Improved Inner-product Encryption with Adaptive Security and Full Attribute-hiding

In this work, we propose two IPE schemes achieving both adaptive security and full attribute-hiding in the prime-order bilinear group, which improve upon the unique existing result satisfying both features from Okamoto and Takashima [Eurocrypt ’12] in terms of efficiency.

– Our first IPE scheme is based on the standard k-LIN assumption and has shorter master public key and shorter secret keys than Okamoto and Takashima’s IPE under weaker DLIN = 2-LIN assumption.

– Our second IPE scheme is adapted from the first one; the security is based on the XDLIN assumption (as Okamoto and Takashima’s IPE) but now it also enjoys shorter ciphertexts.

Technically, instead of starting from composite-order IPE and applying existing transformation, we start from an IPE scheme in a very restricted setting but already in the prime-order group, and then gradually upgrade it to our fullfledged IPE scheme. This method allows us to integrate Chen et al.’s framework [Eurocrypt ’15] with recent new techniques [TCC ’17, Eurocrypt ’18] in an optimized way.