Information-Theoretic Broadcast with Dishonest Majority for Long Messages

Byzantine broadcast is a fundamental primitive for secure computation. In a setting with $n$ parties in the presence of an adversary controlling at most $t$ parties, while a lot of progress in optimizing communication complexity has been made for $t < n/2$, little progress has been made for the general case $t<n$, especially for information-theoretic security. In particular, all information-theoretic secure broadcast protocols for $\ell$-bit messages and $t<n$ and optimal round complexity $\mathcal{O}(n)$ have, so far, required a communication complexity of $\mathcal{O}(\ell n^2)$. A broadcast extension protocol allows a long message to be broadcast more efficiently using a small number of single-bit broadcasts. Through broadcast extension, so far, the best achievable round complexity for $t<n$ setting with the optimal communication complexity of $\mathcal{O}(\ell n)$ is $\mathcal{O}(n^4)$ rounds. In this work, we construct a new broadcast extension protocol for $t<n$ with information-theoretic security. Our protocol improves the round complexity to $\mathcal{O}(n^3)$ while maintaining the optimal communication complexity for long messages. Our result shortens the gap between the information-theoretic setting and the computational setting, and between the optimal communication protocol and the optimal round protocol in the information-theoretic setting for $t<n$

Information-Theoretically Secure Voting Without an Honest Majority

We present three voting protocols with unconditional privacy and information-theoretic correctness, without assuming any bound on the number of corrupt voters or voting authorities. All protocols have polynomial complexity and require private channels and a simultaneous broadcast channel. Our first protocol is a basic voting scheme which allows voters to interact in order to compute the tally. Privacy of the ballot is unconditional, but any voter can cause the protocol to fail, in which case information about the tally may nevertheless transpire. Our second protocol introduces voting authorities which allow the implementation of the first protocol, while reducing the interaction and limiting it to be only between voters and authorities and among the authorities themselves. The simultaneous broadcast is also limited to the authorities. As long as a single authority is honest, the privacy is unconditional, however, a single corrupt authority or a single corrupt voter can cause the protocol to fail. Our final protocol provides a safeguard against corrupt voters by enabling a verification technique to allow the authorities to revoke incorrect votes. We also discuss the implementation of a simultaneous broadcast channel with the use of temporary computational assumptions, yielding versions of our protocols achieving everlasting security

Asymmetric Multi-Party Computation

Current protocols for Multi-Party Computation (MPC) consider the setting where all parties have access to similar resources. For example, all parties have access to channels bounded by the same worst-case delay upper bound ?, and all channels have the same cost of communication. As a consequence, the overall protocol performance (resp. the communication cost) may be heavily affected by the slowest (resp. the most expensive) channel, even when most channels are fast (resp. cheap). Given the state of affairs, we initiate a systematic study of asymmetric MPC. In asymmetric MPC, the parties are divided into two categories: fast and slow parties, depending on whether they have access to high-end or low-end resources. We investigate two different models. In the first, we consider asymmetric communication delays: Fast parties are connected via channels with small delay ? among themselves, while channels connected to (at least) one slow party have a large delay ? ? ?. In the second model, we consider asymmetric communication costs: Fast parties benefit from channels with cheap communication, while channels connected to a slow party have an expensive communication. We provide a wide range of positive and negative results exploring the trade-offs between the achievable number of tolerated corruptions t and slow parties s, versus the round complexity and communication cost in each of the models. Among others, we achieve the following results. In the model with asymmetric communication delays, focusing on the information-theoretic (i-t) setting: - An i-t asymmetric MPC protocol with security with abort as long as t+s < n and t < n/2, in a constant number of slow rounds. - We show that achieving an i-t asymmetric MPC protocol for t+s = n and with number of slow rounds independent of the circuit size implies an i-t synchronous MPC protocol with round complexity independent of the circuit size, which is a major problem in the field of round-complexity of MPC. - We identify a new primitive, asymmetric broadcast, that allows to consistently distribute a value among the fast parties, and at a later time the same value to slow parties. We completely characterize the feasibility of asymmetric broadcast by showing that it is possible if and only if 2t + s < n. - An i-t asymmetric MPC protocol with guaranteed output delivery as long as t+s < n and t < n/2, in a number of slow rounds independent of the circuit size. In the model with asymmetric communication cost, we achieve an asymmetric MPC protocol for security with abort for t+s < n and t < n/2, based on one-way functions (OWF). The protocol communicates a number of bits over expensive channels that is independent of the circuit size. We conjecture that assuming OWF is needed and further provide a partial result in this direction

