Cryptology ePrint Archive: Report 2019/588

Formal Notions of Security for Verifiable Homomorphic Encryption

Jakub Klemsa and Ivana Trummová

Abstract: Homomorphic encryption enables computations with encrypted data, however, in its plain form, it does not guarantee that the computation has been performed honestly. For the Fully Homomorphic Encryption (FHE), a verifiable variant emerged soon after the introduction of FHE itself, for a single-operation homomorphic encryption (HE), particular verifiable variant has been introduced recently, called the VeraGreg Framework. In this paper, we identify a weakness of List Non-Malleability as defined for the VeraGreg Framework—an analogy to the classical Non-Malleability—and suggest its improvement which we show not to be extendable any more in certain sense. Next, we suggest a decomposition of the abstract VeraGreg framework, introduce novel notions of security for the resulting components and show some reductions between them and/or their combinations. Finally, we conjecture that VeraGreg achieves the strongest (and desirable) security guarantee if and only if its building blocks achieve certain, much more tangible properties, in a specific case together with an assumption on hardness of particular kind of the famous Shortest Vector Problem for lattices.

Category / Keywords: foundations / Verifiable homomorphic encryption, Formal notions of security, Non-malleability

Date: received 29 May 2019

Contact author: jakub klemsa at gmail com

Available format(s): PDF | BibTeX Citation

Version: 20190530:203934 (All versions of this report)

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