Authenticated BitGC for Actively Secure Rate-One 2PC

In this paper, we present a constant-round actively secure two-party computation protocol with small communication based on the ring learning with errors (RLWE) assumption with key-dependent message security. Our result builds on the recent BitGC protocol by Liu, Wang, Yang, and Yu (Eurocrypt 2025) with communication of one bit per gate for semi-honest security. First, we achieve a different manner of distributed garbling, where the global correlation is secret-shared among the two parties. The garbler always and only holds the garbled labels corresponding to the wire values when all inputs are zero, while the evaluator holds the labels corresponding to the real evaluation. In the second phase, we run an authentication protocol that requires some extra communication, which allows two parties to check the correct computation of each gate by treating the ciphertext as commitments, now that the global key is distributed. For layered circuits, the extra communication for authentication is $o(1)$ bits per gate, resulting in total communication of $1+o(1)$ bits per gate. For generic circuits, the extra communication cost can be $1$ bit per gate in the worst case, and thus, the total communication cost would be 2 bits per gate.