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Neural partially linear additive model 神经部分线性相加模型
IF 4.2 3区 计算机科学 Q1 Mathematics Pub Date : 2023-12-28 DOI: 10.1007/s11704-023-2662-3
Liangxuan Zhu, Han Li, Xuelin Zhang, Lingjuan Wu, Hong Chen

Interpretability has drawn increasing attention in machine learning. Most works focus on post-hoc explanations rather than building a self-explaining model. So, we propose a Neural Partially Linear Additive Model (NPLAM), which automatically distinguishes insignificant, linear, and nonlinear features in neural networks. On the one hand, neural network construction fits data better than spline function under the same parameter amount; on the other hand, learnable gate design and sparsity regular-term maintain the ability of feature selection and structure discovery. We theoretically establish the generalization error bounds of the proposed method with Rademacher complexity. Experiments based on both simulations and real-world datasets verify its good performance and interpretability.

可解释性越来越受到机器学习的关注。大多数研究都侧重于事后解释,而不是建立一个能自我解释的模型。因此,我们提出了神经部分线性相加模型(NPLAM),它能自动区分神经网络中的不显著特征、线性特征和非线性特征。一方面,在参数量相同的情况下,神经网络构造比样条函数更适合数据;另一方面,可学习的门设计和稀疏正则项保持了特征选择和结构发现的能力。我们从理论上建立了具有 Rademacher 复杂性的拟议方法的泛化误差边界。基于模拟和实际数据集的实验验证了该方法的良好性能和可解释性。
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引用次数: 0
Research on performance optimization of virtual data space across WAN 广域网虚拟数据空间性能优化研究
IF 4.2 3区 计算机科学 Q1 Mathematics Pub Date : 2023-12-28 DOI: 10.1007/s11704-023-3087-8
Jiantong Huo, Zhisheng Huo, Limin Xiao, Zhenxue He

For the high-performance computing in a WAN environment, the geographical locations of national supercomputing centers are scattered and the network topology is complex, so it is difficult to form a unified view of resources. To aggregate the widely dispersed storage resources of national supercomputing centers in China, we have previously proposed a global virtual data space named GVDS in the project of “High Performance Computing Virtual Data Space”, a part of the National Key Research and Development Program of China. The GVDS enables large-scale applications of the high-performance computing to run efficiently across WAN. However, the applications running on the GVDS are often data-intensive, requiring large amounts of data from multiple supercomputing centers across WANs. In this regard, the GVDS suffers from performance bottlenecks in data migration and access across WANs. To solve the above-mentioned problem, this paper proposes a performance optimization framework of GVDS including the multitask-oriented data migration method and the request access-aware IO proxy resource allocation strategy. In a WAN environment, the framework proposed in this paper can make an efficient migration decision based on the amount of migrated data and the number of multiple data sources, guaranteeing lower average migration latency when multiple data migration tasks are running in parallel. In addition, it can ensure that the thread resource of the IO proxy node is fairly allocated among different types of requests (the IO proxy is a module of GVDS), so as to improve the application’s performance across WANs. The experimental results show that the framework can effectively reduce the average data access delay of GVDS while improving the performance of the application greatly.

对于广域网环境下的高性能计算,国家超级计算中心地理位置分散,网络拓扑结构复杂,难以形成统一的资源视图。为了聚合国内分散的国家超级计算中心存储资源,我们曾在国家重点研发计划 "高性能计算虚拟数据空间 "项目中提出了名为GVDS的全球虚拟数据空间。GVDS 可使高性能计算的大规模应用在广域网上高效运行。然而,在 GVDS 上运行的应用往往是数据密集型的,需要跨广域网从多个超级计算中心获取大量数据。因此,GVDS 在跨广域网的数据迁移和访问方面存在性能瓶颈。为解决上述问题,本文提出了 GVDS 性能优化框架,包括面向多任务的数据迁移方法和请求访问感知的 IO 代理资源分配策略。在广域网环境中,本文提出的框架可以根据迁移数据量和多个数据源的数量做出高效的迁移决策,保证在多个数据迁移任务并行运行时降低平均迁移延迟。此外,它还能确保 IO 代理节点的线程资源在不同类型的请求(IO 代理是 GVDS 的一个模块)之间公平分配,从而提高应用程序在广域网中的性能。实验结果表明,该框架能有效降低 GVDS 的平均数据访问延迟,同时大大提高应用程序的性能。
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引用次数: 0
A new design of parity-preserving reversible multipliers based on multiple-control toffoli synthesis targeting emerging quantum circuits 基于多控制托福利合成的奇偶校验保全可逆乘法器新设计,以新兴量子电路为目标
IF 4.2 3区 计算机科学 Q1 Mathematics Pub Date : 2023-12-28 DOI: 10.1007/s11704-023-2492-3
Mojtaba Noorallahzadeh, Mohammad Mosleh, Kamalika Datta

