Welcome to the resource topic for 2024/280
Title:
HARTS: HighThreshold, Adaptively Secure, and Robust Threshold Schnorr Signatures
Authors: Renas Bacho, Julian Loss, Gilad Stern, Benedikt Wagner
Abstract:Threshold variants of the Schnorr signature scheme have recently been at the center of attention due to their applications to Bitcoin, Ethereum, and other cryptocurrencies. However, existing constructions for threshold Schnorr signatures among a set of n parties with corruption threshold t_c suffer from at least one of the following drawbacks: (i) security only against static (i.e., nonadaptive) adversaries, (ii) cubic or higher communication cost to generate a single signature, (iii) strong synchrony assumptions on the network, or (iv) t_c+1 are sufficient to generate a signature, i.e., the corruption threshold of the scheme equals its reconstruction threshold. Especially (iv) turns out to be a severe limitation for many asynchronous realworld applications where t_c < n/3 is necessary to maintain liveness, but a higher signing threshold of nt_c is needed. A recent scheme, ROAST, proposed by Ruffing et al. (ACM CCS `22) addresses (iii) and (iv), but still falls short of obtaining subcubic complexity and adaptive security.
In this work, we present HARTS, the first threshold Schnorr signature scheme to incorporate all these desiderata. More concretely:

HARTS is adaptively secure and remains fully secure and operational even under asynchronous network conditions in the presence of up to t_c < n/3 malicious parties. This is optimal.

HARTS outputs a Schnorr signature of size \lambda with a nearoptimal amortized communication cost of O(\lambda n^2 \log{n}) bits and O(1) rounds per signature.

HARTS is a highthreshold scheme: no fewer than t_r+1 signature shares can be combined to yield a full signature, where t_r\geq 2n/3 > 2t_c. This is optimal.
We prove our result in a modular fashion in the algebraic group model. At the core of our construction, we design a new simple, and adaptively secure highthreshold AVSS scheme which may be of independent interest.
ePrint: https://eprint.iacr.org/2024/280
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