Lattices over number elds arise from a variety of sources in algorithmic algebra and more recently cryptography. Similar to the classical case of Z-lattices, the choice of a nice,...
ded abstract of this work appears in Public Key Cryptography — PKC 2011, ed. R. Gennaro, Springer LNCS 6571 (2011), 1–16. This is the full version. We propose a linearly homom...
Abstract. We describe some constructions of orthonormal lattices in totally real subfields of cyclotomic fields, obtained by endowing their ring of integers with a trace form. We...
Motivated by Ajtai’s worst-case to average-case reduction for lattice problems, we study the complexity of computing short linearly independent vectors (short basis) in a lattic...
We present a lattice algorithm specifically designed for some classical applications of lattice reduction. The applications are for lattice bases with a generalized knapsack-type ...