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Electronic Colloquium on Computational Complexity

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Reports tagged with Closest Vector Problem:
TR98-010 | 22nd January 1998
Phong Nguyen, Jacques Stern

A Converse to the Ajtai-Dwork Security Proof and its Cryptographic Implications

Revisions: 1

Recently, Ajtai discovered a fascinating connection
between the worst-case complexity and the average-case
complexity of some well-known lattice problems.
Later, Ajtai and Dwork proposed a cryptosystem inspired
by Ajtai's work, provably secure if a particular lattice
problem is difficult. We show that there is a converse
to the ... more >>>

TR04-113 | 19th November 2004
MÃ¥rten Trolin

Lattices with Many Cycles Are Dense

We give a method for approximating any $n$-dimensional
lattice with a lattice $\Lambda$ whose factor group
$\mathbb{Z}^n / \Lambda$ has $n-1$ cycles of equal length
with arbitrary precision. We also show that a direct
consequence of this is that the Shortest Vector Problem and the Closest
Vector Problem cannot ... more >>>

TR06-052 | 15th April 2006
Wenbin Chen, Jiangtao Meng

Inapproximability Results for the Closest Vector Problem with Preprocessing over infty Norm

We show that the Closest Vector
Problem with Preprocessing over infty Norm
is NP-hard to approximate to within a factor of $(\log
n)^{1/2-\epsilon}$. The result is the same as Regev and Rosen' result, but our proof methods are different from theirs. Their
reductions are based on norm embeddings. However, ... more >>>

TR11-119 | 4th September 2011
Subhash Khot, Preyas Popat, Nisheeth Vishnoi

$2^{\log^{1-\epsilon} n}$ Hardness for Closest Vector Problem with Preprocessing

We prove that for an arbitrarily small constant $\eps>0,$ assuming NP$\not \subseteq$DTIME$(2^{{\log^{O(1/\epsilon)} n}})$, the preprocessing versions of the closest vector problem and the nearest codeword problem are hard to approximate within a factor better than $2^{\log ^{1-\epsilon}n}.$ This improves upon the previous hardness factor of $(\log n)^\delta$ for some $\delta ... more >>>

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