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- W2128365909 abstract "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 structure, where the target vectors have bounded depth. For such applications, the complexity of the algorithm improves traditional lattice reduction by replacing some dependence on the bit-length of the input vectors by some dependence on the bound for the output vectors. If the bit-length of the target vectors is unrelated to the bit-length of the input, then our algorithm is only linear in the bit-length of the input entries, which is an improvement over the quadratic complexity floating-point LLL algorithms. To illustrate the usefulness of this algorithm we show that a direct application to factoring univariate polynomials over the integers leads to the first complexity bound improvement since 1984. A second application is algebraic number reconstruction, where a new complexity bound is obtained as well." @default.
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- W2128365909 date "2011-03-01" @default.
- W2128365909 modified "2023-09-25" @default.
- W2128365909 title "Gradual Sub-lattice Reduction and a New Complexity for Factoring Polynomials" @default.
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- W2128365909 doi "https://doi.org/10.1007/s00453-011-9500-y" @default.
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