An extension of the fpLLL library to Hermitian lattices

Abstract

We present an Hermitian version of the classical floating-point LLL reduction algorithm of Nguyen and Stehlé[16]. This new variant works on imaginary quadratic fields which are norm-Euclidean and also for some adequate cyclotomic fields. An optimized C++ implementation has been performed, based on the fpLLL code and results show a significant improvement for Hermitian lattices reduction of dimension N when compared to fpLLL reduction on the corresponding Euclidean lattice of dimension 2N. We demonstrate our implementation in the special case of the Gaussian integers.