Hardware architecture of Dillon’s APN permutation for different primitive polynomials

In this study, Field Programmable Gate Array (FPGA) implementation of Conic Section Function Neural Network (CSFNN) for a classification problem focused on iris plant is presented. This work demonstrates for the first time to our knowledge, the feed-forward computation of CSFNN implementation on FPGA. Using l6-bit floating point arithmetic and the look-up tables (LUTs) for the sigmoid function and the square root function, 83% and 72% of slices and LUTs on Spartan 3-E XC3S1600E are used for the realization of CSFNN with five neurons. The classification results obtained from the FPGA implementation and software simulation show that the accuracy error between two platforms is only 0.1%.

Cryptography in digital world must offer integrity and confidentiality using cryptographic algorithms which mainly involve multiplication operation in finite fields. Various algorithms and architectures are proposed in the literature to obtain efficient finite field multiplications in both hardware and software. Here, a modified interleaved multiplication algorithm with reduced computational complexity is proposed based on a novel pre‐computation (PC) technique to perform multiplication over for trinomials. Consequently, an m ‐bit systolic multiplier for trinomials (SMT) is designed by employing the proposed algorithm. Hardware and delay complexity analysis is performed and comparison of the proposed SMT structure with similar multipliers available in the literature is presented. The SMT structure achieves ∼28 and 17% improvement in hardware and area‐delay product, respectively, for m = 233 when compared with the best multiplier available in the literature. The functionality of the proposed SMT structure is also verified by implementing on field‐programmable gate array (FPGA) and application‐specific integrated circuit (ASIC) technologies. It can be observed from FPGA and ASIC implementation results that the proposed SMT structure shows improvement in area, power consumption, area‐delay, and power‐delay products when compared with similar multipliers available in the literature.

Abstract: This study looks into the difficulties of using the Distributed Arithmetic (DA) method for Finite Impulse Response (FIR) filters on Field-Programmable Gate Arrays (FPGAs). It focuses on how coefficients are represented, balancing precision using fixed-point arithmetic and quantization. The research explores ways to optimize memory use, aiming to store data more efficiently within FPGA resources and reduce memory needs. To speed up computations, it examines how to make accessing lookup tables faster and suggests improvements in design. The study also considers how to manage FPGA resources effectively, balancing latency, throughput, and resource use. It looks at specific improvements to the DA method for FIR filters to make better use of resources and enhance performance. Overall, this work provides insights and solutions for algorithm design, memory use, lookup table speed, and FPGA architecture to make DA-based FIR filter implementations on FPGAs more efficient.

This paper proposes a hardware oriented dropout algorithm for an efficient field-programmable gate array (FPGA) implementation. Dropout is a regularization technique, which is commonly used in neural networks such as multilayer perceptrons (MLPs), convolutional neural networks (CNNs), among others. To generate a dropout mask to randomly drop neurons during training phase, random number generators (RNGs) are usually used in software implementations. However, RNGs consume considerable FPGA resources in hardware implementations. The proposed method is able to minimize the resources required for FPGA implementation of dropout by performing a simple rotation operation to a predefined dropout mask. We apply the proposed method to MLPs and CNNs and evaluate them on MNIST and CIFAR-10 classification. In addition, we employ the proposed method in GoogLeNet training using own dataset to develop a vision system for home service robots. The experimental results demonstrate that the proposed method achieves the same regularized effect as the ordinary dropout algorithm. Logic synthesis results show that the proposed method significantly reduces the consumption of FPGA resources in comparison to the ordinary RNG-based approaches.

