A Note on Attribute-Based Group Homomorphic Encryption
Citation:
Clear, M., Mc Goldrick, C., A Note on Attribute-Based Group Homomorphic Encryption, IACR, 2019Download Item:
Abstract:
Group Homomorphic Encryption (GHE), formally defined
by Armknecht, Katzenbeisser and Peter, is a public-key encryption primitive where the decryption algorithm is a group homomorphism. Hence
it supports homomorphic evaluation of a single algebraic operation such
as modular addition or modular multiplication. Most classical homomorphic encryption schemes such as as Goldwasser-Micali and Paillier are
instances of GHE. In this work, we extend GHE to the attribute-based
setting. We introduce and formally define the notion of Attribute-Based
GHE (ABGHE) and explore its properties. We then examine the algebraic structure on attributes induced by the group operation in an
ABGHE. This algebraic stricture is a bounded semilattice. We consider some possible semilattices and how they can be realized by an
ABGHE supporting inner product predicates. We then examine existing schemes from the literature and show that they meet our definition of ABGHE for either an additive or multiplicative homomorphism.
Some of these schemes are in fact Identity-Based Group Homomorphic
Encryption (IBGHE) schemes i.e. instances of ABGHE whose class of
access policies are point functions. We then present a possibility result
for IBGHE from indistinguishability obfuscation for any group (S, ·) for
which a (public-key) GHE scheme exists.
Author's Homepage:
http://people.tcd.ie/cmcgldrkMetadata
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