With the recent demonstration of quantum computers, interests in the field of reversible logic synthesis and optimization have taken a different turn. As every quantum operation is inherently reversible, there is an immense motivation for exploring reversible circuit design and optimization. When it comes to faults in circuits, the parity-preserving feature donates to the detection of permanent and temporary faults. In the context of reversible circuits, the parity-preserving property ensures that the input and output parities are equal. In this paper we suggest six parity-preserving reversible blocks (Z, F, A, T, S, and L) with improved quantum cost. The reversible blocks are synthesized using an existing synthesis method that generates a netlist of multiple-control Toffoli (MCT) gates. Various optimization rules are applied at the reversible circuit level, followed by transformation into a netlist of elementary quantum gates from the NCV library. The designs of full-adder and unsigned and signed multipliers are proposed using the functional blocks that possess parity-preserving properties. The proposed designs are compared with state-of-the-art methods and found to be better in terms of cost of realization. Average savings of 25.04%, 20.89%, 21.17%, and 51.03%, and 18.59%, 13.82%, 13.82%, and 27.65% respectively, are observed for 4-bit unsigned and 5-bit signed multipliers in terms of quantum cost, garbage output, constant input, and gate count as compared to recent works.

随着最近量子计算机的展示,人们对可逆逻辑合成和优化领域的兴趣发生了不同的转变。由于每个量子操作本质上都是可逆的,因此探索可逆电路设计和优化有着巨大的动力。说到电路中的故障,奇偶校验保持特性有助于检测永久性和临时性故障。在可逆电路中,奇偶校验保持特性确保输入和输出奇偶校验相等。在本文中,我们提出了六种奇偶校验保全可逆块(Z、F、A、T、S 和 L),并改进了量子成本。这些可逆块是用现有的合成方法合成的,该方法可生成多控制托福利(MCT)门的网表。在可逆电路层面应用了各种优化规则,然后从 NCV 库中转换成基本量子门的网表。利用具有奇偶校验保护特性的功能块,提出了全梯形、无符号和有符号乘法器的设计方案。所提出的设计与最先进的方法进行了比较,发现在实现成本方面更胜一筹。在量子成本、垃圾输出、恒定输入和门数方面,4 位无符号乘法器和 5 位有符号乘法器的平均节省率分别为 25.04%、20.89%、21.17% 和 51.03%,与最新成果相比,平均节省率分别为 18.59%、13.82%、13.82% 和 27.65%。
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引用次数: 0
Aggregation-based dual heterogeneous task allocation in spatial crowdsourcing 空间众包中基于聚合的双异构任务分配
IF 4.2 3区 计算机科学 Q1 Mathematics Pub Date : 2023-12-28 DOI: 10.1007/s11704-023-3133-6
Xiaochuan Lin, Kaimin Wei, Zhetao Li, Jinpeng Chen, Tingrui Pei

Spatial crowdsourcing (SC) is a popular data collection paradigm for numerous applications. With the increment of tasks and workers in SC, heterogeneity becomes an unavoidable difficulty in task allocation. Existing researches only focus on the single-heterogeneous task allocation. However, a variety of heterogeneous objects coexist in real-world SC systems. This dramatically expands the space for searching the optimal task allocation solution, affecting the quality and efficiency of data collection. In this paper, an aggregation-based dual heterogeneous task allocation algorithm is put forth. It investigates the impact of dual heterogeneous on the task allocation problem and seeks to maximize the quality of task completion and minimize the average travel distance. This problem is first proved to be NP-hard. Then, a task aggregation method based on locations and requirements is built to reduce task failures. Meanwhile, a time-constrained shortest path planning is also developed to shorten the travel distance in a community. After that, two evolutionary task allocation schemes are presented. Finally, extensive experiments are conducted based on real-world datasets in various contexts. Compared with baseline algorithms, our proposed schemes enhance the quality of task completion by up to 25% and utilize 34% less average travel distance.

