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CRYPTO
2011
Springer

Fully Homomorphic Encryption from Ring-LWE and Security for Key Dependent Messages

7 years 12 months ago
Fully Homomorphic Encryption from Ring-LWE and Security for Key Dependent Messages
We present a somewhat homomorphic encryption scheme that is both very simple to describe and analyze, and whose security (quantumly) reduces to the worst-case hardness of problems on ideal lattices. We then transform it into a fully homomorphic encryption scheme using standard “squashing” and “bootstrapping” techniques introduced by Gentry (STOC 2009). One of the obstacles in going from “somewhat” to full homomorphism is the requirement that the somewhat homomorphic scheme be circular secure, namely, the scheme can be used to securely encrypt its own secret key. For all known somewhat homomorphic encryption schemes, this requirement was not known to be achievable under any cryptographic assumption, and had to be explicitly assumed. We take a step forward towards removing this additional assumption by proving that our scheme is in fact secure when encrypting polynomial functions of the secret key. Our scheme is based on the ring learning with errors (RLWE) assumption that wa...
Zvika Brakerski, Vinod Vaikuntanathan
Added 18 Dec 2011
Updated 18 Dec 2011
Type Journal
Year 2011
Where CRYPTO
Authors Zvika Brakerski, Vinod Vaikuntanathan
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