We present a fully homomorphic encryption scheme that is based solely on the (standard) learning with errors (LWE) assumption. Applying known results on LWE, the security of our scheme is based on the worst-case hardness of ``short vector problems'' on arbitrary lattices.

Our construction improves on previous works in two ... more >>>

We present a radically new approach to fully homomorphic encryption (FHE) that dramatically improves performance and bases security on weaker assumptions. A central conceptual contribution in our work is a new way of constructing leveled fully homomorphic encryption schemes (capable of evaluating arbitrary polynomial-size circuits), {\em without Gentry's bootstrapping procedure}.

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A homomorphic encryption scheme is one that allows computing on encrypted data without decrypting it first. In fully homomorphic encryption it is possible to apply any efficiently computable function to encrypted data. We provide a survey on the origins, definitions, properties, constructions and uses of fully homomorphic encryption.

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