Lattice reduction is known to be a very powerful tool in modern cryptanalysis. In the literature, there are many lattice reduction algorithms that have been proposed with various time complexity (from quadratic to subexponential). These algorithms can be utilized to find a short vector of a lattice with a small norm. Over time, shorter vector will be found by incorporating these methods. In thi...

in this paper, the mechanical behavior of three-phase inhomogeneous materials is modeled using the meso-scale model with lattice beams for static and dynamic analyses. the timoshenko beam theory is applied instead of the classical euler-bernoulli beam theory and the mechanical properties of lattice beam connection are derived based on the continuum medium using the non-local continuum theory. t...

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 dimensional lattice L where the shortest vector v is unique in the sense that any other vector whose length is at most n c kvk is parallel to v."