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

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Segment LLL-Reduction with Floating Point Orthogonalization,scaled basis can be accurately computed up to dimension 2. by Householder reflexions in floating point arithmetic . with 53 precision bits..We develop a highly practical fpa-variant of the new . . . of Koy and Schnorr [.]. The LLL-steps are guided in this algorithm by the Gram-Schmidt coefficients o

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The Shortest Vector Problem in Lattices with Many Cycles,.. We give a proof that the shortest vector problem is NP-complete in the max-norm for .-dimensional lattices . where ℤ./. has . — 1 cycles. We also give experimental data that show that the LLL algorithm does not perform significantly better on lattices with a high number of cycles.

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用不完

Segment LLL-Reduction of Lattice Bases,htly weaker notion of reducedness, but speeding up the reduction time of lattices of dimension . by a factor .. We also introduce a variant of LLL-reduction using .. The resulting reduction algorithm runs in . . log. . arithmetic steps for integer lattices of dimension . with basis vectors of length 2..

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Multisequence Synthesis over an Integral Domain,mputational complexity is . .) multiplications in . where . is the length of each sequence. A necessary and sufficient conditions for the uniqueness of minimal polynomials are given. The set of all minimal polynomials is also described.

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