Unbounded Predicate Inner Product Functional Encryption from Pairings

Uddipana Dowerah; Subhranil Dutta; Aikaterini Mitrokotsa; Sayantan Mukherjee; Tapas Pal

Paper 2023/483

Unbounded Predicate Inner Product Functional Encryption from Pairings

Uddipana Dowerah, Chalmers University of Technology, Sweden

Subhranil Dutta, Indian Institute of Technology Kharagpur, India

Aikaterini Mitrokotsa, University of St Gallen, Switzerland

Sayantan Mukherjee, University of St Gallen, Switzerland

Tapas Pal, NTT Social Informatics Laboratories, Japan

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 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 settings. 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.

Note: This paper will appear in the Topical Collection on Computing on Encrypted Data of the Journal of Cryptology.

Metadata

Available format(s): PDF
Category: Public-key cryptography
Publication info: Published by the IACR in JOC 2023
Keywords: inner product functional encryption unbounded fully attribute-hiding weak attribute-hiding semi-adaptive security
Contact author(s): uddipana @ chalmers se
subhranildutta @ iitkgp ac in
katerina mitrokotsa @ unisg ch
csayantan mukherjee @ gmail com
tapas pal wh @ hco ntt co jp
History: 2023-04-05: approved; 2023-04-04: received; See all versions
Short URL: https://ia.cr/2023/483
License: CC BY

BibTeX

@misc{cryptoeprint:2023/483,
      author = {Uddipana Dowerah and Subhranil Dutta and Aikaterini Mitrokotsa and Sayantan Mukherjee and Tapas Pal},
      title = {Unbounded Predicate Inner Product Functional Encryption from Pairings},
      howpublished = {Cryptology {ePrint} Archive, Paper 2023/483},
      year = {2023},
      url = {https://eprint.iacr.org/2023/483}
}