Contemporary cryptography, with security relying on the factorisation and discrete logarithm problems, is ill-prepared for the future: It will collapse with the rise of quantum computers, its costly algorithms require growing resources, and it is utterly ill-fitted for the fast-developing trend of externalising computations to the cloud. The emerging field of *lattice-based cryptography* (LBC) addresses these concerns: it resists would-be quantum computers, trades memory for drastic run-time savings, and enables computations on encrypted data, leading to the prospect of a privacy-preserving cloud economy. LBC could supersede contemporary cryptography within a decade. A major goal of this project is to enable this technology switch. I will strengthen the security foundations, improve its performance, and extend the range of its functionalities.A lattice is the set of integer linear combinations of linearly independent real vectors, called lattice basis. The core computational problem on lattices is the Shortest Vector Problem (SVP): Given a basis, find a shortest non-zero point in the spanned lattice. The hardness of SVP is the security foundation of LBC. In fact, SVP and its variants arise in a great variety of areas, including computer algebra, communications (coding and cryptography), computer arithmetic and algorithmic number theory, further motivating the study of lattice algorithms. In the matter of *algorithm design*, the community is quickly nearing the limits of the classical paradigms. The usual approach, lattice reduction, consists in representing a lattice by a basis and steadily improving its quality. I will assess the full potential of this framework and, in the longer term, develop alternative approaches to go beyond the current limitations.This project aims at studying all computational aspects of lattices, with cryptography as the driving motive. The strength of LattAC lies in its theory-to-practice and interdisciplinary methodological approach