Titlebook: Cryptography and Lattices; International Confer Joseph H. Silverman Conference proceedings 2001 Springer-Verlag Berlin Heidelberg 2001 Latt

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Fast Reduction of Ternary Quadratic Forms,and . is the bit-complexity of s-bit integer multiplication..This result is achieved in two steps. First we prove that the the classical Gaussian algorithm for ternary form reduction, in the variant of Lagarias, has this worst case running time. Then we show that, given a ternary form which is reduc

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,Factoring Polynomials and 0—1 Vectors,ssenhaus. Contrary to Lenstra, Lenstra and Lovász, the lattice reduction is not used to calculate coefficients of a factor but is only used to solve the combinatorial problem, which is a problem with much smaller coefficients and dimension. The factors are then constructed efficiently in the same wa

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Segment LLL-Reduction of Lattice Bases,ize .. Local LLL-reduction of segments is done using local coordinates of dimension ...We introduce ., a variant of LLL-reduced bases achieving a slightly weaker notion of reducedness, but speeding up the reduction time of lattices of dimension . by a factor .. We also introduce a variant of LLL-red