TCS Journal 2024 Journal Article
Fine-grained polynomial functional encryption
- Ziqi Zhu
- Junqing Gong
- Yuyu Wang
- Haifeng Qian
In this work, we present fine-grained secure polynomial functional encryption (PFE) for degree d ≥ 1 over a field F: a ciphertext encrypts x ∈ F n, a key is associated with a degree-d polynomial P and decryption recovers P ( x ) ∈ F. Fine-grained cryptographic primitives are secure against a resources bounded class of adversaries and computed by honest users with less resources than adversaries. In this paper, we construct the fine-grained PFE in these two fine-grained settings: (1) NC 1 PFE: Based on the worst-case assumption NC 1 ⊊ ⊕ L / poly, we construct public-key polynomial functional encryption and achieve (i) selective simulation-based security and (ii) static function-hiding against adversary in NC 1 where all honest algorithms are computable in AC 0 [ 2 ] and ciphertext sizes are O ( n ). (2) AC 0 PFE: We construct a private-key polynomial functional encryption achieve unconditionally selective simulation-based security against adversary in AC 0 where all honest algorithms are computable in AC 0 and ciphertext sizes are O ( n ).