An interface between COde and LAttice-based cryptography – COLA

The main objective of COLA is to transfer techniques between the research areas of codes and lattices in a cryptographic context. Codes and lattices share many mathematical similarities, both objects found similar applications in cryptography and they appear to be resistant against a quantum computer. Some algorithms/techniques have already been transferred in each direction as, for instance, the recent proposition of an LLL algorithm for binary codes. In this project we push further this transfer of algorithmic techniques as well as more theoretical results coming from the mathematical field of complexity theory. It will open new perspectives in term of cryptanalysis and design beyond the theoretical interest of this work. To reach this goal, it will be necessary to bring together the knowledge of lattices and codes with a “common” language. For this we dive our projects into three main topics: theoretic foundation, algorithmic and design.