What is Lattice-based Cryptography?
- Post-quantum Cryptography: An Introduction (Shweta Agrawal)
- Lattice-based Cryptography (Daniele Micciancio and Oded Regev)
- Lattice Cryptography: Understanding Kyber (ML-KEM) and Dilithium (ML-DSA) (Vadim Lyubashevsky)
- Tutorial introduction to the security of lattice-based cryptosystems (Laarhoven et. al.)
Courses and online lectures
- Lattices, Learning with Errors and Post-Quantum Cryptography (Vinod Vaikuntanathan)
- Lattices Algorithms and Applications (Daniele Micciancio)
- An Intensive Introduction to Cryptography (Boaz Barak)
- Lattices in Cryptography (Chris Peikert)
- Lattices in Computer Science (Oded Regev)
- BIU Winter School on Lattice-based Cryptography and Applications (Bar-Ilan University, 2012)
- Workshop on Mathematics of Lattices and Cybersecurity (Brown University, 2015)
- Spring School on Lattice-Based Cryptography (University of Oxford, 2017)
- Lattices: Algorithms, Complexity, and Cryptography (Simons Institute, 2020)
- Foundations and Applications of Lattice-based Cryptography (ICMS, 2022)
Surveys
- A Decade of Lattice Cryptography (Chris Peikert)
- Advances on quantum cryptanalysis of ideal lattices (Léo Ducas)
- Lattice Attacks on NTRU and LWE: A History of Refinements (Martin Albrecht and Léo Ducas)
PhD theses
- Design and Implementation of Lattice-Based Cryptography (Tancrède Lepoint, 2014)
- On the Concrete Security of Lattice-Based Cryptography (Michael Walter, 2017)
- Efficient Lattice-Based Zero-Knowledge Proofs and Applications (Rafaël del Pino, 2018)
- Gadgets and Gaussians in Lattice-Based Cryptography (Nicholas Genise, 2019)
- On ideal lattices and the GGH13 multilinear map (Alice Pellet–Mary, 2019)
- Lattice-based Protocols for Privacy (Cecilia Boschini, 2020)
- Practice-Oriented Techniques in Lattice-Based Cryptography (Muhammed F. Esgin, 2020)
- Extended Security of Lattice-based Cryptography (Mélissa Rossi, 2020)
- Practical lattice-based cryptography over structured lattices (Sarah McCarthy, 2020)
- Efficiency and security aspects of lattice-based cryptography (Carl Bootland, 2021)
- Post-Quantum Cryptography: Cryptanalysis and Implementation (Fernando Vidria, 2021)
- Efficient Implementation Techniques for Lattice-based Cryptosystems (Raymond K. Zhao, 2022)
Other resources
- Collection of resources and links maintained by Daniele Micciancio
- Workshop on Lattices with Symmetry (University of California, Irvine, 2013)
- Computational Challenges in the Theory of Lattices (Brown University, 2018)
- Mathematical Foundations of Asymmetric Cryptography (French Mathematical Society, 2019)
Reading groups and seminars open to the public
Lattice-based primitives selected by NIST for standardization
| Name | Primitive | Description |
|---|---|---|
| CRYSTALS-KYBER | PKE & KEM | Official site |
| CRYSTALS-DILITHIUM | Digital signature | Official site |
| FALCON | Digital signature | Official site |
Implementations of cryptographic primitives
| Name | Language | Author |
|---|---|---|
| CRYSTALS-KYBER | C | Official |
| CRYSTALS-KYBER | Go | Symbolic Software |
| CRYSTALS-KYBER | JavaScript | Anton Tutoveanu |
| CRYSTALS-KYBER | Java | Legion of the Bouncy Castle Inc. |
| CRYSTALS-KYBER | C# | Legion of the Bouncy Castle Inc. |
| CRYSTALS-KYBER | Python | Giacomo Pope |
| CRYSTALS-DILITHIUM | C | Official |
| CRYSTALS-DILITHIUM | Java | Legion of the Bouncy Castle Inc. |
| CRYSTALS-DILITHIUM | C# | Legion of the Bouncy Castle Inc. |
| CRYSTALS-DILITHIUM | Python | Giacomo Pope |
| FALCON | C | Official |
| FALCON | Python | Thomas Prest |
| FALCON | Java | Legion of the Bouncy Castle Inc. |
| FALCON | C# | Legion of the Bouncy Castle Inc. |
| FRODO | C | Official |
| FRODO | Go | Mariia Tuzovska |
| FRODO | Java | Legion of the Bouncy Castle Inc. |
| FRODO | C# | Legion of the Bouncy Castle Inc. |
| NTRU | Rust | Lukas Prokop |
| NTRU | Java | Legion of the Bouncy Castle Inc. |
| NTRU | C# | Legion of the Bouncy Castle Inc. |
| NTRU Prime | Java | Legion of the Bouncy Castle Inc. |
| NTRU Prime | C# | Legion of the Bouncy Castle Inc. |
| SABER | Rust | Lukas Prokop & Lukas Kiem |
| SABER | Java | Legion of the Bouncy Castle Inc. |
| SABER | C# | Legion of the Bouncy Castle Inc. |
Security estimation tools
Lattice.bib
We provide a .bib file with references to lattice-based cryptography papers. Find it here.
About this page
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