Lattice basis reduction: improved practical algorithms and solving subset sum problems
Mathematical Programming: Series A and B
Generating hard instances of lattice problems (extended abstract)
STOC '96 Proceedings of the twenty-eighth annual ACM symposium on Theory of computing
A public-key cryptosystem with worst-case/average-case equivalence
STOC '97 Proceedings of the twenty-ninth 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
A sieve algorithm for the shortest lattice vector problem
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
Lattice Reduction by Random Sampling and Birthday Methods
STACS '03 Proceedings of the 20th Annual Symposium on Theoretical Aspects of Computer Science
A Generalized Birthday Problem
CRYPTO '02 Proceedings of the 22nd Annual International Cryptology Conference on Advances in Cryptology
NTRU: A Ring-Based Public Key Cryptosystem
ANTS-III Proceedings of the Third International Symposium on Algorithmic Number Theory
Noise-tolerant learning, the parity problem, and the statistical query model
Journal of the ACM (JACM)
More on Average Case vs Approximation Complexity
FOCS '03 Proceedings of the 44th Annual IEEE Symposium on Foundations of Computer Science
New lattice-based cryptographic constructions
Journal of the ACM (JACM)
Generalized Compact Knapsacks, Cyclic Lattices, and Efficient One-Way Functions
Computational Complexity
Lossy trapdoor functions and their applications
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
Trapdoors for hard lattices and new cryptographic constructions
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
A Framework for Efficient and Composable Oblivious Transfer
CRYPTO 2008 Proceedings of the 28th Annual conference on Cryptology: Advances in Cryptology
Possibility and Impossibility Results for Encryption and Commitment Secure under Selective Opening
EUROCRYPT '09 Proceedings of the 28th Annual International Conference on Advances in Cryptology: the Theory and Applications of Cryptographic Techniques
Fully homomorphic encryption using ideal lattices
Proceedings of the forty-first annual ACM symposium on Theory of computing
Public-key cryptosystems from the worst-case shortest vector problem: extended abstract
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)
Fast Cryptographic Primitives and Circular-Secure Encryption Based on Hard Learning Problems
CRYPTO '09 Proceedings of the 29th Annual International Cryptology Conference on Advances in Cryptology
EUROCRYPT'08 Proceedings of the theory and applications of cryptographic techniques 27th annual international conference on Advances in cryptology
Proceedings of the forty-second ACM symposium on Theory of computing
Faster exponential time algorithms for the shortest vector problem
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
An efficient and parallel Gaussian sampler for lattices
CRYPTO'10 Proceedings of the 30th annual conference on Advances in cryptology
Public-key cryptographic primitives provably as secure as subset sum
TCC'10 Proceedings of the 7th international 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
Lattice enumeration using extreme pruning
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
The geometry of lattice cryptography
Foundations of security analysis and design VI
Pseudorandom knapsacks and the sample complexity of LWE search-to-decision reductions
CRYPTO'11 Proceedings of the 31st annual conference on Advances in cryptology
Can homomorphic encryption be practical?
Proceedings of the 3rd ACM workshop on Cloud computing security workshop
BKZ 2.0: better lattice security estimates
ASIACRYPT'11 Proceedings of the 17th international conference on The Theory and Application of Cryptology and Information Security
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
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
Towards an interpreter for efficient encrypted computation
Proceedings of the 2012 ACM Workshop on Cloud computing security workshop
Selective document retrieval from encrypted database
ISC'12 Proceedings of the 15th international conference on Information Security
Towards efficient arithmetic for lattice-based cryptography on reconfigurable hardware
LATINCRYPT'12 Proceedings of the 2nd international conference on Cryptology and Information Security in Latin America
On the design of hardware building blocks for modern lattice-based encryption schemes
CHES'12 Proceedings of the 14th international conference on Cryptographic Hardware and Embedded Systems
Ring switching in BGV-Style homomorphic encryption
SCN'12 Proceedings of the 8th international conference on Security and Cryptography for 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
Solving BDD by enumeration: an update
CT-RSA'13 Proceedings of the 13th international conference on Topics in Cryptology
Anonymous lattice-based broadcast encryption
ICT-EurAsia'13 Proceedings of the 2013 international conference on Information and Communication Technology
ML confidential: machine learning on encrypted data
ICISC'12 Proceedings of the 15th international conference on Information Security and Cryptology
Proceedings of the 8th ACM SIGSAC symposium on Information, computer and communications security
Classical hardness of learning with errors
Proceedings of the forty-fifth annual ACM symposium on Theory of computing
Secure pattern matching using somewhat homomorphic encryption
Proceedings of the 2013 ACM workshop on Cloud computing security workshop
On Ideal Lattices and Learning with Errors over Rings
Journal of the ACM (JACM)
Field switching in BGV-style homomorphic encryption
Journal of Computer Security - Advances in Security for Communication Networks
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We analyze the concrete security and key sizes of theoretically sound lattice-based encryption schemes based on the "learning with errors" (LWE) problem. Our main contributions are: (1) a new lattice attack on LWE that combines basis reduction with an enumeration algorithm admitting a time/success tradeoff, which performs better than the simple distinguishing attack considered in prior analyses; (2) concrete parameters and security estimates for an LWE-based cryptosystem that is more compact and efficient than the well-known schemes from the literature. Our new key sizes are up to 10 times smaller than prior examples, while providing even stronger concrete security levels.