Adaptive oblivious transfer with access control from lattice assumptions

Adaptive oblivious transfer (OT) is a protocol where sender initially commits to database {Mi}i=1N. Then, receiver can query the up k times with private indexes ρ1,…,ρk so as obtain Mρ1,…,Mρk and nothing else. Moreover, for each i∈[k], receiver's choice ρi may depend on previously obtained messages {Mρj}j<i. Oblivious access control (OT-AC) flavor of adaptive OT records are protected by distinct policies that specify which credentials should in order Mi. So far, all known OT-AC protocols only support made conjunctions or rely ad hoc assumptions pairing-friendly groups (or both). In this paper, we provide an consist any branching program polynomial length, sufficient realize policy NC1. The security our proved under Learning-with-Errors (LWE) Short-Integer-Solution (SIS) assumptions. As result independent interest, proving correct evaluation committed input.