Privacy is a major concern in large-scale digital applications, such as cloud-computing, machine learning services, and access control. Users want to protect not only their plain data but also their associated attributes (e.g., age, location, etc). Functional encryption (FE) is a cryptographic tool that allows fine-grained access control over encrypted data. However, existing FE fall short as they are either inefficient and far from reality or they leak sensitive user-specific information. We propose SACfe, a novel attribute-based FE scheme that provides secure, fine-grained access control and hides both the user's attributes and the function applied to the data, while preserving the data's confidentiality. Moreover, it enables users to encrypt unbounded-length messages along with an arbitrary number of hidden attributes into ciphertexts. We design SACfe, a protocol for performing linear computation on encrypted data while enforcing access control based on inner product predicates. We show how SACfe can be used for online biometric authentication for privacy-preserving access control. As an additional contribution, we introduce an attribute-based linear FE for unbounded length of messages and functions where access control is realized by monotone span programs. We implement our protocols using the CiFEr cryptographic library and show its efficiency for practical settings.

Abstract Predicate inner product functional encryption (P-IPFE) is essentially attribute-based IPFE (AB-IPFE) which additionally hides attributes associated to ciphertexts. In a P-IPFE, a message $${\textbf {x}}$$ x is encrypted under an attribute $${\textbf {w}}$$ w and a secret key is generated for a pair $$({\textbf {y}}, {\textbf {v}})$$ ( y , v ) such that recovery of $$\langle {{\textbf {x}}}, {{\textbf {y}}}\rangle $$ ⟨ x , y ⟩ requires the vectors $${\textbf {w}}, {\textbf {v}}$$ w , v to satisfy a linear relation. We call a P-IPFE unbounded if it can encrypt unbounded length attributes and message vectors. $$\bullet $$ ∙ zero predicate IPFE. We construct the first unbounded zero predicate IPFE (UZP-IPFE) which recovers $$\langle {{\textbf {x}}}, {{\textbf {y}}}\rangle $$ ⟨ x , y ⟩ if $$\langle {{\textbf {w}}}, {{\textbf {v}}}\rangle =0$$ ⟨ w , v ⟩ = 0 . This construction is inspired by the unbounded IPFE of Tomida and Takashima (ASIACRYPT 2018) and the unbounded zero inner product encryption of Okamoto and Takashima (ASIACRYPT 2012). The UZP-IPFE stands secure against general attackers capable of decrypting the challenge ciphertext. Concretely, it provides full attribute-hiding security in the indistinguishability-based semi-adaptive model under the standard symmetric external Diffie–Hellman assumption. $$\bullet $$ ∙ non-zero predicate IPFE. We present the first unbounded non-zero predicate IPFE (UNP-IPFE) that successfully recovers $$\langle {{\textbf {x}}}, {{\textbf {y}}}\rangle $$ ⟨ x , y ⟩ if $$\langle {{\textbf {w}}}, {{\textbf {v}}}\rangle \ne 0$$ ⟨ w , v ⟩ ≠ 0 . We generically transform an unbounded quadratic FE (UQFE) scheme to weak attribute-hiding UNP-IPFE in both public and secret key setting. Interestingly, our secret key simulation secure UNP-IPFE has succinct secret keys and is constructed from a novel succinct UQFE that we build in the random oracle model. We leave the problem of constructing a succinct public key UNP-IPFE or UQFE in the standard model as an important open problem.