%% converted by LB from authors "thebibliography" section 5-3-2008
%% edited by DB 5-6-2008

@InProceedings{Ajtai,
 author = {M. Ajtai},
 title = {The worst-case behavior of {Schnorr's} algorithm
         approximating the shortest nonzero vector in a lattice},
 booktitle = {Proc. 35th STOC},
 publisher = {ACM Press},
 pages = {396--406},
 year = 2003,
 eprint="stoc:10.1145/780542.780602"
}

@incollection{Ajt1,
 author = {M. Ajtai},
 title = {Generating Hard Instances of Lattice Problems},
 booktitle="Complexity of computations and proofs",
 editor="J. Kraji\v{c}ek",
series="Quaderni di Matematica",
publisher="Seconda Universita di Napoli",
volume=13,
year=2004,
pages="1--32",
 note = {Preliminary version: Proc. 28th STOC, 1996, pp. 99--108.}
}

@InProceedings{Ajt2,
 author = {M. Ajtai},
 title = {Random Lattices and a Conjectured 0---1 Law about their
         Polynomial Time Computable Properties},
 booktitle = {Proc. 43rd FOCS},
 publisher = {IEEE Computer Society},
 year = 2002,
 pages =  {733--742},
 eprint="focs:10.1109/SFCS.2002.1181998"
}

@InProceedings{ARS,
 author =  {M. Ajtai and R. Kumar and D.~Sivakumar},
 title =  {A Sieve Algorithm for the Shortest Lattice Vector Problem},
 booktitle = {Proc. 33rd STOC},
 publisher = {ACM Press},
 year = 1996,
 pages = {601--610},
 eprint="stoc:10.1145/380752.380857"
}

@Article{FK,
 author = {M. L. Furst and R. Kannan},
 title =  {Succinct certificates for almost all subset problems},
 journal = {SIAM Journal on Computing},
 volume = 18,
 year = 1989,
 pages =  {550--558},
 eprint="sicomp:10.1137/0218037"}

@Article{Gauss,
 author = {C. F. Gauss},
 title =  {Recursion der ``Untersuchungen \"uber die Eigenschaften der
           positiven tern\"aren quadratische Formen von Ludwig August
           Seeber, Dr. der Philosophie, ordentl. Professor der Universit\"at
           in Freiburg, 1831, 248 S. in 4."},
 journal = {Journal f\"ur die reine und angewandte Mathematik},
 volume =  20,
 year = 1840,
 pages = {312--320},
}

@Book{GL,
 author = {P. M. Gruber and C. G. Lekkerkerker},
 title =  {Geometry of Numbers, Chapter 3},
 publisher = {North Holland},
 year = 1987}

@Article{Kannan,
 author = {R. Kannan},
 title  = {Minkowski's convex body Theorem and Integer Programming},
 journal = {Mathematics of Operation Research},
 volume = 12,
 number = 3,
 year = 1987,
 pages = {415--440},
}

@Incollection{Kannan1,
 author = {R. Kannan},
 title =  {Algorithmic Geometry of Numbers},
 booktitle = {Annual Review of Computer Science},
 volume = 2,
 year = 1987,
 pages = {231--269},
 editors = {J. Traub},
 publisher = {Annual Reviews Inc.},
}

@Article{LO,
 author = {J. C. Lagarias, A. M. Odlyzko},
 title = {Solving low-density subset sum problems},
 journal = {Journal of the Association for Computing Machinery},
 volume = 32,
 number=1,
 year = 1985,
 pages = {229--246},
 eprint="jacm:10.1145/2455.2461"
}

@Incollection{Lagrange,
 author = {J. L. Lagrange},
 title = {Recherches d'arithm\'etique},
 booktitle = {Oeuvres de Lagrange},
 editor = {M. J.-A. Serret},
 volume = 3,
 pages = {698--701},
 publisher = {Gauthier-Villars},
 year = 1869,
 note = {(article cca 1773)},
}

@Article{LLL,
 author = {A. K. Lenstra and H. W. Lenstra and L. Lov\'asz},
 title =  {Factoring polynomials with rational coefficients},
 journal = {Mathematische Annalen},
 volume = 261,
 pages =  {515--534},
 year = 1982,
eprint="springer:lh1m24436431g068"
}

@Article{OR,
 author = {A. M. Odlyzko and H. te Riele},
 title =  {Disproof of the {Mertens} conjecture},
 journal = {Journal f\"ur die reine und angewandte Mathematik},
 volume = 357,
 year = 1985,
 pages = {138--160},
pdf="http://www.dtc.umn.edu/~odlyzko/doc/arch/mertens.disproof.pdf"
}

@Article{Schnorr,
 author = {C.-P. Schnorr},
 title = {A hierarchy of polynomial time lattice basis reduction algorithms},
 journal = {Theoretical Computer Science},
 volume = 53,
 year = 1987,
 pages = {201--224},
 eprint="tcs:10.1016/0304-3975(87)90064-8"
}

@InProceedings{Schnorr1,
 author = {C.-P. Schnorr},
 title =  {Lattice Reduction by Random Sampling and Birthday Methods},
 booktitle = {Proc. 20th Ann. Symp. on Theoretical Aspects of Computer Science (STACS'03)},
 series =  {Lecture Notes in Computer Science},
 volume = 2607,
 year = 2003,
 publisher = {Springer},
 pages = {145--156},
 eprint="stacs:qjpadpmwabty52g4"
}

@Article{KZ,
author ={A. Korkine and G. Zolotareff},
title  ={Sur les formes quadratiques},
journal = {Mathematische Annalen},
volume =  6,
year   = 1873,
pages  = {366--389},
eprint="springer:p56345710m4p6214"
}