A more efficient algorithm for lattice basis reduction
Journal of Algorithms
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
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
FOCS '04 Proceedings of the 45th Annual IEEE Symposium on Foundations of Computer Science
Trapdoors for hard lattices and new cryptographic constructions
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
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
H-LLL: using householder inside LLL
Proceedings of the 2009 international symposium on Symbolic and algebraic computation
An LLL Algorithm with Quadratic Complexity
SIAM Journal on Computing
NTRUSign: digital signatures using the NTRU lattice
CT-RSA'03 Proceedings of the 2003 RSA conference on The cryptographers' track
The Learning with Errors Problem (Invited Survey)
CCC '10 Proceedings of the 2010 IEEE 25th Annual Conference on Computational Complexity
An efficient and parallel Gaussian sampler for lattices
CRYPTO'10 Proceedings of the 30th annual conference on Advances in cryptology
Lattice basis delegation in fixed dimension and shorter-ciphertext hierarchical IBE
CRYPTO'10 Proceedings of the 30th annual conference on Advances in cryptology
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
Lattice mixing and vanishing trapdoors: a framework for fully secure short signatures and more
PKC'10 Proceedings of the 13th international conference on Practice and Theory in Public Key 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
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
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
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
Attribute-Based functional encryption on lattices
TCC'13 Proceedings of the 10th theory of cryptography conference on Theory of Cryptography
| Hi-index | 0.00 |
Many lattice cryptographic primitives require an efficient algorithm to sample lattice points according to some Gaussian distribution. All algorithms known for this task require long-integer arithmetic at some point, which may be problematic in practice. We study how much lattice sampling can be sped up using floating-point arithmetic. First, we show that a direct floating-point implementation of these algorithms does not give any asymptotic speedup: the floating-point precision needs to be greater than the security parameter, leading to an overall complexity Õ(n3) where n is the lattice dimension. However, we introduce a laziness technique that can significantly speed up these algorithms. Namely, in certain cases such as NTRUSign lattices, laziness can decrease the complexity to Õ(n2) or even Õ(n). Furthermore, our analysis is practical: for typical parameters, most of the floating-point operations only require the double-precision IEEE standard.