期刊：
International Journal of Performability Engineering,2019年15(6):1692-1701 ISSN：0973-1318
通讯作者：
Jiao, G.
作者机构：
College of Computer Science and Technology, Hengyang Normal University, Hengyang, 421002, China;Hunan Provincial Key Laboratory of Intelligent Information Processing and Application, Hengyang, 421002, China
通讯机构：
College of Computer Science and Technology, Hengyang Normal University, Hengyang, China
摘要：
In order to broaden the study of the most popular and general Takagi-Sugeno (TS) system, we propose a complex-valued neuro-fuzzy inference system which realises the zero-order TS system in the complex-valued network architecture and develop it. In the complex domain, boundedness and analyticity cannot be achieved together. The splitting strategy is given by computing the gradients of the real-valued error function with respect to the real and the imaginary parts of the weight parameters independently. Specifically, this system has four layers: in the Gaussian layer, the L-dimensional complex-valued input features are mapped to a Q-dimensional real-valued space, and in the output layer, complex-valued weights are employed to project it back to the complex domain. Hence, split-complex valued gradients of the real-valued error function are obtained, forming the split-complex valued neuro-fuzzy (split-CVNF) learning algorithm based on gradient descent. Another contribution of this paper is that the deterministic convergence of the split-CVNF algorithm is analysed. It is proved that the error function is monotone during the training iteration process, and the sum of gradient norms tends to zero. By adding a moderate condition, the weight sequence itself is also proved to be convergent.
通讯机构：
[Li, Lang] H;Hengyang Normal Univ, Hunan Prov Key Lab Intelligent Informat Proc & Ap, Hengyang 421002, Peoples R China.;Hengyang Normal Univ, Coll Comp Sci & Technol, Hengyang 421002, Peoples R China.
关键词：
Block cipher;Internet of Things;Involution;Lightweight cryptography;SPN structure
摘要：
In past few years, as security ciphers in the Internet of Things (IoT), the research of lightweight block cipher has attracted tremendous attention in cryptography. The SPN structure has been widely used in the design of block cipher. However, the encryption and decryption processes of ciphers based on the SPN structure are different. We design a new SPN structure, which is perfect for lightweight block cipher. The new SPN structure makes that the encryption process is the same as decryption. Moreover, input and output data directions are the same for encryption and decryption processes. Thus, the same process can absolutely be shared in decryption and encryption both for software and hardware implementation. Further, we propose a family of involutional lightweight block cipher, called Loong, based on the proposed SPN structure and components. Rigorous analysis indicates that Loong is of high security against cryptanalysis, especially the differential attack and linear attack. As shown by our experiments and comparisons, Loong is compact in hardware environment and is suitable for the IoT.
摘要：
This paper investigates the split complex gradient descent based neuro-fuzzy algorithm with self-adaptive momentum and L-2 regularizer for training TSK (Takagi-Sugeno-Kang) fuzzy inference models. The major threat for disposing complex data with fuzzy system is contradiction of boundedness and analyticity in the complex domain, as expressed by Liouville's theorem. The proposed algorithm operates a couple of real-valued functions and splits the complex variables into real part and imaginary part. Dynamical momentum is included in the learning mechanism to promote learning speed. L-2 regularizer is also added to control the magnitude of the weight parameters. Furthermore, a detailed convergence analysis of the proposed algorithm is fully studied. The monotonic decreasing property of the error function and convergence of the weight sequence are guaranteed. Plus a mild condition, strong convergence of the weight sequence is deduced. Finally, the simulation results are also demonstrated to verify the theoretical analysis results. (C) 2018 Elsevier B.V. All rights reserved.
