A Tag Based Encoding: An Efficient Encoding for Predicate Encryption in Prime Order Groups

We introduce a tag based encoding, a new generic framework for modular design of Predicate Encryption (PE) schemes in prime order groups. Our framework is equipped with a compiler which is adaptively secure in prime order groups under the standard Decisional Linear Assumption (DLIN). Compared with prior encoding frameworks in prime order groups which require multiple group elements to interpret a tuple of an encoding in a real scheme, our framework has a distinctive feature which is that each element of an encoding can be represented with only a group element and an integer. This difference allows us to construct a more efficient encryption scheme. In the current literature, the most efficient compiler was proposed by Chen, Gay and Wee (CGW) in Eurocrypt’15. It features one tuple of an encoding into two group elements under the Symmetric External Diffie-Hellman assumption (SXDH). Compared with their compiler, our encoding construction saves the size of either private keys or ciphertexts up-to 25 % and reduces decryption time and the size of public key up-to 50 % in 128 security level. Several new schemes such as inner product encryption with short keys, dual spatial encryption with short keys and hierarchical identity based encryption with short ciphertexts are also introduced as instances of our encoding.