Abstract. We construct a pairing based simulation-extractable SNARK (SE-SNARK) that consists of only 3 group elements and has highly efficient verification. By formally linking SE-SNARKs to signatures of knowledge, we then obtain a succinct signature of knowledge consisting of only 3 group elements. SE-SNARKs enable a prover to give a proof that they know a witness to an instance in a manner which is: (1) succinct -proofs are short and verifier computation is small; (2) zero-knowledge -proofs do not reveal the witness; (3) simulation-extractable -it is only possible to prove instances to which you know a witness, even when you have already seen a number of simulated proofs. We also prove that any pairing based signature of knowledge or SE-NIZK argument must have at least 3 group elements and 2 verification equations. Since our constructions match these lower bounds, we have the smallest size signature of knowledge and the smallest size SE-SNARK possible.

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By design, existing (pre-processing) zk-SNARKs embed a secret trapdoor in a relation-dependent common reference strings (CRS). The trapdoor is exploited by a (hypothetical) simulator to prove the scheme is zero knowledge, and the secret-dependent structure facilitates a linear-size CRS and linear-time prover computation. If known by a real party, however, the trapdoor can be used to subvert the security of the system. The structured CRS that makes zk-SNARKs practical also makes deploying zk-SNARKS problematic, as it is difficult to argue why the trapdoor would not be available to the entity responsible for generating the CRS. Moreover, for pre-processing zk-SNARKs a new trusted CRS needs to be computed every time the relation is changed. In this paper, we address both issues by proposing a model where a number of users can update a universal CRS. The updatable CRS model guarantees security if at least one of the users updating the CRS is honest. We provide both a negative result, by showing that zk-SNARKs with private secret-dependent polynomials in the CRS cannot be updatable, and a positive result by constructing a zk-SNARK based on a CRS consisting only of secret-dependent monomials. The CRS is of quadratic size, is updatable, and is universal in the sense that it can be specialized into one or more relation-dependent CRS of linear size with linear-time prover computation.

In this paper we initiate a quantitative study of the decentralization of the governance structures of Bitcoin and Ethereum. In particular, we scraped the open-source repositories associated with their respective codebases and improvement proposals to find the number of people contributing to the code itself and to the overall discussion. We then present different metrics to quantify decentralization, both in each of the cryptocurrencies and, for comparison, in two popular open-source programming languages: Clojure and Rust. We find that for both cryptocurrencies and programming languages, there is usually a handful of people that accounts for most of the discussion. We also look into the effect of forks in Bitcoin and Ethereum, and find that there is little intersection between the communities of the original currencies and those of the forks.

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We give a protocol for Asynchronous Distributed Key Generation (A-DKG) that is optimally resilient (can withstand < 3 faulty parties), has a constant expected number of rounds, has˜( 3 ) expected communication complexity, and assumes only the existence of a PKI. Prior to our work, the best A-DKG protocols required Ω( ) expected number of rounds, and Ω( 4 ) expected communication.Our A-DKG protocol relies on several building blocks that are of independent interest. We define and design a Proposal Election (PE) protocol that allows parties to retrospectively agree on a valid proposal after enough proposals have been sent from different parties.With constant probability the elected proposal was proposed by a nonfaulty party. In building our PE protocol, we design a Verifiable Gather protocol which allows parties to communicate which proposals they have and have not seen in a verifiable manner. The final building block to our A-DKG is a Validated Asynchronous Byzantine Agreement (VABA) protocol. We use our PE protocol to construct a VABA protocol that does not require leaders or an asynchronous DKG setup. Our VABA protocol can be used more generally when it is not possible to use threshold signatures. CCS CONCEPTS• Theory of computation → Distributed algorithms; Cryptographic protocols.

In this paper, we introduce a distributed key generation (DKG) protocol with aggregatable and publicly-verifiable transcripts. Compared with prior publicly-verifiable approaches, our DKG reduces the size of the final transcript and the time to verify it from O(n 2 ) to O(n log n), where n denotes the number of parties. As compared with prior non-publicly-verifiable approaches, our DKG leverages gossip rather than all-to-all communication to reduce verification and communication complexity. We also revisit existing DKG security definitions, which are quite strong, and propose new and natural relaxations. As a result, we can prove the security of our aggregatable DKG as well as that of several existing DKGs, including the popular Pedersen variant. We show that, under these new definitions, these existing DKGs can be used to yield secure threshold variants of popular cryptosystems such as El-Gamal encryption and BLS signatures. We also prove that our DKG can be securely combined with a new efficient verifiable unpredictable function (VUF), whose security we prove in the random oracle model. Finally, we experimentally evaluate our DKG and show that the perparty overheads scale linearly and are practical. For 64 parties, it takes 71 ms to share and 359 ms to verify the overall transcript, while for 8192 parties, it takes 8 s and 42.2 s respectively. cLabs, Ethereum Foundation.

In this paper, we demonstrate that various cryptographic constructions-including ones for broadcast, attribute-based, and hierarchical identity-based encryption-can rely for security on only the static subgroup hiding assumption when instantiated in composite-order bilinear groups, as opposed to the dynamic q-type assumptions on which their security previously was based. This specific goal is accomplished by more generally extending the recent Déjà Q framework (Chase and Meiklejohn, Eurocrypt 2014) in two main directions. First, by teasing out common properties of existing reductions, we expand the q-type assumptions that can be covered by the framework; i.e., we demonstrate broader classes of assumptions that can be reduced to subgroup hiding. Second, while the original framework applied only to asymmetric composite-order bilinear groups, we provide a reduction to subgroup hiding that works in symmetric (as well as asymmetric) composite-order groups. As a bonus, our new reduction achieves a tightness of log(q) rather than q.