On the limits of non-approximability of lattice problems
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
On the complexity of computing short linearly independent vectors and short bases in a lattice
STOC '99 Proceedings of the thirty-first annual ACM symposium on Theory of computing
On polynomial approximation to the shortest lattice vector length
SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
Improved cryptographic hash functions with worst-case/average-case connection
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
A new transference theorem in the geometry of numbers and new bounds for Ajtai's connection factor
Discrete Applied Mathematics - Special issue: Special issue devoted to the fifth annual international computing and combinatories conference (COCOON'99) Tokyo, Japan 26-28 July 1999
Generating Hard Instances of the Short Basis Problem
ICAL '99 Proceedings of the 26th International Colloquium on Automata, Languages and Programming
Closest Vectors, Successive Minima, and Dual HKZ-Bases of Lattices
ICALP '00 Proceedings of the 27th International Colloquium on Automata, Languages and Programming
On the Minimum Volume of a Perturbed Unit Cube
ISAAC '02 Proceedings of the 13th International Symposium on Algorithms and Computation
A Lattice-Based Public-Key Cryptosystem
SAC '98 Proceedings of the Selected Areas in Cryptography
Cryptanalysis of the Goldreich-Goldwasser-Halevi Cryptosystem from Crypto '97
CRYPTO '99 Proceedings of the 19th Annual International Cryptology Conference on Advances in Cryptology
The Two Faces of Lattices in Cryptology
CaLC '01 Revised Papers from the International Conference on Cryptography and Lattices
The Shortest Vector Problem in Lattices with Many Cycles
CaLC '01 Revised Papers from the International Conference on Cryptography and Lattices
New lattice based cryptographic constructions
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
The inapproximability of lattice and coding problems with preprocessing
Journal of Computer and System Sciences - Special issue on computational complexity 2002
New lattice-based cryptographic constructions
Journal of the ACM (JACM)
On lattices, learning with errors, random linear codes, and cryptography
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
ACM Transactions on Algorithms (TALG)
Hardness of approximating the shortest vector problem in lattices
Journal of the ACM (JACM)
Hardness of approximating the Shortest Vector Problem in high ℓp norms
Journal of Computer and System Sciences - Special issue on FOCS 2003
Progress in computational complexity theory
Journal of Computer Science and Technology
Lattices that admit logarithmic worst-case to average-case connection factors
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
Generalized Compact Knapsacks, Cyclic Lattices, and Efficient One-Way Functions
Computational Complexity
Special Issue On Worst-case Versus Average-case Complexity Editors' Foreword
Computational Complexity
Trapdoors for hard lattices and new cryptographic constructions
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
SWIFFT: A Modest Proposal for FFT Hashing
Fast Software Encryption
Explicit Hard Instances of the Shortest Vector Problem
PQCrypto '08 Proceedings of the 2nd International Workshop on Post-Quantum Cryptography
On lattices, learning with errors, random linear codes, and cryptography
Journal of the ACM (JACM)
A new transference theorem in the geometry of numbers
COCOON'99 Proceedings of the 5th annual international conference on Computing and combinatorics
On routing in circulant graphs
COCOON'99 Proceedings of the 5th annual international conference on Computing and combinatorics
Toward basing fully homomorphic encryption on worst-case hardness
CRYPTO'10 Proceedings of the 30th annual conference on Advances in cryptology
The geometry of lattice cryptography
Foundations of security analysis and design VI
Generalized compact knapsacks are collision resistant
ICALP'06 Proceedings of the 33rd international conference on Automata, Languages and Programming - Volume Part II
CRYPTO'06 Proceedings of the 26th annual international conference on Advances in Cryptology
Efficient collision-resistant hashing from worst-case assumptions on cyclic lattices
TCC'06 Proceedings of the Third conference on Theory of Cryptography
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We improve a connection of the worst-case complexity and the average-case complexity of some well-known lattice problems. This fascinating connection was first discovered by Ajtai in 1996. We improve the exponent of this connection from 8 to 3.5+\epsilon.