Abstract
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 \(\tilde{O}(n^{3})\) to \(\tilde{O}(n^{2.5})\). 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.
Keywords
- Homomorphic Encryption
- Homomorphic Encryption Scheme
- Learning With Error
- Decryption Circuit
- Fully Homomorphic Encryption
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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Hiromasa, R., Abe, M., Okamoto, T. (2015). Packing Messages and Optimizing Bootstrapping in GSW-FHE. In: Katz, J. (eds) Public-Key Cryptography -- PKC 2015. PKC 2015. Lecture Notes in Computer Science(), vol 9020. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-46447-2_31
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DOI: https://doi.org/10.1007/978-3-662-46447-2_31
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