# Chris Peikert

Ph.D. (MIT), 2006
Associate Professor
Computer Science and Engineering, University of Michigan (Ann Arbor)

Email: cpeikert [at] umich [dot] edu, Twitter: @ChrisPeikert
Office: Beyster 3601
Phone: 734 . 936 . 2974

Jump to: news — teaching — talks — research.

In 2006 I received my Ph.D. from the MIT Computer Science and Artificial Intelligence Laboratory. My advisor was the incomparable Silvio Micali.

My research interests include cryptography, lattices, coding theory, algorithms, and computational complexity. A particular focus is on cryptographic schemes whose security can be based on the apparent intractability of lattice problems. Further information may be found in my research summary.

- Program committee member: FOCS 2023, EUROCRYPT 2023, CRYPTO 2021 (program co-chair), CRYPTO 2020, CRYPTO 2019, SAC 2019, TCC 2018, FOCS 2017, EUROCRYPT 2017, TCC 2015, PKC 2015, SCN 2014, CRYPTO 2014, TCC 2014, PKC 2013, CRYPTO 2012, ASIACRYPT 2011, PQC 2011, SCPQ 2011, EUROCRYPT 2011, TCC 2011, STOC 2010, PQC 2010, CRYPTO 2009, TCC 2008.

## News

- Aug 2023: Thrilled to have received the Test-of-Time Award from Crypto 2008!
- May 2021: Happy to have lost all adjectives, leaving just "Professor."
- Feb 2019: Finally! Noninteractive Zero Knowledge for all of NP from plain LWE.
- Nov 2017: Thank you to the TCC community for the great honor of the Test-of-Time Award! Here's our talk.
- Mar 2017: I've been appointed the Patrick C. Fischer Development Professor of Theoretical Computer Science. Great thanks to the Fischer family and the University for this honor!
- Aug 2016: Announcing the Ring-LWE Challenges: get cracking!
- May 2016: Announcing Λ ○ λ (pronounced "L O L"), a general-purpose library for lattice-based cryptography! Get the paper or the code.
- Jan 2016: My survey A Decade of Lattice Cryptography is now available.
- Sep 2015: After six great years at Georgia Tech, I've moved to the University of Michigan. Go Blue!
- What does the GCHQ's Soliloquy attack mean for lattice-based cryptography? I explain here. See also the follow-up discussion on the cryptanalytic-algorithms mailing list.
- Thanks to the Google Research Awards program!
- Thank you to the Alfred P. Sloan Foundation!

## Teaching

> "Good teaching is one-fourth preparation and three-fourths theater." — Gail Godwin

- Fall 2017: EECS 376, Foundations of Computer Science
- Winter 2017: EECS 575, Advanced Cryptography
- Fall 2016: EECS 475, Introduction to Cryptography
- Winter 2016: EECS 575, Advanced Cryptography
- Fall 2015: EECS 598, Lattices in Cryptography
- Teaching at Georgia Tech:
  - CS 8803, Lattices in Cryptography (Fall 2013)
  - CS 7560, Theory of Cryptography (Spring 2015, Spring 2013, Spring 2011)
  - CS 4510, Automata and Complexity (Fall 2014)
  - CS 3510/11, Design and Analysis of Algorithms/Honors Algorithms (Spring 2014, Spring 2012, Fall 2011)
  - CS 6260, Applied Cryptography (Fall 2012)
  - CS 4235 / 8803 IIS, Introduction to Information Security, Fall 2010

## Expository Lectures on Lattice-Based Cryptography

Slides from some recent tutorials on lattice-based crypto. (Talks on specific papers are available below.)

- Unexpected Applications of Fully Homomorphic Encryption
  (invited talk at PKC 2023)
- Post-Quantum Cryptography
  (invited tutorial at QIP 2022)
- To Cyclicity and Beyond!
  (from TCC 2017 Test-of-Time Award)
- Lattice-Based Cryptography
  (invited tutorial at QCRYPT 2016)
- Bootstrapping with Small Error Growth and Cryptography from Rings
  (from Summer School on Mathematical and Practical Aspects of Fully Homomorphic Encryption and Multilinear Maps)
- Ideal Lattices and Ring-LWE: Overview and Open Problems
  (from ICERM Workshop on Mathematics of Lattices and Cybersecurity)
- Ring Switching and Bootstrapping FHE
  (from Oberwolfach workshop on cryptography)
- Lattices: ... to Cryptography
  (from Visions of Cryptography)
- Tutorials from crypt@b-it 2013 summer school at Bonn University: Day 1, Day 2, Day 3, Day 4, Day 5
- The Geometry of Rings
  (from the ECRYPT II Summer School on Lattices)
- Learning With Errors 1 and 2 [Video]
  Trapdoors for Lattices 1 and 2 [Video]
  (from the 2nd Bar-Ilan Winter School on Cryptography)
- Trapdoors for Lattices: Signatures, Identity-Based Encryption, and Beyond
  (from the ENS Lattice Crypto Day, Paris)
- Lattices: From Worst-Case, to Average-Case, to Cryptography and
  Peculiar Properties of Lattice-Based Encryption
  (from the CWI Workshop, Amsterdam)
- Some Recent Progress in Lattice-Based Cryptography
  (from invited tutorial at TCC 2009)

