We nd the shortest non-zero vector in the lattice of all integer multiples of the vector a; b modulo m, for given integers 0 < a ; b < m. W e reduce the problem to the computation of a Minkowski-reduced basis for a planar lattice and thereby show that the problem can be solved in Olog mlog logm 2 bit operations.

NTRUEncrypt is a relatively new cryptosystem, introduced in 1996. The best known attacks on the cryptosystem are due to lattice basis reduction. In this Master’s project we have implemented lattice attacks using dimension-reduced and zero-forced lattices. Furthermore, we have reduced a modified version of the zero-forced lattice. This “non-lossy” zero-forced lattice performed better than the or...

Recently, lattice reduction has been widely used for signal detection in multiinput multioutput (MIMO) communications. In this paper, we present three novel lattice reduction algorithms. First, using a unimodular transformation, a significant improvement on an existing Hermite-Korkine-Zolotareff-reduction algorithm is proposed. Then, we present two practical algorithms for constructing Minkowsk...

The Lenstra, Lenstra, and Lovász (abbreviated as LLL) basis reduction algorithm computes a basis of a lattice consisting of short, and near orthogonal vectors. The quality of an LLL reduced basis is expressed by three fundamental inequalities, and it is natural to ask, whether these have a common generalization. In this note we find unifying inequalities. Our main result is Theorem 1. Let b1, ....

Lattice reduction algorithms behave much better in practice than their theoretical analysis predicts, with respect to both output quality and runtime. In this paper we present a probabilistic analysis that proves an average-case bound for the length of the first basis vector of an LLL reduced basis which reflects LLL experiments much better. Additionally, we use the same method to generate aver...

We address to the problem to factor a large composite number by lattice reduction algorithms Schnorr Sc has shown that under a reasonable number theoretic assumptions this problem can be reduced to a simultaneous diophantine approximation problem The latter in turn can be solved by nding su ciently many short vectors in a suitably de ned lattice Using lattice basis reduction algorithms Schnorr ...