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Asynchronous complete secret sharing (ACSS) is a foundational primitive in the design of distributed algorithms and cryptosystems that require confidentiality. ACSS permits a dealer to distribute a secret to a collection of N servers so that everyone holds shares of a polynomial containing the dealer's secret.

This work contributes a new ACSS protocol, called Haven++, that uses packing and batching to make asymptotic and concrete advances in the design and application of ACSS for large secrets. Haven++ allows the dealer to pack multiple secrets in a single sharing phase, and to reconstruct either one or all of them later. For even larger secrets, we contribute a batching technique to amortize the cost of proof generation and verification across multiple invocations of our protocol.

The result is an asymptotic improvement in the worst-case amortized communication and computation complexity, both for ACSS itself and for its application to asynchronous distributed key generation. Our ADKG based on Haven++ achieves, for the first time, an optimal worst case amortized communication complexity of κN without a trusted setup. To show the practicality of Haven++, we implement it and find that it outperforms the work of Yurek et al. (NDSS 2022) by more than an order of magnitude when there are malicious, faulty parties.

 

End-to-end encryption provides strong privacy protections to billions of people, but it also complicates efforts to moderate content that can seriously harm people. To address this concern, Tyagi et al. [CRYPTO 2019] introduced the concept of asymmetric message franking (AMF) so that people can report abusive content to a moderator, while otherwise retaining end-to-end privacy by default and compatibility with anonymous communication systems like Signal’s sealed sender. In this work, we provide a new construction for asymmetric message franking called Hecate that is faster, more secure, and introduces additional functionality compared to Tyagi et al. First, our construction uses fewer invocations of standardized crypto primitives and operates in the plain model. Second, on top of AMF’s accountability and deniability requirements, we also add forward and backward secrecy. Third, we combine AMF with source tracing, another approach to content moderation that has previously been considered only in the setting of non-anonymous networks. Source tracing allows for messages to be forwarded, and a report only identifies the original source who created a message. To provide anonymity for senders and forwarders, we introduce a model of AMF with preprocessing whereby every client authenticates with the moderator out-of-band to receive a token that they later consume when sending a message anonymously. 

This paper studies Byzantine reliable broadcast (BRB) under asynchronous networks, and improves the state-of-the-art protocols from the following aspects. Near-optimal communication cost: We propose two new BRB protocols for n nodes and input message M that has communication cost O(n|M| +n^2 log n), which is near-optimal due to the lower bound of Ω(n|M| +n^2). The first BRB protocol assumes threshold signature but is easy to understand, while the second BRB protocol is error-free but less intuitive. Improved computation: We propose a new construction that improves the computation cost of the state-of-the-art BRB by avoiding the expensive online error correction on the input message, while achieving the same communication cost. Balanced communication: We propose a technique named balanced multicast that can balance the communication cost for BRB protocols where the broadcaster needs to multicast the message M while other nodes only needs to multicast coded fragments of size O(|M|/n + log n). The balanced multicast technique can be applied to many existing BRB protocols as well as all our new constructions in this paper, and can make every node incur about the same communication cost. Finally, we present a lower bound to show the near optimality of our protocol in terms of communication cost at each node. 

Asynchronous verifiable secret sharing (AVSS) protocols protect a secret that is distributed among N parties. Dual-threshold AVSS protocols guarantee consensus in the presence of T Byzantine failures and privacy if fewer than P parties attempt to reconstruct the secret. In this work, we construct a dual-threshold AVSS protocol that is optimal along several dimensions. First, it is a high-threshold AVSS scheme, meaning that it is a dual-threshold AVSS with optimal parameters T < N/3 and P < N - T. Second, it has O(N^2) message complexity, and for large secrets it achieves the optimal O(N) communication overhead, without the need for a public key infrastructure or trusted setup. While these properties have been achieved individually before, to our knowledge this is the first protocol that is achieves all of the above simultaneously. The core component of our construction is a high-threshold AVSS scheme for small secrets based on polynomial commitments that achieves O(N^2 log(N)) communication overhead, as compared to prior schemes that require O(N^3) overhead with T more » « less

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