## Research

> "If we knew what it was we were doing, it would not be called research, would it?" — Albert Einstein (?)

- Cryptanalysis of Lattice-Based Sequentiality Assumptions and Proofs of Sequential Work
  Chris Peikert, Yi Tang.
  Manuscript.
- Functional Commitments for All Functions, with Transparent Setup and from SIS
  Leo de Castro, Chris Peikert.
  In EUROCRYPT 2023.
- Classical and Quantum Security of Elliptic Curve VRF, via Relative Indifferentiability
  Chris Peikert, Jiayu Xu.
  In CT-RSA 2023.
- Hardness of the (Approximate) Shortest Vector Problem: A Simple Proof via Reed-Solomon Codes
  Huck Bennett, Chris Peikert.
  In RANDOM-APPROX 2023.
- Improved Hardness of BDD and SVP Under Gap-(S)ETH
  Huck Bennett, Chris Peikert, Yi Tang.
  In ITCS 2022.
- Lattice (List) Decoding Near Minkowski's Inequality
  Ethan Mook, Chris Peikert.
  IEEE Transactions on Information Theory, 68(2):863-870.
- Vector and Functional Commitments from Lattices
  Chris Peikert, Zachary Pepin, Chad Sharp.
  In TCC 2021.
- F1: A Fast and Programmable Accelerator for Fully Homomorphic Encryption
  Axel Feldmann, Nikola Samardzic, Aleksandar Krastev, Srini Devadas, Ron Dreslinski, Karim Eldefrawy, Nicholas Genise, Chris Peikert, Daniel Sanchez.
  In MICRO 2021. Selected as a MICRO'21 Top Pick.
- Hardness of Bounded Distance Decoding on Lattices in ell_p Norms
  Huck Bennett, Chris Peikert.
  In CCC 2020.
- Improved Discrete Gaussian and Subgaussian Analysis for Lattice Cryptography
  Nicholas Genise, Daniele Micciancio, Chris Peikert, Michael Walter.
  In PKC 2020.
- He Gives C-Sieves on the CSIDH [Slides, Video]
  Chris Peikert.
  In EUROCRYPT 2020.
- Algebraically Structured LWE, Revisited [Slides]
  Chris Peikert, Zachary Pepin.
  In TCC 2019.
- Noninteractive Zero Knowledge for NP from (Plain) Learning With Errors [Slides, TCS+ video]
  Chris Peikert, Sina Shiehian.
  In CRYPTO 2019.
- ALCHEMY: A Language and Compiler for Homomorphic Encryption Made easY
  Eric Crockett, Chris Peikert, Chad Sharp.
  In CCS 2018.
- More Efficient Commitments from Structured Lattice Assumptions
  Carsten Baum, Ivan Damgård, Vadim Lyubashevsky, Sabine Oechsner, Chris Peikert.
  In SCN 2018.
- New (and Old) Proof Systems for Lattice Problems [Slides]
  Navid Alamati, Chris Peikert, Noah Stephens-Davidowitz.
  In PKC 2018.
- Privately Constraining and Programming PRFs, the LWE Way [Slides]
  Chris Peikert, Sina Shiehian.
  In PKC 2018.
- Pseudorandomness of Ring-LWE for Any Ring and Modulus [Slides]
  Chris Peikert, Oded Regev, Noah Stephens-Davidowitz.
  In STOC 2017.
- Challenges for Ring-LWE [website]
  Eric Crockett, Chris Peikert.
  Manuscript.
- Multi-Key FHE from LWE, Revisited
  Chris Peikert, Sina Shiehian.
  In TCC 2016-B.
- Λ ○ λ: Functional Lattice Cryptography [code]
  Eric Crockett, Chris Peikert.
  In CCS 2016.
- How (Not) to Instantiate Ring-LWE [Slides]
  Chris Peikert.
  In SCN 2016.
- Three's Compromised Too: Circular Insecurity for Any Cycle Length from (Ring-)LWE
  Navid Alamati, Chris Peikert.
  In CRYPTO 2016.
- A Decade of Lattice Cryptography
  Chris Peikert.
  Monograph, September 2015 (updated February 2016).
- Recovering Short Generators of Principal Ideals in Cyclotomic Rings
  Ronald Cramer, Léo Ducas, Chris Peikert, Oded Regev.
  In Eurocrypt 2016.