Hardware software co-design plays a crucial part in the embedded processor development especially with the current advancement of reconfigurable platforms. The reconfigurability features offered by platforms such as Field Programmable Gate Array (FPGA) has permitted the modification of the internal processor architecture with lower cost and higher performance. While the hardware architecture could be changed through various methods, the modifications need to be complemented with a compatible assembler that suits the amended architecture. This paper presents a two-pass assembler design technique that adapts to any instruction set architecture (ISA) modifications being applied on a reconfigurable processor. A Reduced Instruction Set Computer (RISC) processor core, which is described in Verilog Hardware Description Language (HDL), is used as the testing platform whereby its ISA is expanded to include new instruction sets. The assembler is developed based on two-pass approach and the assembling process would generate a coefficient file that is used as initialization files during the FPGA implementation of the processor core. The assemblers have been successfully developed with correct output format and verified during the FPGA implementation using Xilinx Spartan-3AN board.

Design of cryptographic applications need special care. For instance, physical attacks like Side-Channel Analysis (SCA) are able to recover the secret key, just by observing the activity of the computation, even for mathematically robust algorithms like AES. SCA considers the "leakage" of a well chosen intermediate variable correlated with the secret. Field programmable gate-arrays (FPGA) are often used for hardware implementations for low to medium volume productions or when flexibility is needed. They offer many possibilities for the computation, like small Look-Up Tables (LUT) and embedded block memories (BRAM). Certain countermeasures can be deployed, like dual-rail logic or masking, to resist SCA on FPGA. However to design an effective countermeasure, it is of prime importance for a designer to know the main leakage sources of the device. In this article, we analyze the leakage source of a Xilinx Virtex V FPGA by studying 3 different AES architectures. The analysis is based on real measurements by using specific leakage models of the sensitive variable, adapted to each architecture. Our results demonstrate that, BRAM which were considered to leak less traditionally, are found to be equally vulnerable if we change the attack target from address register to output latch. Hence by providing important clues about the leakage, this study allows the designers to enhance the robustness of their implementation in FPGA.

This paper presents a thorough discussion of the proposed field-programmable gate array (FPGA) implementation for fringe pattern demodulation using the one-dimensional continuous wavelet transform (1D-CWT) algorithm. This algorithm is also known as wavelet transform profilometry. Initially, the 1D-CWT is programmed using the C programming language and compiled into VHDL using the ImpulseC tool. This VHDL code is implemented on the Altera Cyclone IV GX EP4CGX150DF31C7 FPGA. A fringe pattern image with a size of 512×512 pixels is presented to the FPGA, which processes the image using the 1D-CWT algorithm. The FPGA requires approximately 100 ms to process the image and produce a wrapped phase map. For performance comparison purposes, the 1D-CWT algorithm is programmed using the C language. The C code is then compiled using the Intel compiler version 13.0. The compiled code is run on a Dell Precision state-of-the-art workstation. The time required to process the fringe pattern image is approximately 1 s. In order to further reduce the execution time, the 1D-CWT is reprogramed using Intel Integrated Primitive Performance (IPP) Library Version 7.1. The execution time was reduced to approximately 650 ms. This confirms that at least sixfold speedup was gained using FPGA implementation over a state-of-the-art workstation that executes heavily optimized implementation of the 1D-CWT algorithm.

In this paper we describe a single-node, double precision Field Programmable Gate Array (FPGA) implementation of the Conjugate Gradient algorithm in the context of Lattice Quantum Chromodynamics. As a benchmark of our proposal we invert numerically the Dirac–Wilson operator on a 4-dimensional grid on three Xilinx hardware solutions: Zynq Ultrascale+ evaluation board, the Alveo U250 accelerator and the largest device available on the market, the VU13P device. In our implementation we separate software/hardware parts in such a way that the entire multiplication by the Dirac operator is performed in hardware, and the rest of the algorithm runs on the host. We find out that the FPGA implementation can offer a performance comparable with that obtained using current CPU or Intel’s many core Xeon Phi accelerators. A possible multiple node FPGA-based system is discussed and we argue that power-efficient High Performance Computing (HPC) systems can be implemented using FPGA devices only.

