Zhenliang Lu

Yang Li, Zhenliang Lu, San Ling et al.

Maximum distance separable (MDS) codes and near MDS (NMDS) codes are of particular interest in coding theory due to their optimal error-correcting capabilities and wide applications in communication, cryptography, and storage systems. A family of linear codes is called a family of non-GRS MDS-NMDS codes if for each $[n,k]_q$ code in the family, it is either an $[n,k,n-k+1]_q$ MDS code that is not monomially equivalent to any GRS code or extended GRS code, or an $[n,k,n-k]_q$ NMDS code. This paper develops a unified framework for constructing new families of non-GRS MDS-NMDS codes via deep holes. We show that, starting from a family of $[n,k]_q$ non-GRS MDS-NMDS codes with covering radius $n-k$, one can systematically obtain more $[n+1,k+1]_q$ non-GRS MDS-NMDS codes. The proposed framework is further reformulated in terms of the second kind of extended codes. This reformulation recovers a main result of Wu, Ding, and Chen (IEEE Trans. Inf. Theory, 71(1): 263-272, 2025), provides a provable reduction in the computational complexity compared with the approach of Ma, Kai, and Zhu (Finite Fields Appl., 114, 102844, 2026), and reveals additional structural properties of the resulting codes. As an application, we determine the covering radius and characterize two classes of deep holes of extended subcodes of GRS codes. By applying our framework, we obtain three new families of non-GRS MDS-NMDS codes and investigate the monomial equivalence between the resulting codes and Roth-Lempel codes.

Yingzi Gao, Yuan Lu, Zhenliang Lu et al.

Efficient asynchronous Byzantine agreement (BA) protocols were mostly studied with private setups, e.g., pre-setup threshold cryptosystem. Challenges remain to reduce the large communication in the absence of such setups. Recently, Abraham et al. (PODC'21) presented the first asynchronous validated BA (VBA) with expected $O(n^3)$ messages and $O(1)$ rounds, relying on only public key infrastructure (PKI) setup, but the design still costs $O(λn^3 \log n)$ bits. Here $n$ is the number of parties, and $λ$ is a cryptographic security parameter. In this paper, we reduce the communication of private-setup free asynchronous BA to expected $O(λn^3)$ bits. At the core of our design, we give a systematic treatment of common randomness protocols in the asynchronous network, and proceed as: - We give an efficient reasonably fair common coin protocol in the asynchronous setting with only PKI setup. It costs only $O(λn^3)$ bits and $O(1)$ rounds, and ensures that with at least 1/3 probability, all honest parties can output a common bit that is as if randomly flipped. This directly renders more efficient private-setup free asynchronous binary agreement (ABA) with expected $O(λn^3)$ bits and $O(1)$ rounds. - Then, we lift our common coin to attain perfect agreement by using a single ABA. This gives us a reasonably fair random leader election protocol with expected $O(λn^3)$ communication and expected constant rounds. It is pluggable in all existing VBA protocols (e.g., Cachin et al., CRYPTO'01; Abraham et al., PODC'19; Lu et al., PODC'20) to remove the needed private setup or distributed key generation (DKG). As such, the communication of private-setup free VBA is reduced to expected $O(λn^3)$ bits while preserving fast termination in expected $O(1)$ rounds.

Yuan Lu, Zhenliang Lu, Qiang Tang

An urgent demand of deploying BFT consensus over the Internet is raised for implementing blockchain services. The deterministic (partial) synchronous protocols can be simple and fast in good network conditions, but are subject to denial-of-service when synchrony assumption fails. Asynchronous protocols, on the contrary, are robust against the adversarial network, but are substantially more complicated and slower for the inherent use of randomness. Facing the issues, optimistic asynchronous atomic broadcast ( Kursawe-Shoup, 2002; Ramasamy-Cachin, 2005) was proposed to improve the normal-case performance of the slow asynchronous consensus. They run a deterministic fastlane if the network condition remains good, and can fall back to a fully asynchronous protocol via a pace-synchronization mechanism if the fastlane fails. Unfortunately, existing pace-synchronization directly uses a heavy tool of asynchronous multi-valued validated Byzantine agreement (MVBA). We present Bolt-Dumbo Transformer (BDT), a generic framework for practical optimistic asynchronous atomic broadcast. At the core of BDT, we set forth a new fastlane abstraction that is simple and fast, while preparing honest parties to gracefully face potential fastlane failures caused by malicious leader or bad network. This enables a highly efficient pace-synchronization to handle fallback. The resulting design reduces a cumbersome MVBA to a variant of the conceptually simplest binary agreement only. Besides detailed security analyses, we also give concrete instantiations of our framework and implement them. Extensive experiments demonstrate that BDT can enjoy both the low latency of deterministic protocols (e.g. 2-chain version of HotStuff) and the robustness of state-of-the-art asynchronous protocols in practice.