We construct the first fully homomorphic encryption (FHE) scheme that encrypts matrices and supports homomorphic matrix addition and multiplication. This is a natural extension of packed FHE and thus supports more complicated homomorphic operations. We optimize the bootstrapping procedure of Alperin-Sheriff and Peikert (CRYPTO 2014) by applying our scheme. Our optimization decreases the lattice approximation factor from ÕO (n3) to ÕO(n2.5). By taking a lattice dimension as a larger polynomial in a security parameter, we can also obtain the same approximation factor as the best known one of standard lattice-based public-key encryption without successive dimension-modulus reduction, which was essential for achieving the best factor in prior works on bootstrapping of standard lattice-based FHE.
CITATION STYLE
Hiromasa, R., Abe, M., & Okamoto, T. (2015). Packing messages and optimizing bootstrapping in GSW-FHE. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 9020, pp. 699–715). Springer Verlag. https://doi.org/10.1007/978-3-662-46447-2_31
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