History tells us that is not enough to base security solely on the unfeasability of solving the underlying hard problem of a cryptosystem. In the real world, it is not uncommon for an adversary to get access to some key dependent information potentially helping to perform cryptanalysis. Recently a lot of effort has been put into designing cryptosystems such that the impact of leaking key related information is minimized, this area is mostly known as leakage-resilient cryptography. In this work,

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... we show how to construct a distributed fully homomorphic identity-based encryption secure in the continual auxiliary input model. Our construction is based on the fully homomorphic scheme of Gentry, Sahai and Waters and relies merely on the learning with errors assumption, which is conjectured being resistant against quantum attacks.