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1. On the Communication Complexity of Key-Agreement Protocols

   Haitner, Iftach; Mazor, Noam; Oshman, Rotem; Reingold, Omer; Yehudayoff, Amir (January 2019, Innovations in Theoretical Computer Science Conference)

   In a key-agreement protocol whose security is proven in the random oracle model (ROM), the parties and the eavesdropper can make bounded number of queries to a shared random function (an “oracle”). Such protocol are the alternative to key-agreement protocols whose security is based on “public-key assumptions”, assumptions that being more structured are presumingly more vulnerable to attacks. Barak and Mahmoody [Crypto ’09] (following Impagliazzo and Rudich [STOC ’89]) have shown the ROM key-agreement protocols can only guarantee limited secrecy: the key of any `l-query protocol can be revealed by an O(l^2 )-query adversary, a bound that matches the gap obtained by the Merkle’s Puzzles two-message protocol of Merkle [CACM ’78]. While this quadratic gap might not seem like much, if the honest parties are willing to work “hard enough” and given continuousness improvement in common hash functions evaluation time, this gap yields a good enough advantage (assuming the security of the protocol holds when initiating the random function with a fixed hash function). In this work we consider the communication complexity of ROM key-agreement protocols. In Merkle’s Puzzles, the honest parties need to exchange Ω(l) bits (ignoring logarithmic factors) to obtain secrecy against an eavesdropper that makes roughly l^2 queries, which makes the protocol unrealizable in many settings. We show that for protocols with certain natural properties, such high communication is unavoidable. Specifically, this is the case if the honest parties’ queries are independent and uniformly random, or alternatively if the protocol uses non-adaptive queries and has only two rounds. Since two-round key-agreement protocol are equivalent to public-key encryption scheme (seeing the first message as the public-key), the latter result bounds the public-key and encryption size of public-key encryption scheme whose security is proven in the ROM. 

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2. Towards Multiparty Computation Withstanding Coercion of All Parties

   Canetti, Ran; Poburinnaya, Oxana (November 2021, Theory of Cryptography Conference)

   null (Ed.)

   Incoercible multi-party computation (Canetti-Gennaro ’96) allows parties to engage in secure computation with the additional guarantee that the public transcript of the computation cannot be used by a coercive outsider to verify representations made by the parties regarding their inputs, outputs, and local random choices. That is, it is guaranteed that the only deductions regarding the truthfulness of such representations, made by an outsider who has witnessed the communication among the parties, are the ones that can be drawn just from the represented inputs and outputs alone. To date, all incoercible secure computation protocols withstand coercion of only a fraction of the parties, or else assume that all parties use an execution environment that makes some crucial parts of their local states physically inaccessible even to themselves. We consider, for the first time, the setting where all parties are coerced, and the coercer expects to see the entire history of the computation. We allow both protocol participants and external attackers to access a common reference string which is generated once and for all by an uncorruptable trusted party. In this setting we construct: - A general multi-party function evaluation protocol, for any number of parties, that withstands coercion of all parties, as long as all parties use the prescribed ``faking algorithm'' upon coercion. This holds even if the inputs and outputs represented by coerced parties are globally inconsistent with the evaluated function. - A general two-party function evaluation protocol that withstands even the %``mixed'' case where some of the coerced parties do follow the prescribed faking algorithm. (For instance, these parties might collude with the coercer and disclose their true local states.) This protocol is limited to functions where the input of at least one of the parties is taken from a small (poly-size) domain. It uses fully deniable encryption with public deniability for one of the parties; when instantiated using the fully deniable encryption of Canetti, Park, and Poburinnaya (Crypto'20), it takes 3 rounds of communication. Both protocols operate in the common reference string model, and use fully bideniable encryption (Canetti Park and Poburinnaya, Crypto'20) and sub-exponential indistinguishability obfuscation. Finally, we show that protocols with certain communication pattern cannot be incoercible, even in a weaker setting where only some parties are coerced. 

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3. Interactive Compression to External Information

   Braverman, Mark; Kol, Gillat. (January 2018, ACM Symposium on Theory of Computing)

   We describe a new way of compressing two-party communication protocols to get protocols with potentially smaller communication. We show that every communication protocol that communicates C bits and reveals I bits of information about the participants’ private inputs to an observer that watches the communication, can be simulated by a new protocol that communicates at most poly(I)loglog(C) bits. Our result is tight up to polynomial factors, as it matches the recent work separating communication complexity from external information cost. 

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4. Communication Lower Bounds for Cryptographic Broadcast Protocols

   Blum, Erica; Boyle, Elette; Cohen, Ran; Liu-Zhang, Chen-Da (October 2023, 37th International Symposium on Distributed Computing (DISC 2023))

   Oshman, Rotem (Ed.)

   Broadcast protocols enable a set of n parties to agree on the input of a designated sender, even in the face of malicious parties who collude to attack the protocol. In the honest-majority setting, a fruitful line of work harnessed randomization and cryptography to achieve low-communication broadcast protocols with sub-quadratic total communication and with "balanced" sub-linear communication cost per party. However, comparatively little is known in the dishonest-majority setting. Here, the most communication-efficient constructions are based on the protocol of Dolev and Strong (SICOMP '83), and sub-quadratic broadcast has not been achieved even using randomization and cryptography. On the other hand, the only nontrivial ω(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 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. - Static adversary. We demonstrate a tradeoff between resiliency and communication for randomized protocols secure against n-o(n) static corruptions. For example, Ω(n⋅ polylog(n)) messages are needed when the number of honest parties is n/polylog(n); Ω(n√n) messages are needed for O(√n) honest parties; and Ω(n²) messages are needed for O(1) honest parties. Complementarily, we demonstrate broadcast with O(n⋅polylog(n)) total communication and balanced polylog(n) per-party cost, facing any constant fraction of static corruptions. - Weakly adaptive adversary. 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. Our bound implies limitations on the feasibility of balanced low-communication protocols: For example, ruling out broadcast facing 51% corruptions, in which all non-sender parties have sublinear communication locality. 

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5. High-Threshold AVSS with Optimal Communication Complexity

   AlHaddad, Nicolas; Varia, Mayank; Zhang, Haibin (March 2021, Financial Cryptography and Data Security)

   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 

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