Weijun Fang

Yuan Gao, Haoming Shi, Weijun Fang

Constructing optimal $(r,δ)$-LRCs that attain the Singleton-type bound is an active and important research direction, particularly due to their practical applications in distributed storage systems. In this paper, we focus on the construction of optimal $(r,δ)$-LRCs with flexible minimum distances, especially for the case $δ\geq 3$. We first extend a general framework -- originally proposed by Li \textit{et al.} (IEEE Trans. Inf. Theory, vol. 65, no. 1, 2019) and Ma and Xing (J. Comb. Theory Ser. A., vol. 193, 2023) -- for constructing optimal $r$-LRCs via automorphism groups of elliptic function fields to the case of $(r,δ)$-LRCs. This newly extended general framework relies on certain conditions concerning the group law of elliptic curves. By carefully selecting elliptic function fields suitable for this framework, we arrive at several families of explicit $q$-ary optimal $(r,3)$-LRCs and $(2,δ)$-LRCs with lengths slightly less than $q + 2\sqrt{q}$. Next, by employing automorphism groups of hyperelliptic function fields of genus $2$, we develop a framework for constructing optimal $(r,3)$-LRCs and obtain a family of explicit $q$-ary optimal $(4,3)$-LRCs with code lengths slightly below $q+4\sqrt{q}$. We then consider the construction of optimal $(r,δ)$-LRCs via hyperelliptic function fields of arbitrary genus $g \geq 2$, yielding a class of explicit $q$-ary optimal $(g+1-g',g+1+g')$-LRCs for $0 \leq g' \leq g-1$ with lengths up to $q + 2g\sqrt{q}$. Finally, applying certain superelliptic curves derived from modified Norm-Trace curves, we construct two families of explicit optimal $(r,δ)$-LRCs with even longer code lengths and more flexible parameters. Notably, many of the newly constructed optimal $(r,δ)$-LRCs attain the largest known lengths among existing constructions with flexible minimum distances.

Jing Qiu, Weijun Fang, Shu-Tao Xia et al.

Maximum distance separable (MDS) codes are widely used in distributed storage, but naively repairing a single failure in an $(n,k)$ MDS code requires downloading the full contents of $k$ surviving nodes. Minimum storage regenerating (MSR) codes, introduced by Dimakis et al., minimize repair bandwidth while preserving the MDS property by contacting $d>k$ helper nodes and downloading only a fraction of each helper. For scalar MDS codes, Guruswami and Wootters established a linear repair framework, and Tamo, Ye, and Barg subsequently gave the first explicit Reed-Solomon (RS) codes achieving the MSR point. Their construction yields RS-MSR codes with subpacketization $\ell=s\prod_{i=1}^n p_i$, where $s=d+1-k$ and the distinct primes $p_i$ satisfy $p_i\equiv 1\pmod{s}$. In this paper, we show that this congruence condition is not intrinsic to the RS repair problem. We develop a basis-transformation approach to the construction of repair-enabling subspaces. The approach consists of three deterministic operations -- Euclidean Square Partition, Transposition, and Column Aggregation -- which construct the required repair-enabling subspaces directly from the standard monomial basis of the repair field. Consequently, we obtain RS-MSR codes with subpacketization $\ell=s\prod_{i=1}^n p_i$ for arbitrary distinct primes $p_i>s$. For fixed $s$, this improves the subpacketization of the Tamo--Ye--Barg construction by a factor asymptotic to $φ(s)^{n+\mathrm{o}(n)}$, where $φ(\cdot)$ denotes Euler's totient function.

Xiang Wang, Weijun Fang, Han Li et al.

Levenshtein first introduced the sequence reconstruction problem in $2001$. In the realm of combinatorics, the sequence reconstruction problem is equivalent to determining the value of $N(n,d,t)$, which represents the maximum size of the intersection of two metric balls of radius $t$, given that the distance between their centers is at least $d$ and the sequence length is $n$. In this paper, We present a lower bound on $N(n,3,t)$ for $n\geq \max\{13,t+8\}$ and $t \geq 4$. For $t=4$, we prove that this lower bound is tight. This settles an open question posed by Pham, Goyal, and Kiah, confirming that $N(n,3,4)=20n-166$ for all $n \geq 13$.

Xue Yang, Depan Peng, Yan Feng et al.

Bidirectional privacy-preservation federated learning is crucial as both local gradients and the global model may leak privacy. However, only a few works attempt to achieve it, and they often face challenges such as excessive communication and computational overheads, or significant degradation of model accuracy, which hinders their practical applications. In this paper, we design an efficient and high-accuracy bidirectional privacy-preserving scheme for federated learning to complete secure model training and secure aggregation. To efficiently achieve bidirectional privacy, we design an efficient and accuracy-lossless model perturbation method on the server side (called $\mathbf{MP\_Server}$) that can be combined with local differential privacy (LDP) to prevent clients from accessing the model, while ensuring that the local gradients obtained on the server side satisfy LDP. Furthermore, to ensure model accuracy, we customize a distributed differential privacy mechanism on the client side (called $\mathbf{DDP\_Client}$). When combined with $\mathbf{MP\_Server}$, it ensures LDP of the local gradients, while ensuring that the aggregated result matches the accuracy of central differential privacy (CDP). Extensive experiments demonstrate that our scheme significantly outperforms state-of-the-art bidirectional privacy-preservation baselines (SOTAs) in terms of computational cost, model accuracy, and defense ability against privacy attacks. Particularly, given target accuracy, the training time of SOTAs is approximately $200$ times, or even over $1000$ times, longer than that of our scheme. When the privacy budget is set relatively small, our scheme incurs less than $6\%$ accuracy loss compared to the privacy-ignoring method, while SOTAs suffer up to $20\%$ accuracy loss. Experimental results also show that the defense capability of our scheme outperforms than SOTAs.

Xue Yang, Yan Feng, Weijun Fang et al.

Although federated learning improves privacy of training data by exchanging local gradients or parameters rather than raw data, the adversary still can leverage local gradients and parameters to obtain local training data by launching reconstruction and membership inference attacks. To defend such privacy attacks, many noises perturbation methods (like differential privacy or CountSketch matrix) have been widely designed. However, the strong defence ability and high learning accuracy of these schemes cannot be ensured at the same time, which will impede the wide application of FL in practice (especially for medical or financial institutions that require both high accuracy and strong privacy guarantee). To overcome this issue, in this paper, we propose \emph{an efficient model perturbation method for federated learning} to defend reconstruction and membership inference attacks launched by curious clients. On the one hand, similar to the differential privacy, our method also selects random numbers as perturbed noises added to the global model parameters, and thus it is very efficient and easy to be integrated in practice. Meanwhile, the random selected noises are positive real numbers and the corresponding value can be arbitrarily large, and thus the strong defence ability can be ensured. On the other hand, unlike differential privacy or other perturbation methods that cannot eliminate the added noises, our method allows the server to recover the true gradients by eliminating the added noises. Therefore, our method does not hinder learning accuracy at all.