Zvika Brakerski (
We present a new tensoring technique for LWE-based fully homomorphic encryption. While in all previous works, the ciphertext noise grows quadratically ($B \to B^2\cdot\poly(n)$) with every multiplication (before “refreshing”), our noise only grows linearly ($B \to B\cdot\poly(n)$).
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 to the worst-case hardness of the GapSVP problem (with quasi-polynomial approximation factor), whereas previous constructions could only exhibit a quantum reduction to GapSVP.