### A Note on Attribute-Based Group Homomorphic Encryption

Michael Clear and Ciaran McGoldrick

##### 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 for which a (public-key) GHE scheme exists.

Note: Revised paper; added section on semilattices.

Available format(s)
Category
Public-key cryptography
Publication info
Preprint. MINOR revision.
Keywords
homomorphic encryptionattribute-based encryption
Contact author(s)
clearm @ tcd ie
History
2019-02-19: revised
See all versions
Short URL
https://ia.cr/2017/752

CC BY

BibTeX

@misc{cryptoeprint:2017/752,
author = {Michael Clear and Ciaran McGoldrick},
title = {A Note on Attribute-Based Group Homomorphic Encryption},
howpublished = {Cryptology ePrint Archive, Paper 2017/752},
year = {2017},
note = {\url{https://eprint.iacr.org/2017/752}},
url = {https://eprint.iacr.org/2017/752}
}

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