---
title: "Bibliography"
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---

# Bibliography

<a id="cite-closest-point-search"></a>
- **[AEVZ02]** E. Agrell, T. Eriksson, A. Vardy, and K. Zeger. Closest point search in lattices. *IEEE Transactions on Information Theory*, 48(8):2201–2214, 2002.
<a id="cite-ajtai98"></a>
- **[Ajt98]** Miklós Ajtai. The Shortest Vector Problem in L2 is NP-hard for Randomized Reductions (Extended Abstract). In *Proceedings of the 30th Symposium on the Theory of Computing (STOC 1998)*, 10–19. ACM, 1998.
<a id="cite-akhavi"></a>
- **[Akh02]** Ali Akhavi. Random lattices, threshold phenomena and efficient reduction algorithms. *Theoretical Computer Science*, 287(2):359–385, 2002.
<a id="cite-deweger"></a>
- **[dW87]** Benne M.M. de Weger. Solving exponential Diophantine equations using lattice basis reduction algorithms. *J. Number Th.*, 26:325–367, 1987.
<a id="cite-fipo83"></a>
- **[FP83]** U. Fincke and M. Pohst. A procedure for determining algebraic integers of given norm. In *EUROCAL*, volume 162 of LNCS, 194–202. Springer, 1983.
<a id="cite-hast07"></a>
- **[HS07]** Guillaume Hanrot and Damien Stehlé. Improved Analysis of Kannan's Shortest Lattice Vector Algorithm (Extended Abstract). In *Advances in cryptology—CRYPTO 2007*, volume 4622 of LNCS, 170–186. Springer, 2007.
<a id="cite-conwaysloane"></a>
- **[JC98]** N.J.A. Sloane J.H. Conway. *Sphere Packings, Lattices and Groups*. Volume 290 of Grundlehren der Mathematischen Wissenschaften. Springer, New York–Berlin–Heidelberg, 3rd edition, 1998.
<a id="cite-kannan83"></a>
- **[Kan83]** R. Kannan. Improved algorithms for integer programming and related lattice problems. In *Proceedings of the 15th Symposium on the Theory of Computing (STOC 1983)*, 99–108. ACM, 1983.
<a id="cite-kneser"></a>
- **[Kne57]** M. Kneser. Klassenzahlen indefiniter quadratischer Formen in drei oder mehr Veränderlichen. *Archiv Math.*, 8:241–250, 1957.
<a id="cite-lll"></a>
- **[LLL82]** Arjen K. Lenstra, Hendrik W. Lenstra, and László Lovász. Factoring polynomials with rational coefficients. *Mathematische Annalen*, 261:515–534, 1982.
<a id="cite-migo"></a>
- **[MG02]** Daniele Micciancio and Shafi Goldwasser. *Complexity of lattice problems: a cryptographic perspective*. Volume 671 of The Kluwer International Series in Engineering and Computer Science. Kluwer Academic Publishers, 2002. ISBN 0-7923-7688-9.
<a id="cite-latticecatalogue"></a>
- **[NS01a]** G. Nebe and N.J.A. Sloane. The Catalogue of Lattices. http://www.research.att.com/$\sim$njas/lattices/, 2001.
<a id="cite-lattice-db"></a>
- **[NS01b]** Gabriele Nebe and Neil J.A. Sloane. A Catalogue of Lattices. http://akpublic.research.att.com/$\sim$njas/lattices/index.html, 2001.
<a id="cite-nguyenstehle06"></a>
- **[NS]** P. Nguyen, D. Stehlé. “LLL on the Average.” 238–256.
<a id="cite-nguyenstehle09"></a>
- **[NS09a]** Phong Nguyen and Damien Stehlé. An LLL Algorithm with Quadratic Complexity. *SIAM Journal on Computing*, 39(3):874–903, 2009.
<a id="cite-ngst09"></a>
- **[NS09c]** Phong Q. Nguyen and Damien Stehlé. Low-dimensional lattice basis reduction revisited. *ACM Trans. Algorithms*, 5(4):Art. 46, 48, 2009. URL: [https://doi.org/10.1145/1597036.1597050](https://doi.org/10.1145/1597036.1597050), [doi:10.1145/1597036.1597050](https://doi.org/10.1145/1597036.1597050).
<a id="cite-paulus98latticebasis"></a>
- **[Pau98]** Sachar Paulus. Lattice Basis Reduction in Function Fields. In *In ANTS-3 : Algorithmic*, 567–575. Springer-Verlag, 1998.
<a id="cite-mlll"></a>
- **[Poh87]** Michael Pohst. A Modification of the LLL Reduction Algorithm. *J. Symbolic Comp.*, 4(1):123–127, 1987.
<a id="cite-mpfr"></a>
- **[Pro]** The SPACES Project. MPFR, a LGPL-library for multiple-precision floating-point computations with exact rounding. http://www.mpfr.org/.
<a id="cite-pust08"></a>
- **[PS08]** Xavier Pujol and Damien Stehlé. Rigorous and efficient short lattice vectors enumeration. In *Advances in Cryptology—AsiaCrypt 2008*, LNCS. Springer, 2008.
<a id="cite-schnorreuchner"></a>
- **[SE94]** Claus-Peter Schnorr and Michael Euchner. Lattice Basis Reduction: Improved Practical Algorithms and Solving Subset Sum Problems. *Mathematics of Programming*, 66:181–199, 1994.
<a id="cite-schnorrhorner"></a>
- **[SH95]** Claus-Peter Schnorr and Horst Helmut Hörner. Attacking the Chor-Rivest Cryptosystem by Improved Lattice Reduction. In *Advances in Cryptology—EuroCrypt 1995*, volume 921 of LNCS, 1–12. Springer-Verlag, 1995.
<a id="cite-schulze-pillot"></a>
- **[SP91]** Rainer Schulze-Pillot. An algorithm for computing genera of ternary and quaternary quadratic forms. In Stephen M. Watt, editor, *Proceedings ISSAC'91*, 134–143. Bonn, 1991.
<a id="cite-ntl"></a>
- **[Sho]** Victor Shoup. NTL, Number Theory C++ Library. http://www.shoup.net/ntl/.
<a id="cite-simon"></a>
- **[Sim05b]** Denis Simon. Solving quadratic equations using reduced unimodular quadratic forms. *Math. Comp.*, 74(251):1531–1543 (electronic), 2005.
<a id="cite-stehle09"></a>
- **[Ste09]** Damien Stehlé. *Floating-point LLL: theoretical and practical aspects*. Springer-Verlag, 2009, To appear.
<a id="cite-emde81"></a>
- **[vEB81]** Peter van Emde Boas. Another NP-complete partition problem and the complexity of computing short vectors in a lattice. Technical report 81-04, Mathematisch Instituut, Universiteit van Amsterdam, 1981.