A Verifiable Shuffle for the GSW Cryptosystem
We provide the first verifiable shuffle specifically for fully homomorphic schemes. A verifiable shuffle is a way to ensure that if a node receives and sends encrypted lists, the content will be the same, even though no adversary can trace individual list items through the node. Shuffles are useful in e-voting, traffic routing and other applications.
We build our shuffle on the ideas and techniques of Groth’s 2010 shuffle, but make necessary modifications for a less ideal setting where the randomness and ciphertexts admit no group structure.
The protocol relies heavily on the properties of the so-called gadget matrices, so we have included a detailed introduction to these.
KeywordsVerifiable shuffle Fully homomorphic encryption Post-quantum
The author wishes to thank Jens Groth for his useful comments to an early version of this manuscript, as well as to the anonymous reviewers.
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