Optimal Error-Free Multi-Valued Byzantine Agreement

Byzantine agreement (BA) is a distributed consensus problem where n processors want to reach agreement on an ?-bit message or value, but up to t of the processors are dishonest or faulty. The challenge of this BA problem lies in achieving agreement despite the presence of dishonest processors who may arbitrarily deviate from the designed protocol. In this work by using coding theory, together with graph theory and linear algebra, we design a coded BA protocol (termed as COOL) that achieves consensus on an ?-bit message with optimal resilience, asymptotically optimal round complexity, and asymptotically optimal communication complexity when ? ? t log t, simultaneously. The proposed COOL is a deterministic BA protocol that is guaranteed to be correct in all executions (error free) and does not rely on cryptographic technique such as signatures, hashing, authentication and secret sharing (signature free). It is secure against computationally unbounded adversary who takes full control over the dishonest processors (information-theoretic secure). The main idea of the proposed COOL is to use a carefully-crafted error correction code that provides an efficient way of exchanging "compressed" information among distributed nodes, while keeping the ability of detecting errors, masking errors, and making a consistent and validated agreement at honest distributed nodes. We show that our results can also be extended to the setting of Byzantine broadcast, aka Byzantine generals problem, where the honest processors want to agree on the message sent by a leader who is potentially dishonest. The results reveal that coding is an effective approach for achieving the fundamental limits of Byzantine agreement and its variants. Our protocol analysis borrows tools from coding theory, graph theory and linear algebra

Communication Lower Bounds for Cryptographic Broadcast Protocols

Broadcast protocols enable a set of $n$ parties to agree on the input of a designated sender, even facing attacks by malicious parties. In the honest-majority setting, randomization and cryptography were harnessed to achieve low-communication broadcast with sub-quadratic total communication and balanced sub-linear cost per party. However, comparatively little is known in the dishonest-majority setting. Here, the most communication-efficient constructions are based on Dolev and Strong (SICOMP '83), and sub-quadratic broadcast has not been achieved. On the other hand, the only nontrivial $\omega(n)$ communication lower bounds are restricted to deterministic protocols, or against strong adaptive adversaries that can perform "after the fact" removal of messages. We provide new communication lower bounds in this space, which hold against arbitrary cryptography and setup assumptions, as well as a simple protocol showing near tightness of our first bound. 1) We demonstrate a tradeoff between resiliency and communication for protocols secure against $n-o(n)$ static corruptions. For example, $\Omega(n\cdot {\sf polylog}(n))$ messages are needed when the number of honest parties is $n/{\sf polylog}(n)$; $\Omega(n\sqrt{n})$ messages are needed for $O(\sqrt{n})$ honest parties; and $\Omega(n^2)$ messages are needed for $O(1)$ honest parties. Complementarily, we demonstrate broadcast with $O(n\cdot{\sf polylog}(n))$ total communication facing any constant fraction of static corruptions. 2) Our second bound considers $n/2 + k$ corruptions and a weakly adaptive adversary that cannot remove messages "after the fact." We show that any broadcast protocol within this setting can be attacked to force an arbitrary party to send messages to $k$ other parties. This rules out, for example, broadcast facing 51% corruptions in which all non-sender parties have sublinear communication locality.Comment: A preliminary version of this work appeared in DISC 202

Practical unconditionally secure signature schemes and related protocols

The security guarantees provided by digital signatures are vital to many modern applications such as online banking, software distribution, emails and many more. Their ubiquity across digital communications arguably makes digital signatures one of the most important inventions in cryptography. Worryingly, all commonly used schemes – RSA, DSA and ECDSA – provide only computational security, and are rendered completely insecure by quantum computers. Motivated by this threat, this thesis focuses on unconditionally secure signature (USS) schemes – an information theoretically secure analogue of digital signatures. We present and analyse two new USS schemes. The first is a quantum USS scheme that is both information-theoretically secure and realisable with current technology. The scheme represents an improvement over all previous quantum USS schemes, which were always either realisable or had a full security proof, but not both. The second is an entirely classical USS scheme that uses minimal resources and is vastly more efficient than all previous schemes, to such an extent that it could potentially find real-world application. With the discovery of such an efficient classical USS scheme using only minimal resources, it is difficult to see what advantage quantum USS schemes may provide. Lastly, we remain in the information-theoretic security setting and consider two quantum protocols closely related to USS schemes – oblivious transfer and quantum money. For oblivious transfer, we prove new lower bounds on the minimum achievable cheating probabilities in any 1-out-of-2 protocol. For quantum money, we present a scheme that is more efficient and error tolerant than all previous schemes. Additionally, we show that it can be implemented using a coherent source and lossy detectors, thereby allowing for the first experimental demonstration of quantum coin creation and verification