**Bootstrapping Consensus Without Trusted Setup: Fully Asynchronous Distributed Key Generation**

*Eleftherios Kokoris-Kogias and Alexander Spiegelman and Dahlia Malkhi and Ittai Abraham*

**Abstract: **In this paper, we present the first fully asynchronous distributed key generation (ADKG) algorithm as well as the first distributed key generation algorithm that can create keys with a dual $(f,2f+1)-$threshold that are necessary for scalable consensus (which so far needs a trusted dealer assumption).

In order to create a DKG with a dual $(f,2f+1)-$ threshold we first answer in the affirmative the open question posed by Cachin et al. how to create an AVSS protocol with recovery thresholds $ f+1 < k \le 2f+1$, which is of independent interest. Our High-threshold-AVSS (\textit{HAVSS}) uses an asymmetric bi-variate polynomial, where the secret shared is hidden from any set of $k$ nodes but an honest node that did not participate in the sharing phase can still recover his share with only $n-2f$ shares, hence be able to contribute in the secret reconstruction.

Another building block for ADKG is a novel \textit{Eventually Perfect} Common Coin (EPCC) abstraction and protocol that enables the participants to create a common coin that might fail to agree at most $f+1$ times (even if invoked a polynomial number of times). Using \textit{EPCC} we implement an Eventually Efficient Asynchronous Binary Agreement (EEABA) in which each instance takes $O(n^2)$ bits and $O(1)$ rounds in expectation, except for at most $f+1$ instances which may take $O(n^4)$ bits and $O(n)$ rounds in total.

Using EEABA we construct the first fully Asynchronous Distributed Key Generation (ADKG) which has the same overhead and expected runtime as the best partially-synchronous DKG ($O(n^4)$ words, $O(n)$ rounds). As a corollary of our ADKG we can also create the first Validated Asynchronous Byzantine Agreement (VABA) in the authenticated setting that does not need a trusted dealer to setup threshold signatures of degree $n-f$. Our VABA has an overhead of expected $O(n^2)$ words and $O(1)$ time per instance after an initial $O(n^4)$ words and $O(n)$ time bootstrap via ADKG.

**Category / Keywords: **public-key cryptography / threshold cryptography, distributed cryptography, asynchronous consensus, secret sharing

**Date: **received 9 Sep 2019, last revised 10 Sep 2019

**Contact author: **eleftherios kokoriskogias at epfl ch

**Available format(s): **PDF | BibTeX Citation

**Version: **20190910:131021 (All versions of this report)

**Short URL: **ia.cr/2019/1015

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