Chapter 17 Lattice Basis Reduction
نویسنده
چکیده
Reduction of lattice bases of rank 2 in R was given by Lagrange and Gauss. The algorithm is closely related to Euclid’s algorithm and we briefly present it in Section 17.1. The main goal of this section is to present the lattice basis reduction algorithm of Lenstra, Lenstra and Lovász, known as the LLL or L algorithm. This is a very important algorithm for practical applications. Some basic references for the LLL algorithm are Section 14.3 of Smart [571], Section 2.6 of Cohen [135] and Chapter 17 of Trappe and Washington [608]. More detailed treatments are given in von zur Gathen and Gerhard [237], Grötschel, Lovász and Schrijver [268], Section 1.2 of Lovász [394], and Nguyen and Vallée [463]. I also highly recommend the original paper [372].
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