空间众包(SC)是一种流行的数据收集模式,应用范围广泛。随着 SC 中任务和工作人员的增加,异构性成为任务分配中不可避免的难题。现有研究只关注单一异构任务分配。然而,在现实世界的 SC 系统中,各种异构对象并存。这极大地扩展了搜索最佳任务分配方案的空间,影响了数据收集的质量和效率。本文提出了一种基于聚合的双异构任务分配算法。它研究了双异构对任务分配问题的影响,并寻求任务完成质量最大化和平均行程距离最小化。首先证明了该问题的 NP 难度。然后,建立了一种基于位置和要求的任务聚合方法,以减少任务失败。同时,还开发了一种时间限制的最短路径规划,以缩短社区内的旅行距离。随后,介绍了两种进化任务分配方案。最后,基于真实世界的数据集,在各种情况下进行了广泛的实验。与基线算法相比,我们提出的方案提高了任务完成质量达 25%,平均旅行距离缩短了 34%。
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引用次数: 0
Federated learning-outcome prediction with multi-layer privacy protection 具有多层隐私保护功能的联合学习成果预测
IF 4.2 3区 计算机科学 Q1 Mathematics Pub Date : 2023-12-28 DOI: 10.1007/s11704-023-2791-8

Abstract

Learning-outcome prediction (LOP) is a longstanding and critical problem in educational routes. Many studies have contributed to developing effective models while often suffering from data shortage and low generalization to various institutions due to the privacy-protection issue. To this end, this study proposes a distributed grade prediction model, dubbed FecMap, by exploiting the federated learning (FL) framework that preserves the private data of local clients and communicates with others through a global generalized model. FecMap considers local subspace learning (LSL), which explicitly learns the local features against the global features, and multi-layer privacy protection (MPP), which hierarchically protects the private features, including model-shareable features and not-allowably shared features, to achieve client-specific classifiers of high performance on LOP per institution. FecMap is then achieved in an iteration manner with all datasets distributed on clients by training a local neural network composed of a global part, a local part, and a classification head in clients and averaging the global parts from clients on the server. To evaluate the FecMap model, we collected three higher-educational datasets of student academic records from engineering majors. Experiment results manifest that FecMap benefits from the proposed LSL and MPP and achieves steady performance on the task of LOP, compared with the state-of-the-art models. This study makes a fresh attempt at the use of federated learning in the learning-analytical task, potentially paving the way to facilitating personalized education with privacy protection.

摘要 学习成绩预测(LOP)是教育路线中一个长期存在的关键问题。许多研究为开发有效的模型做出了贡献,但由于隐私保护问题,这些模型往往受到数据短缺和对不同机构普适性低的困扰。为此,本研究利用联盟学习(FL)框架,提出了一种分布式成绩预测模型,命名为 FecMap,该框架保留了本地客户端的隐私数据,并通过全局通用模型与其他客户端进行通信。FecMap 考虑了局部子空间学习(LSL)和多层隐私保护(MPP),前者明确地针对全局特征学习局部特征,后者分层保护隐私特征,包括可共享模型特征和不可共享特征,从而实现特定客户分类器在每个机构 LOP 上的高性能。然后,通过在客户端训练一个由全局部分、局部部分和分类头组成的局部神经网络,并在服务器上平均来自客户端的全局部分,以迭代的方式实现 FecMap,所有数据集都分布在客户端上。为了评估 FecMap 模型,我们收集了三个高等教育数据集,其中包括工科专业学生的学业记录。实验结果表明,与最先进的模型相比,FecMap 模型得益于所提出的 LSL 和 MPP,并在 LOP 任务中取得了稳定的性能。这项研究为联盟学习在学习分析任务中的应用做出了新的尝试,有可能为促进具有隐私保护的个性化教育铺平道路。
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引用次数: 0
IP2vec: an IP node representation model for IP geolocation IP2vec:用于 IP 地理定位的 IP 节点表示模型
IF 4.2 3区 计算机科学 Q1 Mathematics Pub Date : 2023-12-28 DOI: 10.1007/s11704-023-2616-9
Fan Zhang, Meijuan Yin, Fenlin Liu, Xiangyang Luo, Shuodi Zu

