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Lattices in Computer Science

Objective

A lattice is defined as the set of all integer combinations of $n$ linearly independent vectors in $\R^n$. These geometrical objects possess a rich combinatorial structure that has attracted the attention of great mathematicians over the last two centuries. Lattices have an impressive number of applications in mathematics and computer science, from number theory and Diophantine approximation to complexity theory and cryptography. Over the last two decades, the computational study of lattices has witnessed several remarkable discoveries. Most notable are the development of the LLL algorithm by Lenstra, Lenstra and Lovasz and Ajtai's discovery of lattice-based cryptographic constructions. I propose to pursue these research directions and attempt to discover new connections between lattices and computer science. A particular focus will be put on applications in cryptography, as these can lead to many advances in the field and are also of great practical importance. I believe that the extraordinary properties of lattices have the potential to revolutionize many other areas of computer science such as complexity, cryptography, machine learning theory, quantum computation, and more. My scientific goals include obtaining stronger and more practical lattice-based cryptographic constructions, resolving important questions regarding the complexity of lattice problems, finding sub-exponential time algorithms for lattice problems and exploring some novel applications of lattices to areas such as Markov chains and machine learning theory.

Field of science

  • /natural sciences/computer and information sciences/computer security/cryptography
  • /natural sciences/mathematics/pure mathematics/arithmetic
  • /natural sciences/computer and information sciences/artificial intelligence/machine learning

Call for proposal

ERC-2007-StG
See other projects for this call

Funding Scheme

ERC-SG - ERC Starting Grant

Host institution

CENTRE NATIONAL DE LA RECHERCHE SCIENTIFIQUE CNRS
Address
Rue Michel Ange 3
75794 Paris
France
Activity type
Research Organisations
EU contribution
€ 483 000
Principal investigator
Oded Regev (Prof.)
Administrative Contact
Louis Avigdor (Mr.)

Beneficiaries (2)

CENTRE NATIONAL DE LA RECHERCHE SCIENTIFIQUE CNRS
France
EU contribution
€ 483 000
Address
Rue Michel Ange 3
75794 Paris
Activity type
Research Organisations
Principal investigator
Oded Regev (Prof.)
Administrative Contact
Louis Avigdor (Mr.)
TEL AVIV UNIVERSITY

Participation ended

Israel
EU contribution
€ 339 000
Address
Ramat Aviv
69978 Tel Aviv
Activity type
Higher or Secondary Education Establishments
Administrative Contact
Rafi Elishav (Mr.)