Annual report of the Board of Regents of the Smithsonian Institution, showing the operations, expenditures, and condition of the institution for the year 1871.

Annual Report of the Smithsonian Institution. [1482] Research related to the American Indian; mounds in Dakota and Kentucky; the Pima Indians of Arizona; on the language of the Dakota or Sioux Indians

State Female Normal School Catalogue, Twenty-Fourth Session, 1907-1908

https://digitalcommons.longwood.edu/catalogs/1010/thumbnail.jp

Fast Practical Lattice Reduction through Iterated Compression

We introduce a new lattice basis reduction algorithm with approximation guarantees analogous to the LLL algorithm and practical performance that far exceeds the current state of the art. We achieve these results by iteratively applying precision management techniques within a recursive algorithm structure and show the stability of this approach. We analyze the asymptotic behavior of our algorithm, and show that the heuristic running time is $O(n^{\omega}(C+n)^{1+\varepsilon})$ for lattices of dimension $n$, $\omega\in (2,3]$ bounding the cost of size reduction, matrix multiplication, and QR factorization, and $C$ bounding the log of the condition number of the input basis $B$. This yields a running time of $O\left(n^\omega (p + n)^{1 + \varepsilon}\right)$ for precision $p = O(\log \|B\|_{max})$ in common applications. Our algorithm is fully practical, and we have published our implementation. We experimentally validate our heuristic, give extensive benchmarks against numerous classes of cryptographic lattices, and show that our algorithm significantly outperforms existing implementations

State Female Normal School Catalogue, Twenty-Fifth Session, 1908-1909

https://digitalcommons.longwood.edu/catalogs/1011/thumbnail.jp