Fine-grained polynomial functional encryption

In this work, we present fine-grained secure polynomial functional encryption (PFE) for degree d≥1 over a field F: a ciphertext encrypts x∈Fⁿ, 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) NC¹ PFE: Based on the worst-case assumption NC¹⊊⊕L/poly, we construct public-key polynomial functional encryption and achieve (i) selective simulation-based security and (ii) static function-hiding against adversary in NC¹ where all honest algorithms are computable in AC⁰[2] and ciphertext sizes are O(n). (2) AC⁰ PFE: We construct a private-key polynomial functional encryption achieve unconditionally selective simulation-based security against adversary in AC⁰ where all honest algorithms are computable in AC⁰ and ciphertext sizes are O(n).