Fully selective opening secure IBE from LWE

Selective opening security ensures that, when an adversary is given multiple ciphertexts and corrupts a subset of the senders (thereby obtaining the plaintexts and the senders’ randomness), the privacy of the remaining ciphertexts is still preserved. Previous selective opening secure IBE schemes encrypt messages bit-by-bit, or only achieve selective-id security. In this paper, we present the first adaptive-id, selective opening secure identity-based encryption (IBE) tightly from LWE. To achieve this, we introduce a new primitive called delegatable all-but-many lossy trapdoor functions (DABM-LTDF) and provide a generic construction that converts DABM-LTDF into an adaptive-id, selective opening secure IBE through a tight security reduction. Finally, we construct a concrete DABM-LTDF from the LWE assumption, resulting in the first adaptive-id, selective opening secure IBE from LWE.