Ph.D. 2013, Princeton; assistant professor, Northwestern)
  • Anindya De (Ph.D. 2013, UC Berkeley; assistant professor, Northwestern)
  • Jop Briët, joint with Assaf Naor (Ph.D. 2011, CWI, Amsterdam; researcher, CWI, Amsterdam)
  • Daniel Dadush, joint with Assaf Naor (Ph.D. 2012, Georgia Tech; researcher, CWI, Amsterdam)
  • Divesh Aggarwal, joint with Yevgeniy Dodis (Ph.D. 2012, ETH Zurich; assistant professor, NUS)
  • Vadim Lyubashevsky (Ph.D. 2008, UC San Diego; researcher in IBM Zurich)
  • Dan Gutfreund (Ph.D. 2005, Hebrew University; researcher in IBM Cambridge)

Teaching

Funding

NSF
Simons Foundation

Short Bio

Oded Regev is a professor in the Courant Institute of Mathematical Sciences of New York University. Prior to joining NYU, he was affiliated with Tel Aviv University and the École Normale Supérieure, Paris under the French National Centre for Scientific Research (CNRS). He received his Ph.D. in computer science from Tel Aviv University in 2001. He is the recipient of a European Research Council (ERC) Starting Grant in 2008, the 2018 Gödel Prize, the 2019 Simons Investigator award, as well as best paper awards in STOC 2003 and Eurocrypt 2006. His main research areas include theoretical computer science, cryptography, quantum computation and complexity theory. A main focus of his research is in the area of lattice-based cryptography, where he introduced several key concepts, including the Learning with Errors (LWE) problem and the use of Gaussian measures.

Professional activities

  • Organizer and co-founder of TCS+, an online seminar series in theoretical computer science, accessible to the widest possible audience, and ensuring a carbon-free dissemination of ideas across the globe.
  • Theory of Computing (Associate Editor-in-Chief)
  • Program committee member in STOC 2004, CCC 2005, TCC 2007, ANTS 2008, STOC 2008, CCC 2009, STOC 2010, STOC 2012