IP geolocation is essential for the territorial analysis of sensitive network entities, location-based services (LBS) and network fraud detection. It has important theoretical significance and application value. Measurement-based IP geolocation is a hot research topic. However, the existing IP geolocation algorithms cannot effectively utilize the distance characteristics of the delay, and the nodes’ connection relation, resulting in high geolocation error. It is challenging to obtain the mapping between delay, nodes’ connection relation, and geographical location. Based on the idea of network representation learning, we propose a representation learning model for IP nodes (IP2vec for short) and apply it to street-level IP geolocation. IP2vec model vectorizes nodes according to the connection relation and delay between nodes so that the IP vectors can reflect the distance and topological proximity between IP nodes. The steps of the street-level IP geolocation algorithm based on IP2vec model are as follows: Firstly, we measure landmarks and target IP to obtain delay and path information to construct the network topology. Secondly, we use the IP2vec model to obtain the IP vectors from the network topology. Thirdly, we train a neural network to fit the mapping relation between vectors and locations of landmarks. Finally, the vector of target IP is fed into the neural network to obtain the geographical location of target IP. The algorithm can accurately infer geographical locations of target IPs based on delay and topological proximity embedded in the IP vectors. The cross-validation experimental results on 10023 target IPs in New York, Beijing, Hong Kong, and Zhengzhou demonstrate that the proposed algorithm can achieve street-level geolocation. Compared with the existing algorithms such as Hop-Hot, IP-geolocater and SLG, the mean geolocation error of the proposed algorithm is reduced by 33%, 39%, and 51%, respectively.

IP 地理定位对于敏感网络实体的地域分析、基于位置的服务(LBS)和网络欺诈检测至关重要。它具有重要的理论意义和应用价值。基于测量的 IP 地理定位是一个热门研究课题。然而,现有的 IP 地理定位算法不能有效利用延迟的距离特性和节点的连接关系,导致地理定位误差较大。如何获取延迟、节点连接关系和地理位置之间的映射关系是一项挑战。基于网络表示学习的思想,我们提出了一种 IP 节点表示学习模型(简称 IP2vec),并将其应用于街道级 IP 地理定位。IP2vec 模型根据节点之间的连接关系和延迟对节点进行矢量化,从而使 IP 矢量能够反映 IP 节点之间的距离和拓扑接近程度。基于 IP2vec 模型的街道级 IP 地理定位算法步骤如下:首先,测量地标和目标 IP,获取延迟和路径信息,构建网络拓扑。其次,利用 IP2vec 模型从网络拓扑结构中获取 IP 向量。第三,我们训练神经网络来拟合向量与地标位置之间的映射关系。最后,将目标 IP 的向量输入神经网络,以获得目标 IP 的地理位置。该算法可以根据 IP 向量中蕴含的延迟和拓扑邻近性准确推断出目标 IP 的地理位置。对纽约、北京、香港和郑州的 10023 个目标 IP 的交叉验证实验结果表明,所提出的算法可以实现街道级地理定位。与 Hop-Hot、IP-geolocater 和 SLG 等现有算法相比,所提算法的平均地理定位误差分别减少了 33%、39% 和 51%。
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引用次数: 0
A program logic for obstruction-freedom 不受阻碍的程序逻辑
IF 4.2 3区 计算机科学 Q1 Mathematics Pub Date : 2023-12-28 DOI: 10.1007/s11704-023-2774-9
Zhao-Hui Li, Xin-Yu Feng

Though obstruction-free progress property is weaker than other non-blocking properties including lock-freedom and wait-freedom, it has advantages that have led to the use of obstruction-free implementations for software transactional memory (STM) and in anonymous and fault-tolerant distributed computing. However, existing work can only verify obstruction-freedom of specific data structures (e.g., STM and list-based algorithms).

In this paper, to fill this gap, we propose a program logic that can formally verify obstruction-freedom of practical implementations, as well as verify linearizability, a safety property, at the same time. We also propose informal principles to extend a logic for verifying linearizability to verifying obstruction-freedom. With this approach, the existing proof for linearizability can be reused directly to construct the proof for both linearizability and obstruction-freedom. Finally, we have successfully applied our logic to verifying a practical obstruction-free double-ended queue implementation in the first classic paper that has proposed the definition of obstruction-freedom.

