This study presents a description of an efficient hardware implementation of an elliptic curve cryptography processor (ECP) for modern security applications. A high‐performance elliptic curve scalar multiplication (ECSM), which is the key operation of an ECP, is developed both in affine and Jacobian coordinates over a prime field of size p using the National Institute of Standards and Technology standard. A novel combined point doubling and point addition architecture is proposed using efficient modular arithmetic to achieve high speed and low hardware utilisation of the ECP in Jacobian coordinates. This new architecture has been synthesised both in application‐specific integrated circuit (ASIC) and field‐programmable gate array (FPGA). A 65 nm CMOS ASIC implementation of the proposed ECP in Jacobian coordinates takes between 0.56 and 0.73 ms for 224‐bit and 256‐bit elliptic curve cryptography, respectively. The ECSM is also implemented in an FPGA and provides a better delay performance than previous designs. The implemented design is area‐efficient and this means that it requires not many resources, without any digital signal processing (DSP) slices, on an FPGA. Moreover, the area–delay product of this design is very low compared with similar designs. To the best of the authors’ knowledge, the ECP proposed in this study over Fp performs better than available hardware in terms of area and timing.
Background and objectives
Diabetic retinopathy (DR) is the leading cause of blindness worldwide, and therefore its early detection is important in order to reduce disease-related eye injuries. DR is diagnosed by inspecting fundus images. Since microaneurysms (MA) are one of the main symptoms of the disease, distinguishing this complication within the fundus images facilitates early DR detection. In this paper, an automatic analysis of retinal images using convolutional neural network (CNN) is presented.
Methods
Our method incorporates a novel technique utilizing a two-stage process with two online datasets which results in accurate detection while solving the imbalance data problem and decreasing training time in comparison with previous studies. We have implemented our proposed CNNs using the Keras library.
Results
In order to evaluate our proposed method, an experiment was conducted on two standard publicly available datasets, i.e., Retinopathy Online Challenge dataset and E-Ophtha-MA dataset. Our results demonstrated a promising sensitivity value of about 0.8 for an average of >6 false positives per image, which is competitive with state of the art approaches.
Conclusion
Our method indicates significant improvement in MA-detection using retinal fundus images for monitoring diabetic retinopathy.
In this paper, we propose a novel parallel architecture for fast hardware implementation of elliptic curve point multiplication (ECPM), which is the key operation of an elliptic curve cryptography processor. The point multiplication over binary fields is synthesized on both FPGA and ASIC technology by designing fast elliptic curve group operations in Jacobian projective coordinates. A novel combined point doubling and point addition (PDPA) architecture is proposed for group operations to achieve high speed and low hardware requirements for ECPM. It has been implemented over the binary field which is recommended by the National Institute of Standards and Technology (NIST). The proposed ECPM supports two Koblitz and random curves for the key sizes 233 and 163 bits. For group operations, a finite-field arithmetic operation, e.g. multiplication, is designed on a polynomial basis. The delay of a 233-bit point multiplication is only 3.05 and 3.56 μs, in a Xilinx Virtex-7 FPGA, for Koblitz and random curves, respectively, and 0.81 μs in an ASIC 65-nm technology, which are the fastest hardware implementation results reported in the literature to date. In addition, a 163-bit point multiplication is also implemented in FPGA and ASIC for fair comparison which takes around 0.33 and 0.46 μs, respectively. The area-time product of the proposed point multiplication is very low compared to similar designs. The performance () and Area × Time × Energy (ATE) product of the proposed design are far better than the most significant studies found in the literature.
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