Miklos Ajtai

We give a random class of n dimensional lattices so that, if

there is a probabilistic polynomial time algorithm which finds a short

vector in a random lattice with a probability of at least 1/2

then there is also a probabilistic polynomial time algorithm which

solves the following three ...
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Miklos Ajtai, Cynthia Dwork

We present a probabilistic public key cryptosystem which is

secure unless the following worst-case lattice problem can be solved in

polynomial time:

"Find the shortest nonzero vector in an n dimensional lattice

L where the shortest vector v is unique in the sense that any other

vector whose ...
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Miklos Ajtai

We show that the shortest vector problem in lattices

with L_2 norm is NP-hard for randomized reductions. Moreover we

also show that there is a positive absolute constant c, so that to

find a vector which is longer than the shortest non-zero vector by no

more than a factor of ...
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Daniele Micciancio

Lattices have received considerable attention as a potential source of computational hardness to be used in cryptography, after a breakthrough result of Ajtai (STOC 1996) connecting the average-case and worst-case complexity of various lattice problems. The purpose of this paper is twofold. On the expository side, we present a rigorous ... more >>>