虽然无阻塞进度特性弱于其他非阻塞特性(包括锁自由和等待自由),但它的优势已被用于软件事务内存(STM)以及匿名和容错分布式计算中的无阻塞实现。然而,现有的工作只能验证特定数据结构(如 STM 和基于列表的算法)的无阻塞性。在本文中,为了填补这一空白,我们提出了一种程序逻辑,它可以正式验证实际实现的无阻塞性,并同时验证线性化(一种安全属性)。我们还提出了一些非正式原则,将验证线性化的逻辑扩展到验证无阻塞性。通过这种方法,现有的线性化证明可直接用于构建线性化和无障碍证明。最后,我们成功地将我们的逻辑应用于验证一个实用的无障碍双端队列实现,这是第一篇提出无障碍定义的经典论文。
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引用次数: 0
Model gradient: unified model and policy learning in model-based reinforcement learning 模型梯度:基于模型的强化学习中的统一模型和策略学习
IF 4.2 3区 计算机科学 Q1 Mathematics Pub Date : 2023-12-27 DOI: 10.1007/s11704-023-3150-5

Abstract

Model-based reinforcement learning is a promising direction to improve the sample efficiency of reinforcement learning with learning a model of the environment. Previous model learning methods aim at fitting the transition data, and commonly employ a supervised learning approach to minimize the distance between the predicted state and the real state. The supervised model learning methods, however, diverge from the ultimate goal of model learning, i.e., optimizing the learned-in-the-model policy. In this work, we investigate how model learning and policy learning can share the same objective of maximizing the expected return in the real environment. We find model learning towards this objective can result in a target of enhancing the similarity between the gradient on generated data and the gradient on the real data. We thus derive the gradient of the model from this target and propose the Model Gradient algorithm (MG) to integrate this novel model learning approach with policy-gradient-based policy optimization. We conduct experiments on multiple locomotion control tasks and find that MG can not only achieve high sample efficiency but also lead to better convergence performance compared to traditional model-based reinforcement learning approaches.

摘要 基于模型的强化学习是通过学习环境模型来提高强化学习样本效率的一个有前途的方向。以往的模型学习方法以拟合过渡数据为目标,通常采用监督学习方法来最小化预测状态与真实状态之间的距离。然而,有监督的模型学习方法偏离了模型学习的最终目标,即优化模型中的学习策略。在这项工作中,我们研究了模型学习和策略学习如何在真实环境中实现预期收益最大化这一相同目标。我们发现,为实现这一目标而进行的模型学习可以提高生成数据上的梯度与真实数据上的梯度之间的相似度。因此,我们从这一目标中推导出模型梯度,并提出了模型梯度算法(MG),将这种新颖的模型学习方法与基于策略梯度的策略优化相结合。我们在多个运动控制任务上进行了实验,发现与传统的基于模型的强化学习方法相比,MG 不仅能实现较高的采样效率,还能带来更好的收敛性能。
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引用次数: 0
ARCHER: a ReRAM-based accelerator for compressed recommendation systems ARCHER:基于 ReRAM 的压缩推荐系统加速器
IF 4.2 3区 计算机科学 Q1 Mathematics Pub Date : 2023-12-23 DOI: 10.1007/s11704-023-3397-x
Xinyang Shen, Xiaofei Liao, Long Zheng, Yu Huang, Dan Chen, Hai Jin

Modern recommendation systems are widely used in modern data centers. The random and sparse embedding lookup operations are the main performance bottleneck for processing recommendation systems on traditional platforms as they induce abundant data movements between computing units and memory. ReRAM-based processing-in-memory (PIM) can resolve this problem by processing embedding vectors where they are stored. However, the embedding table can easily exceed the capacity limit of a monolithic ReRAM-based PIM chip, which induces off-chip accesses that may offset the PIM profits. Therefore, we deploy the decomposed model on-chip and leverage the high computing efficiency of ReRAM to compensate for the decompression performance loss. In this paper, we propose ARCHER, a ReRAM-based PIM architecture that implements fully on-chip recommendations under resource constraints. First, we make a full analysis of the computation pattern and access pattern on the decomposed table. Based on the computation pattern, we unify the operations of each layer of the decomposed model in multiply-and-accumulate operations. Based on the access observation, we propose a hierarchical mapping schema and a specialized hardware design to maximize resource utilization. Under the unified computation and mapping strategy, we can coordinate the inter-processing elements pipeline. The evaluation shows that ARCHER outperforms the state-of-the-art GPU-based DLRM system, the state-of-the-art near-memory processing recommendation system RecNMP, and the ReRAM-based recommendation accelerator REREC by 15.79×, 2.21×, and 1.21× in terms of performance and 56.06×, 6.45×, and 1.71× in terms of energy savings, respectively.

