International Association for Cryptologic Research

International Association
for Cryptologic Research


Paper: Achievable CCA2 Relaxation for Homomorphic Encryption

Adi Akavia , University of Haifa, Israel
Craig Gentry , TripleBlind, USA
Shai Halevi , Algorand, USA
Margarita Vald , Intuit Inc., Israel
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Presentation: Slides
Conference: TCC 2022
Abstract: Homomorphic encryption (HE) protects data in-use, but can be computationally expensive. To avoid the costly bootstrapping procedure that refreshes ciphertexts, some works have explored client-aided outsourcing protocols, where the client intermittently refreshes ciphertexts for a server that is performing homomorphic computations. But is this approach secure against malicious servers? We present a CPA-secure encryption scheme that is completely insecure in this setting. We define a new notion of security, called \emph{funcCPA}, that we prove is sufficient. Additionally, we show: - Homomorphic encryption schemes that have a certain type of circuit privacy -- for example, schemes in which ciphertexts can be ``sanitized" -- are funcCPA-secure. - In particular, assuming certain existing HE schemes are CPA-secure, they are also funcCPA-secure. - For certain encryption schemes, like Brakerski-Vaikuntanathan, that have a property that we call oblivious secret key extraction, funcCPA-security implies circular security -- i.e., that it is secure to provide an encryption of the secret key in a form usable for bootstrapping (to construct fully homomorphic encryption). Namely, funcCPA-security lies strictly between CPA-security and CCA2-security (under reasonable assumptions), and has an interesting relationship with circular security, though it is not known to be equivalent.
  title={Achievable CCA2 Relaxation for Homomorphic Encryption},
  author={Adi Akavia and Craig Gentry and Shai Halevi and Margarita Vald},