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Fast Lattice Basis Reduction Suitable for Massive Parallelization and Its Application to the Shortest Vector Problem
lattice basis reduction massive parallelization shortest vector problem
2018/1/11
The hardness of the shortest vector problem for lattices is a fundamental assumption underpinning the security of many lattice-based cryptosystems, and therefore, it is important to evaluate its diffi...
Improved Reduction from the Bounded Distance Decoding Problem to the Unique Shortest Vector Problem in Lattices
Lattices Bounded Distance Decoding Problem Unique Shortest Vector Problem
2016/12/12
We present a probabilistic polynomial-time reduction from the lattice Bounded Distance Decoding (BDD) problem with parameter 1/(2√⋅γ2⋅γ) to the unique Shortest Vector Problem (uSVP) with p...
Polynomial Time Reduction from Approximate Shortest Vector Problem to Principal Ideal Problem for Lattices in Some Cyclotomic Rings
Cyclotomic Rings Principal Ideal Problem
2015/12/29
Many cryptographic schemes have been established based on the hardness of lattice problems. For the asymptotic efficiency, ideal lattices in the ring of cyclotomic integers are suggested to be used in...
A Three-Level Sieve Algorithm for the Shortest Vector Problem
Lattice Shortest Vector Problem
2014/3/10
In AsiaCCS 2011, Wang et al. proposed a two-level heuristic sieve algorithm for the shortest vector problem in lattices, which improves the Nguyen-Vidick sieve algorithm. Inspired by their idea, we pr...
Improved Nguyen-Vidick Heuristic Sieve Algorithm for Shortest Vector Problem
lattice shortest vector sieve heuristic sphere covering
2010/12/22
In this paper, we present an improvement of the Nguyen-Vidick heuristic sieve algorithm for shortest vector problem in general lattices, which time complexity is 2^{0.3836n} polynomial computations, a...
The nc-Unique Shortest Vector Problem is Hard
nc-Unique Shortest Vector Problem GapSVP uSVP
2009/6/10
The unique Shortest Vector Problem (uSVP) gained prominence because it was the problem
upon which the first provably-secure lattice-based cryptosystems were built. But it was an open problem as to wh...
Public-Key Cryptosystems from the Worst-Case Shortest Vector Problem
Lattice-based cryptography learning with errors quantum computation
2009/6/10
We construct public-key cryptosystems that are secure assuming the worst-case hardness of approximating
the length of a shortest nonzero vector in an n-dimensional lattice to within a small poly(n) f...
Unique Shortest Vector Problem for max norm is NP-hard
unique closest vector problem unique subspace avoiding problem Lattice
2009/6/8
The unique Shortest vector problem (uSVP) in lattice theory plays a crucial role in many
public-key cryptosystems. The security of those cryptosystems bases on the hardness of uSVP. However,
so far ...
Explicit hard instances of the shortest vector problem
Lattice reduction lattice-based cryptography challenge
2009/6/5
Building upon a famous result due to Ajtai, we propose a sequence of lattice
bases with growing dimension, which can be expected to be hard instances of the shortest
vector problem (SVP) and which c...