We give a random class of lattices in Z n so that, if there is a probabilistic polynomial time algorithm which nds a short vector in a random lattice with a probability of at least 1 2 then there is… (More)

We give a random class of lattices in Zn whose elements can be generated together with a short vector in them so that, if there is a probabilistic polynomial time algorithm which finds a short vector… (More)

The purpose of this paper is to describe a sorting network of size 0(n log n) and depth 0(log n).
A natural way of sorting is through consecutive halvings: determine the upper and lower halves of… (More)

We present a probabilistic public key cryptosystem which is secure unless the worst case of the following lattice problem can be solved in polynomial time: “Find the shortest nonzero vector in an n… (More)

We present a randomized 2^{<italic>O(n)</italic>} time algorithm to compute a shortest non-zero vector in an <italic>n</italic>-dimensional rational lattice. The best known time upper bound for this… (More)

We show that the shortest vector problem in lattices with La norm is NP-hard for randomized reductions. Moreover we also show that there is an absolute constant E > 0 so that to find a vector which… (More)