Paper 2024/226

Attribute-based Keyed (Fully) Homomorphic Encryption

Abstract

Keyed homomorphic public key encryption (KHPKE) is a variant of homomorphic public key encryption, where only users who have a homomorphic evaluation key can perform a homomorphic evaluation. Then, KHPKE satisfies the CCA2 security against users who do not have a homomorphic evaluation key, while it satisfies the CCA1 security against users who have the key. Thus far, several KHPKE schemes have been proposed under the standard Diffie-Hellman-type assumptions and keyed fully homomorphic encryption (KFHE) schemes have also been proposed from lattices although there are no KFHE schemes secure solely under the LWE assumption in the standard model. As a natural extension, there is an identity-based variant of KHPKE; however, the security is based on a $q$-type assumption and there are no attribute-based variants. Moreover, there are no identity-based variants of KFHE schemes due to the complex design of the known KFHE schemes. In this paper, we provide two constructions of attribute-based variants. First, we propose an attribute-based KFHE (ABKFHE) scheme from lattices. We start by designing the first KFHE scheme secure solely under the LWE assumption in the standard model. Since the design is conceptually much simpler than known KFHE schemes, we replace their building blocks with attribute-based ones and obtain the proposed ABKFHE schemes. Next, we propose an efficient attribute-based KHPKE (ABKHE) scheme from a pair encoding scheme (PES). Due to the benefit of PES, we obtain various ABKHE schemes that contain the first identity-based KHPKE scheme secure under the standard $k$-linear assumption and the first pairing-based ABKHE schemes supporting more expressive predicates.