- Key-Homomorphic Constrained Pseudorandom Functions
  Abhishek Banerjee, Georg Fuchsbauer, Chris Peikert, Krzysztof Pietrzak, Sophie Stevens.
  In TCC 2015.
- Lattice Cryptography for the Internet [Slides]
  Chris Peikert.
  In PQCrypto 2014.
- Faster Bootstrapping with Polynomial Error [Slides]
  Jacob Alperin-Sheriff, Chris Peikert.
  In CRYPTO 2014.
- New and Improved Key-Homomorphic Pseudorandom Functions [Slides]
  Abhishek Banerjee, Chris Peikert.
  In CRYPTO 2014.
- Using Fully Homomorphic Hybrid Encryption to Minimize Non-interactive Zero-Knowledge Proofs
  Craig Gentry, Jens Groth, Yuval Ishai, Chris Peikert, Amit Sahai, Adam Smith.
  Journal of Cryptology, 28(4):820-843.
- SPRING: Fast Pseudorandom Functions from Rounded Ring Products
  Abhishek Banerjee, Hai Brenner, Gaëtan Leurent, Chris Peikert, Alon Rosen.
  In FSE 2014.
- Practical Bootstrapping in Quasilinear Time [Slides]
  Jacob Alperin-Sheriff, Chris Peikert.
  In CRYPTO 2013. Invited to Journal of Cryptology.
- Hardness of SIS and LWE with Small Parameters
  Daniele Micciancio, Chris Peikert.
  In CRYPTO 2013. Invited to Journal of Cryptology.
- How to Share a Lattice Trapdoor: Threshold Protocols for Signatures and (H)IBE
  Rikke Bendlin, Sara Krehbiel, Chris Peikert.
  In ACNS 2013.
- On the Lattice Smoothing Parameter Problem
  Kai-Min Chung, Daniel Dadush, Feng-Hao Liu, Chris Peikert.
  In CCC 2013.
- Classical Hardness of Learning with Errors
  Zvika Brakersi, Adeline Langlois, Chris Peikert, Oded Regev, Damien Stehlé.
  In STOC 2013.
- A Toolkit for Ring-LWE Cryptography [Slides]
  Vadim Lyubashevsky, Chris Peikert, Oded Regev.
  In Eurocrypt 2013.
- Field Switching in BGV-Style Homomorphic Encryption
  Craig Gentry, Shai Halevi, Chris Peikert, Nigel Smart.
  Journal of Computer Security, 21(5):663–684. Preliminary version in SCN 2012.
- List Decoding Barnes-Wall Lattices
  Elena Grigorescu, Chris Peikert.
  In CCC 2012.
- Circular and KDM Security for Identity-Based Encryption
  Jacob Alperin-Sheriff, Chris Peikert.
  In PKC 2012.
- Trapdoors for Lattices: Simpler, Tighter, Faster, Smaller [Slides]
  Daniele Micciancio, Chris Peikert.
  In Eurocrypt 2012. Invited to Journal of Cryptology.
- Pseudorandom Functions and Lattices [Slides]
  Abhishek Banerjee, Chris Peikert, Alon Rosen.
  In Eurocrypt 2012.
- Identity-Based (Lossy) Trapdoor Functions and Applications
  Mihir Bellare, Eike Kiltz, Chris Peikert, Brent Waters.
  In Eurocrypt 2012.
- Enumerative Algorithms for Lattice Problems in Any Norm via M-Ellipsoid Coverings
  Daniel Dadush, Chris Peikert, Santosh Vempala.
  In FOCS 2011.
- Bi-Deniable Public-Key Encryption [Slides, Video]
  Adam O'Neill, Chris Peikert, Brent Waters.
  In CRYPTO 2011.
- Better Key Sizes (and Attacks) for LWE-Based Encryption
  Richard Lindner, Chris Peikert.
  In CT-RSA 2011.
- An Efficient and Parallel Gaussian Sampler for Lattices [Slides]
  Chris Peikert.
  In CRYPTO 2010.
- Bonsai Trees, or How to Delegate a Lattice Basis
  David Cash, Dennis Hofheinz, Eike Kiltz, Chris Peikert.
  (Merged version of this and this.)
  Journal of Cryptology, 25(4):601-639. Awarded Best Paper, Eurocrypt 2010, invited to Journal of Cryptology.
- On Ideal Lattices and Learning with Errors Over Rings [Slides]
  Vadim Lyubashevsky, Chris Peikert, Oded Regev.
