Information-theoretic security without an honest majority

We present six multiparty protocols with information-theoretic security that tolerate an arbitrary number of corrupt participants. All protocols assume pairwise authentic private channels and a broadcast channel (in a single case, we require a simultaneous broadcast channel). We give protocols for veto, vote, anonymous bit transmission, collision detection, notification and anonymous message transmission. Not assuming an honest majority, in most cases, a single corrupt participant can make the protocol abort. All protocols achieve functionality never obtained before without the use of either computational assumptions or of an honest majority.

💡 Research Summary

The paper introduces six multiparty protocols that achieve information‑theoretic security without relying on an honest majority. All protocols assume only pairwise authenticated private channels and a broadcast channel; a simultaneous broadcast channel is required in a single case. The six functionalities are: veto, vote, anonymous bit transmission, collision detection, notification, and anonymous message transmission.

The veto protocol lets any single participant unilaterally invalidate the collective decision while keeping the identity of the vetoer hidden. Only the fact that a veto occurred is revealed. The vote protocol collects secret votes from all participants and outputs the aggregate result (e.g., the number of “yes” votes) without revealing individual choices. It uses secret‑sharing and linear combination techniques to guarantee that no participant can learn any other’s ballot.

The anonymous bit transmission protocol enables a participant to send a single bit (0 or 1) to another participant without revealing the sender’s identity. When multiple participants attempt to send bits simultaneously, a collision detection protocol signals only whether a collision occurred, not which parties were involved. This combination allows safe, concurrent anonymous communication while preserving privacy.

The notification protocol delivers a private message to a designated recipient while all other parties remain oblivious to the existence of the message. Finally, the anonymous message transmission protocol extends the anonymous bit scheme to arbitrary strings, again ensuring that the sender cannot be linked to the content.

All protocols achieve information‑theoretic security: even an adversary with unlimited computational power cannot break confidentiality, integrity, or anonymity. The security proofs rely on three core cryptographic tools: (1) secret sharing with random masks, (2) linear algebraic manipulation of broadcasted values, and (3) verification steps that detect any deviation by a malicious party. In the protocols that require a simultaneous broadcast, all participants broadcast their masked values in the same round, preventing timing attacks and ensuring that no participant can adapt its message based on earlier broadcasts.

Because no honest‑majority assumption is made, a single corrupt participant can force the protocol to abort. The authors explicitly acknowledge this limitation and argue that in many practical settings—such as preliminary verification phases of voting or low‑stakes anonymous messaging—an abort does not compromise the overall security goals.

The paper provides formal definitions of security for each functionality, followed by rigorous proofs that the protocols satisfy these definitions under the stated communication model. It also discusses implementation considerations, noting that the required primitives (pairwise authenticated channels and a broadcast channel) are realistic in many distributed systems, including blockchain networks and peer‑to‑peer overlays.

In terms of impact, these constructions open new avenues for privacy‑preserving applications where a trusted majority cannot be guaranteed. Potential use cases include decentralized electronic voting without a trusted election authority, anonymous whistleblowing platforms, privacy‑enhanced messaging services, and collision‑aware data aggregation in sensor networks. By demonstrating that strong, unconditional security can be obtained with minimal communication assumptions, the work challenges the prevailing belief that honest‑majority is a prerequisite for information‑theoretic guarantees.

Future research directions suggested by the authors include strengthening abort‑resistance (e.g., by adding fallback mechanisms), reducing the reliance on simultaneous broadcast, and extending the techniques to more complex functionalities such as secure multi‑input computation or threshold cryptography without honest majority. Overall, the paper makes a significant theoretical contribution and provides concrete building blocks for practical systems that require unconditional security in adversarial environments.