Selected Publications

  • A Reverse Minkowski Theorem (link)
    Oded Regev, Noah Stephens-Davidowitz
    STOC 2017
  • Towards Strong Reverse Minkowski-type Inequalities for Lattices (link)
    Daniel Dadush, Oded Regev
    FOCS 2016
  • Counterexamples to a conjecture of Woods (link)
    Oded Regev, Uri Shapira, Barak Weiss
    Duke J Math
  • Recovering Short Generators of Principal Ideals in Cyclotomic Rings (link)
    Ronald Cramer, Léo Ducas, Chris Peikert, Oded Regev
    EUROCRYPT 2016
  • Tight Hardness of the Non-commutative Grothendieck Problem (link)
    Jop Briët, Oded Regev, Rishi Saket
    FOCS 2015
  • Solving the Shortest Vector Problem in 2^n Time via Discrete Gaussian Sampling (link)
    Divesh Aggarwal, Daniel Dadush, Oded Regev, Noah Stephens-Davidowitz
    STOC 2015
  • On the Lattice Isomorphism Problem (link)
    Ishay Haviv, Oded Regev
    SODA 2014
  • Classical Hardness of Learning with Errors (link)
    Zvika Brakerski, Adeline Langlois, Chris Peikert, Oded Regev, Damien Stehlé
    STOC 2013
  • Efficient rounding for the noncommutative Grothendieck inequality (link)
    Assaf Naor, Oded Regev, and Thomas Vidick
    STOC 2013
  • Locally decodable codes and the failure of cotype for projective tensor products (link)
    Jop Briët, Assaf Naor, Oded Regev
    Electronic Research Announcements in Mathematical Sciences 19 (2012) 120--130
  • Quantum XOR Games (link)
    Thomas Vidick, Oded Regev
    CCC 2013
  • Elementary Proofs of Grothendieck Theorems for Completely Bounded Norms (link)
    Thomas Vidick, Oded Regev
    Journal of Operator Theory
  • Entropy-based Bounds on Dimension Reduction in L1 (link)
    Oded Regev
    Israel Journal of Mathematics
  • Quantum One-Way Communication can be Exponentially Stronger Than Classical Communication (link,pptx)
    Bo'az Klartag, Oded Regev
    STOC 2011
  • An Optimal Lower Bound on the Communication Complexity of Gap-Hamming-Distance (link,pptx)
    Amit Chakrabarti, Oded Regev
    STOC 2011
  • The Learning with Errors Problem (pdf,ppt)
    Oded Regev
    Invited survey in CCC 2010
  • Lattice Enumeration using Extreme Pruning
    Nicolas Gama, Phong Q. Nguyen, Oded Regev
    Eurocrypt 2010
  • On Ideal Lattices and Learning with Errors Over Rings (pdf,link)
    Vadim Lyubashevsky, Chris Peikert, Oded Regev
    Eurocrypt 2010
  • No Strong Parallel Repetition with Entangled and Non-signaling Provers (link)
    Julia Kempe, Oded Regev
    CCC 2010
  • Lattice-based Cryptography (pdf)
    Daniele Micciancio, Oded Regev
    Book chapter in Post-quantum Cryptography, D. J. Bernstein and J. Buchmann (eds.), Springer (2008)
  • Unique Games with Entangled Provers are Easy (link,ppt)
    Julia Kempe, Oded Regev, Ben Toner
    SIAM Journal on Computing 39(7), pp. 3207--3229, 2010. Preliminary version in Proc. of FOCS 2008
  • Simulating Quantum Correlations with Finite Communication (link,ppt)
    Oded Regev, Ben Toner
    SIAM Journal on Computing 39(4), pp. 1562--1580, 2009. Preliminary version in Proc. of FOCS 2007
  • On the Complexity of Lattice Problems with Polynomial Approximation Factors (ps,pdf)
    Oded Regev
    Survey paper prepared for the LLL+25 conference. Appears in this book
  • Tensor-based Hardness of the Shortest Vector Problem to within Almost Polynomial Factors (link)
    Ishay Haviv, Oded Regev
    Theory of Computing 8(23), pp. 513-531, 2012. Preliminary version in STOC 2007
  • Lattice-based Cryptography (ps,pdf,ppt)
    Oded Regev
    Tutorial given in CRYPTO 2006
  • Learning a Parallelepiped: Cryptanalysis of GGH and NTRU Signatures (pdf,ppt)
    Phong Q. Nguyen, Oded Regev
    Eurocrypt 2006
  • On the Hardness of Satisfiability with Bounded Occurrences in the Polynomial-Time Hierarchy (ps,pdf)
    Ishay Haviv, Oded Regev, Amnon Ta-Shma
    Theory of Computing 3(3), pp. 45-60, 2007.
  • Conditional Hardness for Approximate Coloring (pdf)
    Irit Dinur, Elchanan Mossel, Oded Regev
    SIAM Journal on Computing 39(3), pp. 843--873, 2009. Preliminary version in Proc. of STOC 2006
  • On Lattices, Learning with Errors, Random Linear Codes, and Cryptography (pdf,ppt)
    Oded Regev
    Journal of the ACM 56(6), article 34, 2009. Preliminary version in Proc. of STOC 2005
  • The Complexity of the Local Hamiltonian Problem (link)
    Julia Kempe, Alexei Kitaev, Oded Regev
    SIAM Journal on Computing 35(5), pp. 1070-1097, 2006. Preliminary version in Proc. of FSTTCS 2004
  • A Subexponential Time Algorithm for the Dihedral Hidden Subgroup Problem with Polynomial Space (link)
    Oded Regev
  • Worst-case to Average-case Reductions based on Gaussian Measures (ps,pdf)
    Daniele Micciancio, Oded Regev
    SIAM Journal on Computing 37(1) pp. 267-302, 2007. Preliminary version in Proc. of FOCS 2004
  • Randomised Nearest Neighbour Lower Bound (pdf)
    Amit Chakrabarti, Oded Regev
    SIAM Journal on Computing 39(5) pp. 1919-1940, 2010. Preliminary version in Proc. of FOCS 2004
  • Adiabatic Quantum Computation is Equivalent to Standard Quantum Computation (link)
    Dorit Aharonov, Wim van Dam, Julia Kempe, Zeph Landau, Seth Lloyd, Oded Regev
    SIAM Journal on Computing 37(1) pp. 166-194, 2007. Preliminary version in Proc. of FOCS 2004
  • New Lattice Based Cryptographic Constructions (psgz,pdf,ppt)
    Oded Regev
    Journal of the ACM 51(6), pp. 899-942, 2004. Preliminary version in Proc. of STOC 2003
  • Vertex Cover Might be Hard to Approximate to within 2-ε (ps,pdf)
    Subhash Khot, Oded Regev
    Journal of Computer and System Sciences 74(3), pp. 335-349, 2008. Preliminary version in Proc. of CCC 2003

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