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Published in:
2012 | OriginalPaper | Chapter
Fully Homomorphic Encryption without Modulus Switching from Classical GapSVP
Author : Zvika Brakerski
Published in: Advances in Cryptology – CRYPTO 2012
Publisher: Springer Berlin Heidelberg
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We present a new tensoring technique for LWE-based fully homomorphic encryption. While in all previous works, the ciphertext noise grows quadratically (
B
→
B
2
·poly(
n
)) with every multiplication (before “refreshing”), our noise only grows linearly (
B
→
B
·poly(
n
)).
We use this technique to construct a
scale-invariant
fully homomorphic encryption scheme, whose properties only depend on the ratio between the modulus
q
and the initial noise level
B
, and not on their absolute values.
Our scheme has a number of advantages over previous candidates: It uses the same modulus throughout the evaluation process (no need for “modulus switching”), and this modulus can take arbitrary form. In addition, security can be
classically
reduced from the worst-case hardness of the GapSVP problem (with quasi-polynomial approximation factor), whereas previous constructions could only exhibit a quantum reduction from GapSVP.