Defense Against Chip Cloning Attacks Based on Fractional Hopfield Neural Networks.

This paper presents a state-of-the-art application of fractional hopfield neural networks (FHNNs) to defend against chip cloning attacks, and provides insight into the reason that the proposed method is superior to physically unclonable functions (PUFs). In the past decade, PUFs have been evolving as one of the best types of hardware security. However, the development of the PUFs has been somewhat limited by its implementation cost, its temperature variation effect, its electromagnetic interference effect, the amount of entropy in it, etc. Therefore, it is imperative to discover, through promising mathematical methods and physical modules, some novel mechanisms to overcome the aforementioned weaknesses of the PUFs. Motivated by this need, in this paper, we propose applying the FHNNs to defend against chip cloning attacks. At first, we implement the arbitrary-order fractor of a FHNN. Secondly, we describe the implementation cost of the FHNNs. Thirdly, we propose the achievement of the constant-order performance of a FHNN when ambient temperature varies. Fourthly, we analyze the electrical performance stability of the FHNNs under electromagnetic disturbance conditions. Fifthly, we study the amount of entropy of the FHNNs. Lastly, we perform experiments to analyze the pass-band width of the fractor of an arbitrary-order FHNN and the defense against chip cloning attacks capability of the FHNNs. In particular, the capabilities of defense against chip cloning attacks, anti-electromagnetic interference, and anti-temperature variation of a FHNN are illustrated experimentally in detail. Some significant advantages of the FHNNs are that their implementation cost is considerably lower than that of the PUFs, their electrical performance is much more stable than that of the PUFs under different temperature conditions, their electrical performance stability of the FHNNs under electromagnetic disturbance conditions is much more robust than that of the PUFs, and their amount of entropy is significantly higher than that of the PUFs with the same rank circuit scale.

Fractional Hopfield Neural Networks: Fractional Dynamic Associative Recurrent Neural Networks.

This paper mainly discusses a novel conceptual framework: fractional Hopfield neural networks (FHNN). As is commonly known, fractional calculus has been incorporated into artificial neural networks, mainly because of its long-term memory and nonlocality. Some researchers have made interesting attempts at fractional neural networks and gained competitive advantages over integer-order neural networks. Therefore, it is naturally makes one ponder how to generalize the first-order Hopfield neural networks to the fractional-order ones, and how to implement FHNN by means of fractional calculus. We propose to introduce a novel mathematical method: fractional calculus to implement FHNN. First, we implement fractor in the form of an analog circuit. Second, we implement FHNN by utilizing fractor and the fractional steepest descent approach, construct its Lyapunov function, and further analyze its attractors. Third, we perform experiments to analyze the stability and convergence of FHNN, and further discuss its applications to the defense against chip cloning attacks for anticounterfeiting. The main contribution of our work is to propose FHNN in the form of an analog circuit by utilizing a fractor and the fractional steepest descent approach, construct its Lyapunov function, prove its Lyapunov stability, analyze its attractors, and apply FHNN to the defense against chip cloning attacks for anticounterfeiting. A significant advantage of FHNN is that its attractors essentially relate to the neuron's fractional order. FHNN possesses the fractional-order-stability and fractional-order-sensitivity characteristics.

Fractional extreme value adaptive training method: fractional steepest descent approach.

The application of fractional calculus to signal processing and adaptive learning is an emerging area of research. A novel fractional adaptive learning approach that utilizes fractional calculus is presented in this paper. In particular, a fractional steepest descent approach is proposed. A fractional quadratic energy norm is studied, and the stability and convergence of our proposed method are analyzed in detail. The fractional steepest descent approach is implemented numerically and its stability is analyzed experimentally.

Efficient CT metal artifact reduction based on fractional-order curvature diffusion.

We propose a novel metal artifact reduction method based on a fractional-order curvature driven diffusion model for X-ray computed tomography. Our method treats projection data with metal regions as a damaged image and uses the fractional-order curvature-driven diffusion model to recover the lost information caused by the metal region. The numerical scheme for our method is also analyzed. We use the peak signal-to-noise ratio as a reference measure. The simulation results demonstrate that our method achieves better performance than existing projection interpolation methods, including linear interpolation and total variation.

A new CT metal artifacts reduction algorithm based on fractional-order sinogram inpainting.

In this paper, we propose a new metal artifacts reduction algorithm based on fractional-order total-variation sinogram inpainting model for X-ray computed tomography (CT). The numerical algorithm for our fractional-order framework is also analyzed. Simulations show that, both quantitatively and qualitatively, our method is superior to conditional interpolation methods and the classic integral-order total variation model.

Fractional differential mask: a fractional differential-based approach for multiscale texture enhancement.

In this paper, we intend to implement a class of fractional differential masks with high-precision. Thanks to two commonly used definitions of fractional differential for what are known as GrUmwald-Letnikov and Riemann-Liouville, we propose six fractional differential masks and present the structures and parameters of each mask respectively on the direction of negative x-coordinate, positive x-coordinate, negative y-coordinate, positive y-coordinate, left downward diagonal, left upward diagonal, right downward diagonal, and right upward diagonal. Moreover, by theoretical and experimental analyzing, we demonstrate the second is the best performance fractional differential mask of the proposed six ones. Finally, we discuss further the capability of multiscale fractional differential masks for texture enhancement. Experiments show that, for rich-grained digital image, the capability of nonlinearly enhancing complex texture details in smooth area by fractional differential-based approach appears obvious better than by traditional intergral-based algorithms.