# Function-Hiding Zero Predicate Inner Product Functional Encryption from Pairings

INFORMATION SECURITY, ISC 2023（2023）

摘要

In this work, we investigate the possibility of constructing function-hiding predicate functional encryption (FH-P-FE), which provides full attribute-hiding and function-hiding securities. Concretely, the security of FH-P-FE guarantees that (1), the functional secret keys hide the underlying functions and (2), the decryption works with an access control as in predicate encryption (PE). Our results show that the new paradigm is achievable. To achieve this goal, we first give a formal definition of FH-P-FE and its security model under an indistinguishabilitybased notion. Then we construct a secret-key function-hiding zero predicate inner product functional encryption (FH-ZP-IPFE) from pairings. In a FH-ZP-IPFE, both secret keys and ciphertexts are associated with vectors. Given a secret key for a policy x epsilon Z(q)(n) and a function u epsilon Z(q)(m), and a ciphertext for an attribute y epsilon Z(q)(n) and a message v. Zmq, a decryptor learns the inner product value < u, v > if and only if < x, y > - 0 mod q. Our construction is efficient, where the functional secret key and ciphertext both contain (n+m+1) group elements. We prove the security in the generic group model of bilinear groups.

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关键词

Predicate Encryption,Function Privacy,Inner Product,Functional Encryption,Generic Group Model

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