J. Buchmann, V. Kessler, Computing a reduced lattice basis from a generating system with applications, Preprint 1990.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....with time constrained in our set up by L d ( 1 2 ; 5= p 8 o(1) However, it seems very likely that the methods of this paper, perhaps in combination with those of [Abe94] should yield a more eOEcient algorithm for this question, too. In [Abe94] Abel shows following closely [Buc89] and [BK92] how to control the logarithms of suitably modied generators of the relations so that a suOEciently precise approximation of a generator of the lattice spanned by these logarithms can be computed. 6 Conclusion We have analysed the DL problem in two environments for which there have been proposed ....

J. Buchmann and V. Kessler. Computing a reduced lattice basis from a generating system. Unpublished manuscript, 1992.

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J. Buchmann, V. Kessler, Computing a reduced lattice basis from a generating system with applications, Preprint 1990.

.... the kernel modulo n [11] ffl bigint lattice and bigfloat lattice classes whose functionality comprises lattice algorithms for computing reduced lattice bases (e.g. Schnorr Euchner algorithm [10, 12] computing relations from a given generating system (e.g. Buchmann Kessler algorithm [5]) handling Gram matrices as well as computing shortest and closest vectors [1, 7, 8] 3 TEMPLATE MODULES AND KERNELS In the classes described in the previous section, many variations of the same basic algorithm have to be implemented depending on the various information stored in the bit ....

....systems. This approach was turned down because there was no real practical use for the class diversity. As already mentioned before, the lattice classes in LiDIA offer algorithms for computing reduced lattice bases, computing relations from generating systems, handling Gram matrices etc. [5, 7, 10, 12]. For most algorithms the classes do not only contain an implementation of the original algorithm but also comprise several variations (e.g. using different scalar products) In order to keep the code basis small but very efficient and variable, we have developed a new concept which we will ....

Buchmann, J., and Kessler, V.: Computing a Reduced Lattice Basis from a Generating System. Preprint, Universit at des Saarlandes (1992).

....whose binary length is polynomially bounded in log D. As in [11] we can compute both the Hermite and the Smith normal form of E 0 in time L[4fi] where again fi 2 R 0 is such that c = L(D) fi . The Smith normal form will yield the class number and the structure of the class group. According to [5] the generating system for the lattice L c can be transformed into a basis in time L[9fi] It is, however, very likely that there is a faster way of doing this. The regulator computation therefore takes L[9fi] operations. We can now discuss the optimal choice for fi. Since the computation of the ....

J. Buchmann, V. Kessler, Computing a reduced lattice basis from a generating system with applications, Preprint 1990.

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J. Buchmann and V. Kessler. Computing a reduced lattice basis from a generating system. Unpublished manuscript, 1992.

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