Cryptology ePrint Archive: Report 2017/752

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.

Category / Keywords: public-key cryptography / homomorphic encryption, attribute-based encryption

Date: received 3 Aug 2017, last revised 19 Feb 2019

Contact author: clearm at tcd ie

Available format(s): PDF | BibTeX Citation

Note: Revised paper; added section on semilattices.

Version: 20190219:152929 (All versions of this report)

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