Paper 2023/719

Lower Bounds for Lattice-based Compact Functional Encryption

Erkan Tairi, TU Wien
Akın Ünal, ETH Zurich

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.

Available format(s)
Public-key cryptography
Publication info
Lower BoundsLattice-based CryptographyFunctional EncryptionCompact
Contact author(s)
erkan tairi @ tuwien ac at
akin uenal @ inf ethz ch
2023-05-22: approved
2023-05-18: received
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      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{}},
      url = {}
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