Functional encryption for computational hiding in prime order groups via pair encodings

Lewko and Waters introduced the computational hiding technique in Crypto’12. In their technique, two computational assumptions that achieve selective and co-selective security proofs lead to adaptive security of an encryption scheme. Later, pair encoding framework was introduced by Attrapadung in Eurocrypt’14. The pair encoding framework generalises the computational hiding technique for functional encryption (FE). It has been used to achieve a number of new FE schemes such as FE for regular languages and unbounded attribute based encryption allowing multi-use of attributes. Nevertheless, the generalised construction of Attrapadung’s pair encoding for those schemes is adaptively secure only in composite order groups, which leads to efficiency loss. It remains a challenging task to explore constructions in prime order groups for gaining efficiency improvement, which leaves the research gap in the existing literature. In this work, we aim to address this drawback by proposing a new generalised construction for pair encodings in prime order groups. Our construction will lead to a number of new FE schemes in prime order groups, which have been previously introduced only in composite order groups by Attrapadung.