Solving low-density subset sum problems
Journal of the ACM (JACM)
Improved low-density subset sum algorithms
Computational Complexity
An introduction to Kolmogorov complexity and its applications (2nd ed.)
An introduction to Kolmogorov complexity and its applications (2nd ed.)
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
Approximating the SVP to within a factor (1+1/dimE) is NP-Hard under randomized reductions
Journal of Computer and System Sciences
The Shortest Vector in a Lattice is Hard to Approximate to within Some Constant
SIAM Journal on Computing
Random Lattices and a Conjectured 0 - 1 Law about Their Polynomial Time Computable Properties
FOCS '02 Proceedings of the 43rd Symposium on Foundations of Computer Science
NTRU: A Ring-Based Public Key Cryptosystem
ANTS-III Proceedings of the Third International Symposium on Algorithmic Number Theory
Hardness of Approximating the Shortest Vector Problem in Lattices
FOCS '04 Proceedings of the 45th Annual IEEE Symposium on Foundations of Computer Science
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
EUROCRYPT'97 Proceedings of the 16th annual international conference on Theory and application of cryptographic techniques
ANTS'06 Proceedings of the 7th international conference on Algorithmic Number Theory
Choosing parameter sets for NTRUEncrypt with NAEP and SVES-3
CT-RSA'05 Proceedings of the 2005 international conference on Topics in Cryptology
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Finding the shortest vector of a lattice is one of the most important problems in computational lattice theory. For a random lattice, one can estimate the length of the shortest vector using the Gaussian heuristic. However, no rigorous proof can be provided for some classes of lattices, as the Gaussian heuristic may not hold for them. In this paper, we propose a general method to estimate lower bounds of the shortest vector lengths for random integral lattices in certain classes, which is based on the incompressibility method from the theory of Kolmogorov complexity. As an application, we can prove that for a random NTRU lattice, with an overwhelming probability, the ratio between the length of the shortest vector and the length of the target vector, which corresponds to the secret key, is at least a constant, independent of the rank of the lattice.