Paper 2023/719

Lower Bounds for Lattice-based Compact Functional Encryption

Erkan Tairi, DIENS, École normale supérieure, CNRS, Inria, PSL University, Paris, France
Akın Ünal, ISTA, Klosterneuburg, Austria
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 the question if there are some mathematical barriers that 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 ciphertexts of linear size and secret keys of minimal degree. 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
A major revision of an IACR publication in EUROCRYPT 2024
Keywords
Lower BoundsLattice-based CryptographyFunctional EncryptionCompact
Contact author(s)
erkan tairi @ gmail com
akin uenal @ posteo de
History
2024-02-27: revised
2023-05-18: received
See all versions
Short URL
https://ia.cr/2023/719
License
Creative Commons Attribution
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},
      url = {https://eprint.iacr.org/2023/719}
}
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