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» On lattices, learning with errors, random linear codes, and ...
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STOC
2005
ACM
198views Algorithms» more  STOC 2005»
14 years 4 months ago
On lattices, learning with errors, random linear codes, and cryptography
Our main result is a reduction from worst-case lattice problems such as GAPSVP and SIVP to a certain learning problem. This learning problem is a natural extension of the `learnin...
Oded Regev
PKC
2011
Springer
219views Cryptology» more  PKC 2011»
12 years 7 months ago
Linearly Homomorphic Signatures over Binary Fields and New Tools for Lattice-Based Signatures
ded abstract of this work appears in Public Key Cryptography — PKC 2011, ed. R. Gennaro, Springer LNCS 6571 (2011), 1–16. This is the full version. We propose a linearly homom...
Dan Boneh, David Mandell Freeman
PKC
2012
Springer
255views Cryptology» more  PKC 2012»
11 years 7 months ago
Strongly Secure Authenticated Key Exchange from Factoring, Codes, and Lattices
Abstract. An unresolved problem in research on authenticated key exchange (AKE) is to construct a secure protocol against advanced attacks such as key compromise impersonation and ...
Atsushi Fujioka, Koutarou Suzuki, Keita Xagawa, Ka...
FOCS
1999
IEEE
13 years 9 months ago
Hardness of Approximating the Minimum Distance of a Linear Code
We show that the minimum distance of a linear code is not approximable to within any constant factor in random polynomial time (RP), unless nondeterministic polynomial time (NP) eq...
Ilya Dumer, Daniele Micciancio, Madhu Sudan
ICALP
2011
Springer
12 years 8 months ago
New Algorithms for Learning in Presence of Errors
We give new algorithms for a variety of randomly-generated instances of computational problems using a linearization technique that reduces to solving a system of linear equations...
Sanjeev Arora, Rong Ge