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| Lattice-based cryptography | |
|---|---|
| Name | Lattice-based cryptography |
| Introduced | 1990s |
| Inventor | Miklós Ajtai, Oded Regev |
| Relevant | Post-quantum cryptography, Cryptography |
| Based on | Lattice (group), Computational hardness assumptions |
Lattice-based cryptography is a family of cryptographic primitives and protocols whose security relies on computational hardness of problems in mathematical lattices. Emerging from foundational work by Miklós Ajtai and practical constructions by Oded Regev, the area connects research from Institute for Advanced Study, Massachusetts Institute of Technology, Stanford University, École Normale Supérieure, and industrial labs such as IBM Research, Google, and Microsoft Research. It is central to contemporary efforts at National Institute of Standards and Technology standardization and Post-quantum cryptography transition initiatives.
Lattice-based approaches produce primitives including public-key cryptography, digital signature, homomorphic encryption, and key exchange schemes grounded in problems on integer lattices studied by researchers at University of California, Berkeley, Technische Universität Darmstadt, University of Waterloo, Tel Aviv University, ETH Zurich, and Carnegie Mellon University. The field spans algorithm design influenced by work at Bell Labs, Princeton University, Harvard University, and Cornell University and threat models considered by agencies such as National Security Agency and European Union Agency for Cybersecurity. Practical deployment involves companies like Amazon Web Services, Cloudflare, Intel, and Qualcomm collaborating with standards bodies including IETF and IEEE.
Foundations draw from lattice geometry advanced by researchers at University of Cambridge, University of Oxford, Imperial College London, and historical mathematics from École Polytechnique. Central algebraic structures relate to modules studied at University of Chicago and algorithmic number theory contributions from Brown University, University of Michigan, University of Tokyo, and Seoul National University. Core analytic tools trace to work linked to Institute for Advanced Study seminars and textbooks from Princeton University Press authors. Complexity-theoretic context involves interactions with results from Stanford University, California Institute of Technology, Yale University, and Columbia University.
Standard hardness assumptions include problems such as Shortest Vector Problem studied by groups at University College London and ETH Zurich, Closest Vector Problem researched at University of Bonn and RUHR University Bochum, Learning With Errors introduced by Oded Regev and extended in collaborations with Massachusetts Institute of Technology and University of California, San Diego, and Short Integer Solution analyzed at University of Aarhus and KTH Royal Institute of Technology. These problems are linked to reductions connected to complexity classes studied at Carnegie Mellon University and University of Pennsylvania and to worst-case to average-case frameworks examined at Weizmann Institute of Science and Technion – Israel Institute of Technology.
Prominent constructions include encryption schemes derived from Learning With Errors and signatures from NTRU family with contributions from NTRU Cryptosystems, Inc., Boston University, McGill University, and innovators at Duke University. Homomorphic encryption schemes leverage lattice techniques developed at IBM Research and Microsoft Research with deployments examined by University of Bristol and University of Edinburgh. Key exchange and KEM designs have been advanced in projects at Google and Cloudflare, while signature schemes have been proposed by teams at NIST, ISARA Corporation, PQShield, and academic groups at University of Maryland, University of California, Santa Barbara, and University of Illinois Urbana-Champaign.
Security analyses rely on worst-case to average-case reductions pioneered by Miklós Ajtai and extended by researchers at MIT, Université Paris-Saclay, Columbia University, and École Polytechnique Fédérale de Lausanne. Proof techniques use lattice basis reduction algorithms such as LLL developed at Technische Universität Berlin and BKZ researched by teams at University of Geneva and Max Planck Institute for Informatics. Quantum-era adversary models incorporate results from Google Quantum AI, IBM Quantum, Institute for Quantum Computing, and theoretical frameworks from Perimeter Institute for Theoretical Physics and University of Waterloo.
Implementation research spans hardware acceleration by Intel Corporation and ARM Ltd., software libraries maintained by OpenSSL Project, BoringSSL, libsodium, and projects at MIT Lincoln Laboratory and Sandia National Laboratories. Performance benchmarks are produced in collaborations involving University of Bristol, Queen Mary University of London, Technische Universität München, and industry partners such as Amazon and Cloudflare. Side-channel and fault-attack mitigations have been studied by groups at TU Darmstadt, KU Leuven, EPFL, and Aalto University.
Standardization efforts are coordinated by National Institute of Standards and Technology with inputs from European Telecommunications Standards Institute, IETF, ISO, and vendors including Google, Microsoft, Amazon Web Services, and Cloudflare. Applications target secure messaging by companies like Signal Messenger and WhatsApp, secure web transport by Mozilla Corporation and Apple Inc., and enterprise key management in firms such as IBM, Oracle Corporation, Cisco Systems, and Salesforce. Research collaborations span DARPA programs, Horizon Europe projects, and academic consortia at University of Oxford, Harvard University, and Stanford University.