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Most of the existing functional encryption schemes in use today are based on the presumed hardness of the discrete-log and the integer-factorization problems, which are known to be insecure with respect to quantum computers. To prevent the collapse of the cryptographic protocols relying on these schemes, it is important to develop alternative solutions based on mathematical problems that are unrelated to factoring and discrete log and that may be impervious to attacks by quantum computers. Hence, one of the main goals of WP4 is to design quantum-safe functional encryption alternatives that use lattices as their source of computational hardness. In this deliverable, we describe our progress towards this goal. More precisely, we describe a new multi-input functional encryption construction for the inner- product functionality developed by Abdalla et al. [3] in the context of the FENTEC project, which was the rst such scheme based on lattice problems. Since their construction is generic and can be based on any single-input functional inner-product encryption satisfying some common structural properties, we describe two possible lattice instantiations based on the problem of Learning With Errors (LWE). In addition to being quantum-safe, another advantage of these schemes is that they also allow for the computation of inner products of arbitrary sizes.
