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 assumption and has shorter master public key and shorter secret keys than Okamoto and Takashima’s IPE under weaker assumption. Our second IPE scheme is adapted from the first one; the security is based on the 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 full-fledged 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.