现代推荐系统广泛应用于现代数据中心。在传统平台上,随机和稀疏的嵌入查找操作是处理推荐系统的主要性能瓶颈,因为这些操作会导致大量数据在计算单元和内存之间移动。基于 ReRAM 的内存处理(PIM)可以在嵌入向量存储的地方对其进行处理,从而解决这一问题。但是,嵌入表很容易超出基于 ReRAM 的单片式 PIM 芯片的容量限制,从而导致片外访问,这可能会抵消 PIM 的利润。因此,我们在芯片上部署分解模型,并利用 ReRAM 的高计算效率来弥补解压缩性能的损失。在本文中,我们提出了基于 ReRAM 的 PIM 架构 ARCHER,该架构可在资源限制条件下实现完全片上推荐。首先,我们对分解表的计算模式和访问模式进行了全面分析。根据计算模式,我们将分解模型各层的操作统一为乘法累加操作。根据访问观察结果,我们提出了分层映射模式和专用硬件设计,以最大限度地提高资源利用率。在统一的计算和映射策略下,我们可以协调处理元素间的流水线。评估结果表明,ARCHER 在性能方面分别优于最先进的基于 GPU 的 DLRM 系统、最先进的近内存处理推荐系统 RecNMP 和基于 ReRAM 的推荐加速器 REREC 15.79 倍、2.21 倍和 1.21 倍,在节能方面分别优于最先进的基于 GPU 的 DLRM 系统、最先进的近内存处理推荐系统 RecNMP 和基于 ReRAM 的推荐加速器 REREC 56.06 倍、6.45 倍和 1.71 倍。
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引用次数: 0
Provable secure authentication key agreement for wireless body area networks 无线体域网络的可证明安全认证密钥协议
IF 4.2 3区 计算机科学 Q1 Mathematics Pub Date : 2023-12-23 DOI: 10.1007/s11704-023-2548-4
Yuqian Ma, Wenbo Shi, Xinghua Li, Qingfeng Cheng

Wireless body area networks (WBANs) guarantee timely data processing and secure information preservation within the range of the wireless access network, which is in urgent need of a new type of security technology. However, with the speedy development of hardware, the existing security schemes can no longer meet the new requirements of anonymity and lightweight. New solutions that do not require complex calculations, such as certificateless cryptography, attract great attention from researchers. To resolve these difficulties, Wang et al. designed a new authentication architecture for the WBANs environment, which was claimed to be secure and efficient. However, in this paper, we will show that this scheme is prone to ephemeral key leakage attacks. Further, based on this authentication scheme, an anonymous certificateless scheme is proposed for lightweight devices. Meanwhile, user anonymity is fully protected. The proposed scheme is proved to be secure under a specific security model. In addition, we assess the security attributes our scheme meets through BAN logic and Scyther tool. The comparisons of time consumption and communication cost are given at the end of the paper, to demonstrate that our scheme performs prior to several previous schemes.

无线体域网(WBAN)保证了无线接入网范围内数据的及时处理和信息的安全保存,迫切需要一种新型的安全技术。然而,随着硬件的飞速发展,现有的安全方案已无法满足匿名和轻量级的新要求。无需复杂计算的新方案,如无证书加密技术,引起了研究人员的极大关注。为了解决这些难题,Wang 等人为无线局域网环境设计了一种新的身份验证架构,并声称这种架构既安全又高效。然而,在本文中,我们将证明这种方案容易受到短暂密钥泄漏攻击。此外,在此认证方案的基础上,我们还为轻量级设备提出了一种匿名无证书方案。同时,用户的匿名性得到了充分保护。在特定的安全模型下,所提出的方案被证明是安全的。此外,我们还通过 BAN 逻辑和 Scyther 工具评估了我们的方案所满足的安全属性。本文末尾还给出了时间消耗和通信成本的比较,以证明我们的方案优于之前的几种方案。
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引用次数: 0
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