Algorithms to construct Minkowski reduced and Hermite reduced lattice bases
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Minkowski's convex body theorem and integer programming
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A hierarchy of polynomial time lattice basis reduction algorithms
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Generating hard instances of lattice problems (extended abstract)
STOC '96 Proceedings of the twenty-eighth annual ACM symposium on Theory of computing
The shortest vector problem in L2 is NP-hard for randomized reductions (extended abstract)
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
Noise-tolerant learning, the parity problem, and the statistical query model
STOC '00 Proceedings of the thirty-second 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
On the limits of nonapproximability of lattice problems
Journal of Computer and System Sciences - 30th annual ACM symposium on theory of computing
On polynomial approximation to the shortest lattice vector length
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The Shortest Vector in a Lattice is Hard to Approximate to within Some Constant
FOCS '98 Proceedings of the 39th Annual Symposium on Foundations of Computer Science
Sparse polynomial approximation in finite fields
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
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Improved cryptographic hash functions with worst-case/average-case connection
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Security of most significant bits of gx2
Information Processing Letters
Lattice Reduction by Random Sampling and Birthday Methods
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A Generalized Birthday Problem
CRYPTO '02 Proceedings of the 22nd Annual International Cryptology Conference on Advances in Cryptology
Hidden Number Problem with the Trace and Bit Security of XTR and LUC
CRYPTO '02 Proceedings of the 22nd Annual International Cryptology Conference on Advances in Cryptology
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Chinese Remaindering for Algebraic Numbers in a Hidden Field
ANTS-V Proceedings of the 5th International Symposium on Algorithmic Number Theory
Dimension Reduction Methods for Convolution Modular Lattices
CaLC '01 Revised Papers from the International Conference on Cryptography and Lattices
An Overview of the Sieve Algorithm for the Shortest Lattice Vector Problem
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The Two Faces of Lattices in Cryptology
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Noise-tolerant learning, the parity problem, and the statistical query model
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The Insecurity of the Elliptic Curve Digital Signature Algorithm with Partially Known Nonces
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Noisy Chinese remaindering in the Lee norm
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Representing hard lattices with O(n log n) bits
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
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Hardness of approximating the shortest vector problem in lattices
Journal of the ACM (JACM)
Hardness of Approximating the Closest Vector Problem with Pre-Processing
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Lattice problems and norm embeddings
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Fast LLL-type lattice reduction
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Hardness of approximating the Shortest Vector Problem in high ℓp norms
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Reconstructing noisy polynomial evaluation in residue rings
Journal of Algorithms
Tensor-based hardness of the shortest vector problem to within almost polynomial factors
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
Lattices that admit logarithmic worst-case to average-case connection factors
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
Designs, Codes and Cryptography
Foundations and Trends® in Theoretical Computer Science
Generalized Compact Knapsacks, Cyclic Lattices, and Efficient One-Way Functions
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Efficient reductions among lattice problems
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
Jug measuring: Algorithms and complexity
Theoretical Computer Science
Trapdoors for hard lattices and new cryptographic constructions
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
Finding short lattice vectors within mordell's inequality
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
On agnostic boosting and parity learning
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
Limits on the Hardness of Lattice Problems in lp Norms
Computational Complexity
Cryptanalysis of General Lu-Lee Type Systems
Information Security and Cryptology
Noninteractive Statistical Zero-Knowledge Proofs for Lattice Problems
CRYPTO 2008 Proceedings of the 28th Annual conference on Cryptology: Advances in Cryptology
Efficient lattice-based signature scheme
International Journal of Applied Cryptography
Explicit Hard Instances of the Shortest Vector Problem
PQCrypto '08 Proceedings of the 2nd International Workshop on Post-Quantum Cryptography
Rigorous and Efficient Short Lattice Vectors Enumeration
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SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
Sampling methods for shortest vectors, closest vectors and successive minima
Theoretical Computer Science
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)
Fiat-Shamir with Aborts: Applications to Lattice and Factoring-Based Signatures
ASIACRYPT '09 Proceedings of the 15th International Conference on the Theory and Application of Cryptology and Information Security: Advances in Cryptology
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
Fast LLL-type lattice reduction
Information and Computation
Improved analysis of Kannan's shortest lattice vector algorithm
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Algorithmic problems for metrics on permutation groups
SOFSEM'08 Proceedings of the 34th conference on Current trends in theory and practice of computer science
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Lattice-based identification schemes secure under active attacks
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A digital signature scheme based on CV P∞
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On the complexity of circuit satisfiability
Proceedings of the forty-second ACM symposium on Theory of computing
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Faster exponential time algorithms for the shortest vector problem
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
Accelerating lattice reduction with FPGAs
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Parallel enumeration of shortest lattice vectors
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Adaptively secure identity-based identification from lattices without random oracles
SCN'10 Proceedings of the 7th international conference on Security and cryptography for networks
An improvement of key generation algorithm for Gentry's homomorphic encryption scheme
IWSEC'10 Proceedings of the 5th international conference on Advances in information and computer security
Better key sizes (and attacks) for LWE-based encryption
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Analysis of gauss-sieve for solving the shortest vector problem in lattices
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Improved Nguyen-Vidick heuristic sieve algorithm for shortest vector problem
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Covering cubes and the closest vector problem
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Algorithms for the shortest and closest lattice vector problems
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Analyzing blockwise lattice algorithms using dynamical systems
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A parallel implementation of GaussSieve for the shortest vector problem in lattices
PaCT'11 Proceedings of the 11th international conference on Parallel computing technologies
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Generalized compact knapsacks are collision resistant
ICALP'06 Proceedings of the 33rd international conference on Automata, Languages and Programming - Volume Part II
On stern's attack against secret truncated linear congruential generators
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Cryptanalysis of the quadratic generator
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On ideal lattices and learning with errors over rings
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Lattice enumeration using extreme pruning
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Rankin's constant and blockwise lattice reduction
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CRYPTO'06 Proceedings of the 26th annual international conference on Advances in Cryptology
Parallel shortest lattice vector enumeration on graphics cards
AFRICACRYPT'10 Proceedings of the Third international conference on Cryptology in Africa
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BKZ 2.0: better lattice security estimates
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The leakage-resilience limit of a computational problem is equal to its unpredictability entropy
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Secret key leakage from public key perturbation of DLP-Based cryptosystems
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Approximation algorithms for semi-random partitioning problems
STOC '12 Proceedings of the forty-fourth annual ACM symposium on Theory of computing
A O(1/ε2)n-time sieving algorithm for approximate integer programming
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Lossy Trapdoor Functions and Their Applications
SIAM Journal on Computing
Sampling methods for shortest vectors, closest vectors and successive minima
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Attribute-based encryption for circuits
Proceedings of the forty-fifth annual ACM symposium on Theory of computing
Reusable garbled circuits and succinct functional encryption
Proceedings of the forty-fifth annual ACM symposium on Theory of computing
On Ideal Lattices and Learning with Errors over Rings
Journal of the ACM (JACM)
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We present a randomized 2^{O(n)} time algorithm to compute a shortest non-zero vector in an n-dimensional rational lattice. The best known time upper bound for this problem was 2^{O(n\log n)} first given by Kannan [7] in 1983. We obtain several consequences of this algorithm for related problems on lattices and codes, including an improvement for polynomial time approximations to the shortest vector problem. In this improvement we gain a factor of log log n in the exponent of the approximating factor.