Paper 2023/719
Lower Bounds for Lattice-based Compact Functional Encryption
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
-
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} }