The history of the LLL-algorithm

Abstract

The 25th birthday of the LLL-algorithm was celebrated in Caen from 29th June to 1st July 2007. The three day conference kicked off with a historical session of four talks about the origins of the algorithm. The speakers were the three L’s and close bystander Peter van Emde Boas. These were the titles of their talks. A tale of two papers – Peter van Emde Boas. The early history of LLL – Hendrik Lenstra. The ellipsoid method and basis reduction – László Lovász. Polynomial factorization and lattices in the very early 1980s – Arjen Lenstra. This chapter is based on those talks, conversations with these four historic characters, the notes that Peter van Emde Boas and Arjen Lenstra wrote for the preproceedings, and many artifacts from the phenomenal archive of Van Emde Boas.