Abstract
In this paper, we construct a fully homomorphic encryption (FHE) scheme over integers with the message space \(\mathbb {Z}_Q\) for any prime \(Q\). Even for the binary case \(Q=2\), our decryption circuit has a smaller degree than that of the previous scheme; the multiplicative degree is reduced from \(O(\lambda (\log \lambda )^2)\) to \(O(\lambda )\), where \(\lambda \) is the security parameter. We also extend our FHE scheme to a batch FHE scheme.
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Nuida, K., Kurosawa, K. (2015). (Batch) Fully Homomorphic Encryption over Integers for Non-Binary Message Spaces. In: Oswald, E., Fischlin, M. (eds) Advances in Cryptology -- EUROCRYPT 2015. EUROCRYPT 2015. Lecture Notes in Computer Science(), vol 9056. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-46800-5_21
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DOI: https://doi.org/10.1007/978-3-662-46800-5_21
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