Lower Bounds for Lattice-based Compact Functional Encryption

Erkan Tairi; Akın Ünal

Paper 2023/719

Lower Bounds for Lattice-based Compact Functional Encryption

Erkan Tairi

, TU Wien

Akın Ünal

, ETH Zurich

Abstract

Functional encryption (FE) is a primitive where the holder of a master secret key can control which functions a user can evaluate on encrypted data. It is a powerful primitive that even implies indistinguishability obfuscation (iO), given sufficiently compact ciphertexts (Ananth-Jain, CRYPTO'15 and Bitansky-Vaikuntanathan, FOCS'15). However, despite being extensively studied, there are FE schemes, such as function-hiding inner-product FE (Bishop-Jain-Kowalczyk, AC'15, Abdalla-Catalano-Fiore-Gay-Ursu, CRYPTO’18) and compact quadratic FE (Baltico-Catalano-Fiore-Gay, Lin, CRYPTO’17), that can be only realized using pairings. This raises whether there are some mathematical barriers which hinder us from realizing these FE schemes from other assumptions. In this paper, we study the difficulty of constructing lattice-based compact FE. We generalize the impossibility results of Ünal (EC'20) for lattice-based function-hiding FE, and extend it to the case of compact FE. Concretely, we prove lower bounds for lattice-based compact FE schemes which meet some (natural) algebraic restrictions at encryption and decryption, and have messages and ciphertexts of constant dimensions. We see our results as important indications of why it is hard to construct lattice-based FE schemes for new functionalities, and which mathematical barriers have to be overcome.

Metadata

Available format(s): PDF
Category: Public-key cryptography
Publication info: Preprint.
Keywords: Lower Bounds Lattice-based Cryptography Functional Encryption Compact
Contact author(s): erkan tairi @ tuwien ac at
akin uenal @ inf ethz ch
History: 2023-05-22: approved; 2023-05-18: received; See all versions
Short URL: https://ia.cr/2023/719
License: CC BY

BibTeX

@misc{cryptoeprint:2023/719,
      author = {Erkan Tairi and Akın Ünal},
      title = {Lower Bounds for Lattice-based Compact Functional Encryption},
      howpublished = {Cryptology ePrint Archive, Paper 2023/719},
      year = {2023},
      note = {\url{https://eprint.iacr.org/2023/719}},
      url = {https://eprint.iacr.org/2023/719}
}