Single-round collapse of the computational Bell test

Determine whether knowledge assumptions can collapse the three-round computational Bell test of Kahanamoku-Meyer et al. to a single-round protocol.

Background

The paper notes that replacing the BCMVV adaptive-hardcore-bit test with the computational Bell test of Kahanamoku-Meyer et al. could avoid the need for the carry-predicate assumption, since that test relies only on the claw-free structure of the trapdoor family. However, the computational Bell test has three rounds of interaction, and it is unknown whether knowledge assumptions can reduce it to a single round as they do for the BCMVV protocol.