Unbounded Predicate Inner Product Functional Encryption from Pairings
Journal article, 2023

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 x is encrypted under an attribute w and a secret key is generated for a pair (y, v) such that recovery of ⟨ x, y⟩ requires the vectors w, v to satisfy a linear relation. We call a P-IPFE unbounded if it can encrypt unbounded length attributes and message vectors. ∙ zero predicate IPFE. We construct the first unbounded zero predicate IPFE (UZP-IPFE) which recovers ⟨ x, y⟩ if ⟨ 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. ∙ non-zero predicate IPFE. We present the first unbounded non-zero predicate IPFE (UNP-IPFE) that successfully recovers ⟨ x, y⟩ if ⟨ 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.

Inner product functional encryption

Unbounded

Weak attribute-hiding

Inner product predicate

Semi-adaptive security.

Fully attribute-hiding

Author

Uddipana Dowerah

Network and Systems

Subhranil Dutta

Indian Institute of Technology

Aikaterini Mitrokotsa

University of St Gallen

Sayantan Mukherjee

University of St Gallen

Tapas Pal

Nippon Telegraph and Telephone Corporation

Journal of Cryptology

0933-2790 (ISSN) 1432-1378 (eISSN)

Vol. 36 3 29

Areas of Advance

Information and Communication Technology

Subject Categories

Computer Science

DOI

10.1007/s00145-023-09458-2

More information

Latest update

5/29/2024