  Journal of the ACM, 60(6):43:1–43:35. Preliminary version in Eurocrypt 2010.
- Public-Key Encryption Schemes with Auxiliary Inputs
  Yevgeniy Dodis, Shafi Goldwasser, Yael Kalai, Chris Peikert, Vinod Vaikuntanathan.
  In TCC 2010.
- Robustness of the Learning with Errors Assumption
  Shafi Goldwasser, Yael Kalai, Chris Peikert, Vinod Vaikuntanathan.
  In ICS 2010.
- Fast Cryptographic Primitives and Circular-Secure Encryption Based on Hard Learning Problems
  Benny Applebaum, David Cash, Chris Peikert, Amit Sahai.
  In CRYPTO 2009.
- Public-Key Cryptosystems from the Worst-Case Shortest Vector Problem [Slides, Video]
  Chris Peikert.
  In STOC 2009. Awarded Best Paper.
- Generating Shorter Bases for Hard Random Lattices
  Joel Alwen, Chris Peikert.
  Theory of Computing Systems, 48(3):535-553, April 2011. By invitation to special issue on STACS 2009.
- SWIFFTX: A Proposal for the SHA-3 Standard
  Yuriy Arbitman, Gil Dogon, Vadim Lyubashevsky, Daniele Micciancio, Chris Peikert, Alon Rosen.
  Submitted to NIST SHA-3 Competition.
- Limits on the Hardness of Lattice Problems in l_p Norms [Slides]
  Chris Peikert.
  Computational Complexity, 17(2):300-351, May 2008. By invitation to special issue on Complexity 2007.
- Lossy Trapdoor Functions and Their Applications [Slides]
  Chris Peikert, Brent Waters.
  SIAM J. Computing, 40(6):1803-1844, December 2011. By invitation to special issue on STOC 2008.
- Noninteractive Statistical Zero-Knowledge Proofs for Lattice Problems
  Chris Peikert, Vinod Vaikuntanathan.
  In CRYPTO 2008.
- A Framework for Efficient and Composable Oblivious Transfer [Slides]
  Chris Peikert, Vinod Vaikuntanathan, Brent Waters.
  In CRYPTO 2008.
- Trapdoors for Hard Lattices and New Cryptographic Constructions [Slides]
  Craig Gentry, Chris Peikert, Vinod Vaikuntanathan.
  In STOC 2008.
- SWIFFT: A Modest Proposal for FFT Hashing
  Vadim Lyubashevsky, Daniele Micciancio, Chris Peikert, Alon Rosen.
  In FSE 2008.
- Lattices that Admit Logarithmic Worst-Case to Average-Case Connection Factors [Slides]
  Chris Peikert, Alon Rosen.
  In STOC 2007.
- Provably Secure FFT Hashing
  Vadim Lyubashevsky, Daniele Micciancio, Chris Peikert, Alon Rosen.
  In 2nd NIST Cryptographic Hash Function Workshop, 2006.
- Efficient Collision-Resistant Hashing from Worst-Case Assumptions on Cyclic Lattices [Slides]
  Chris Peikert, Alon Rosen.
  In TCC 2006.
- On Error Correction in the Exponent [Slides]
  Chris Peikert.
  In TCC 2006.
- Optimal Error Correction Against Computationally Bounded Noise
  Silvio Micali, Chris Peikert, Madhu Sudan, David A. Wilson.
  IEEE Transactions on Information Theory, 56(11):5673-5680, November 2010. Preliminary version in TCC 2005.
- Completely Fair SFE and Coalition-Safe Cheap Talk
  Matt Lepinski, Silvio Micali, Chris Peikert, abhi shelat.
  In PODC 2004.
- Lower Bounds for Collusion-Secure Fingerprinting
  Chris Peikert, Adam Smith, abhi shelat.
  In SODA 2003.
- Adaptive Security in the Threshold Setting: From Cryptosystems to Signature Schemes
  Anna Lysyanskaya, Chris Peikert.
  In ASIACRYPT 2001.
- March Madness is (NP-)Hard
  David Liben-Nowell, Moses Liskov, Chris Peikert, abhi shelat, Adam Smith, Grant Wang.
  Unpublished manuscript.

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