Computational aspects of geometry of numbers have been revolutionized by
the Lenstra-Lenstra-Lovasz ´ lattice reduction algorithm (LLL), which
has led to bre- throughs in elds as diverse as computer algebra,
cryptology, and algorithmic number theory. After its publication in
1982, LLL was immediately recognized as one of the most important
algorithmic achievements of the twentieth century, because of its broad
applicability and apparent simplicity. Its popularity has kept growing
since, as testi ed by the hundreds of citations of the original article,
and the ever more frequent use of LLL as a synonym to lattice reduction.
As an unfortunate consequence of the pervasiveness of the LLL algorithm,
researchers studying and applying it belong to diverse scienti c
communities, and seldom meet. While discussing that particular issue
with Damien Stehle ´ at the 7th Algorithmic Number Theory Symposium
(ANTS VII) held in Berlin in July 2006, John Cremona
accuratelyremarkedthat 2007would be the 25th anniversaryof LLL and this
deserveda meetingto celebrate that event. The year 2007was also involved
in another arithmetical story. In 2003 and 2005, Ali Akhavi, Fabien
Laguillaumie, and Brigitte Vallee ´ with other colleagues organized two
workshops on cryptology and algorithms with a strong emphasis on lattice
reduction: CAEN '03 and CAEN '05, CAEN denoting both the location and
the content (Cryptologie et Algori- miqueEn Normandie).
Veryquicklyafterthe ANTSconference, AliAkhavi, Fabien Laguillaumie, and
Brigitte Vallee ´ were thus readily contacted and reacted very
enthusiastically about organizing the LLL birthday conference. The
organization committee was formed.
