What is Lattice-based Cryptography?

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

• Monash Cybersecurity Seminars
• ENSL/CWI/RHUL Joint Online Cryptography Seminars

Lattice-based primitives selected by NIST for standardization

Implementations of cryptographic primitives

Security estimation tools

• Lattice estimator
• Leaky LWE estimator (Dachman-Soled et. al.)

Lattice.bib

We provide a .bib file with references to lattice-based cryptography papers. Find it here.

About this page

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