Generating hard instances of lattice problems (extended abstract)
STOC '96 Proceedings of the twenty-eighth annual ACM symposium on Theory of computing
Finding the closest lattice vector when it's unusually close
SODA '00 Proceedings of the eleventh annual ACM-SIAM symposium on Discrete algorithms
Generating Hard Instances of the Short Basis Problem
ICAL '99 Proceedings of the 26th International Colloquium on Automata, Languages and Programming
NTRU: A Ring-Based Public Key Cryptosystem
ANTS-III Proceedings of the Third International Symposium on Algorithmic Number Theory
Worst-Case to Average-Case Reductions Based on Gaussian Measures
SIAM Journal on Computing
Generalized Compact Knapsacks, Cyclic Lattices, and Efficient One-Way Functions
Computational Complexity
Trapdoors for hard lattices and new cryptographic constructions
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
Noninteractive Statistical Zero-Knowledge Proofs for Lattice Problems
CRYPTO 2008 Proceedings of the 28th Annual conference on Cryptology: Advances in Cryptology
Learning a Parallelepiped: Cryptanalysis of GGH and NTRU Signatures
Journal of Cryptology
Fully homomorphic encryption using ideal lattices
Proceedings of the forty-first annual ACM symposium on Theory of computing
On lattices, learning with errors, random linear codes, and cryptography
Journal of the ACM (JACM)
Efficient Public Key Encryption Based on Ideal Lattices
ASIACRYPT '09 Proceedings of the 15th International Conference on the Theory and Application of Cryptology and Information Security: Advances in Cryptology
NTRUSign: digital signatures using the NTRU lattice
CT-RSA'03 Proceedings of the 2003 RSA conference on The cryptographers' track
Asymptotically efficient lattice-based digital signatures
TCC'08 Proceedings of the 5th conference on Theory of cryptography
On ideal lattices and learning with errors over rings
EUROCRYPT'10 Proceedings of the 29th Annual international conference on Theory and Applications of Cryptographic Techniques
Bonsai trees, or how to delegate a lattice basis
EUROCRYPT'10 Proceedings of the 29th Annual international conference on Theory and Applications of Cryptographic Techniques
Efficient lattice (H)IBE in the standard model
EUROCRYPT'10 Proceedings of the 29th Annual international conference on Theory and Applications of Cryptographic Techniques
Adaptively secure identity-based identification from lattices without random oracles
SCN'10 Proceedings of the 7th international conference on Security and cryptography for networks
Better key sizes (and attacks) for LWE-based encryption
CT-RSA'11 Proceedings of the 11th international conference on Topics in cryptology: CT-RSA 2011
Functional encryption for inner product predicates from learning with errors
ASIACRYPT'11 Proceedings of the 17th international conference on The Theory and Application of Cryptology and Information Security
Trapdoors for lattices: simpler, tighter, faster, smaller
EUROCRYPT'12 Proceedings of the 31st Annual international conference on Theory and Applications of Cryptographic Techniques
Pseudorandom functions and lattices
EUROCRYPT'12 Proceedings of the 31st Annual international conference on Theory and Applications of Cryptographic Techniques
Lattice signatures without trapdoors
EUROCRYPT'12 Proceedings of the 31st Annual international conference on Theory and Applications of Cryptographic Techniques
Circular and KDM security for identity-based encryption
PKC'12 Proceedings of the 15th international conference on Practice and Theory in Public Key Cryptography
Fully anonymous attribute tokens from lattices
SCN'12 Proceedings of the 8th international conference on Security and Cryptography for Networks
Security and Communication Networks
Faster gaussian lattice sampling using lazy floating-point arithmetic
ASIACRYPT'12 Proceedings of the 18th international conference on The Theory and Application of Cryptology and Information Security
Learning a zonotope and more: cryptanalysis of NTRUSign countermeasures
ASIACRYPT'12 Proceedings of the 18th international conference on The Theory and Application of Cryptology and Information Security
Classical hardness of learning with errors
Proceedings of the forty-fifth annual ACM symposium on Theory of computing
How to share a lattice trapdoor: threshold protocols for signatures and (H)IBE
ACNS'13 Proceedings of the 11th international conference on Applied Cryptography and Network Security
Lattice-based completely non-malleable public-key encryption in the standard model
Designs, Codes and Cryptography
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At the heart of many recent lattice-based cryptographic schemes is a polynomial-time algorithm that, given a 'high-quality' basis, generates a lattice point according to a Gaussian-like distribution. Unlike most other operations in lattice-based cryptography, however, the known algorithm for this task (due to Gentry, Peikert, and Vaikuntanathan; STOC 2008) is rather inefficient, and is inherently sequential. We present a new Gaussian sampling algorithm for lattices that is efficient and highly parallelizable. We also show that in most cryptographic applications, the algorithm's efficiency comes at almost no cost in asymptotic security. At a high level, our algorithm resembles the "perturbation" heuristic proposed as part of NTRUSign (Hoffstein et al., CTRSA 2003), though the details are quite different. To our knowledge, this is the first algorithm and rigorous analysis demonstrating the security of a perturbation-like technique.