Primitive polynomials are important in hardware realizations for error control codes, cryptography, and other signal processing and communication-based designs. These primitive polynomials over a finite field in association with the core concepts of a particular area of study can be easily implemented on hardware. Researchers have used existing databases of primitive polynomials of various degrees in most cases, generated using a software-based logic. However, not much study has been carried out to implement the logic for computation of primitive polynomials on hardware. This paper describes an implementation of a scalable primitive polynomial circuit. The circuit can compute the primitive polynomial of any degree for a finite field and uses shift registers for the said purpose. This scalable circuit is synthesized on ASIC with a 45 nm CMOS process using Synopsys Design Compiler to assess standard cell area and power. The standard cell area and power consumed by the scalable circuit for various degrees of the primitive polynomial are also analyzed in this paper.

This article describes a field-programmable gate array (FPGA) cryptographic architecture, which combines the elliptic curve--based Ed25519 digital signature algorithm and the X25519 key establishment scheme in a single module. Cryptographically, these are high-security elliptic curve cryptography algorithms with short key sizes and impressive execution times in software. Our goal is to provide a lightweight FPGA module that enables them on resource-constrained devices, specifically for Internet of Things (IoT) applications. In addition, we aim at extensibility with customisable countermeasures against timing and differential power analysis side-channel attacks and fault-injection attacks. For the former, we offer a choice between time-optimised versus constant-time execution, with or without Z -coordinate randomisation and base-point blinding; and for the latter, we offer enabling or disabling default-case statements in the Finite State Machine (FSM) descriptions. To obtain compactness and at the same time fast execution times, we make maximum use of the Digital Signal Processing (DSP) slices on the FPGA. We designed a single arithmetic unit that is flexible to support operations with two moduli and non-modulus arithmetic. In addition, our design benefits in-place memory management and the local storage of inputs into DSP slices’ pipeline registers and takes advantage of distributed memory. These eliminate a memory access bottleneck. The flexibility is offered by a micro-code supported instruction-set architecture. Our design targets 7-Series Xilinx FPGAs and is prototyped on a Zynq System-on-Chip (SoC). The base design combining Ed25519 and X25519 in a single module, and its implementation requires only around 11.1K Lookup Tables (LUTs), 2.6K registers, and 16 DSP slices. Also, it achieves performance of 1.6ms for a signature generation and 3.6ms for a signature verification for a 1024-bit message with an 82MHz clock. Moreover, the design can be optimised only for X25519, which gives the most compact FPGA implementation compared to previously published X25519 implementations.

Finite field multipliers are the basic building blocks in many applications such as cryptography, error-control coding and digital signal processing. The design of efficient dedicated finite field multiplier architectures can lead to dramatic improvement on the overall system performance. For a given multiplier architecture, its hardware complexity, computation time and power consumption are highly dependent on primitive polynomial p(x). Generally, primitive polynomial is selected to optimize application-oriented parameters, such as minimizing decoding error probability in error-control coding. A secondary selection criterion should be to improve the implementation efficiency, i.e., minimizing area and power consumption while meeting the speed requirement. In this paper, the effects of different primitive polynomials on area and power consumption of semi-systolic finite field multipliers are analyzed. It is shown that the hardware complexity and the total number of transitions can be reduced by selecting the primitive polynomials with less Hamming weight. The optimum primitive polynomials for low area and low power semi-systolic multipliers over different finite field GF(2/sup m/) are provided based on the analysis results.

This paper presents a hardware implementation of multilayer feedforward neural networks (NN) using reconfigurable field-programmable gate arrays (FPGAs). Despite improvements in FPGA densities, the numerous multipliers in an NN limit the size of the network that can be implemented using a single FPGA, thus making NN applications not viable commercially. The proposed implementation is aimed at reducing resource requirement, without much compromise on the speed, so that a larger NN can be realized on a single chip at a lower cost. The sequential processing of the layers in an NN has been exploited in this paper to implement large NNs using a method of layer multiplexing. Instead of realizing a complete network, only the single largest layer is implemented. The same layer behaves as different layers with the help of a control block. The control block ensures proper functioning by assigning the appropriate inputs, weights, biases, and excitation function of the layer that is currently being computed. Multilayer networks have been implemented using Xilinx FPGA "XCV400hq240". The concept used is shown to be very effective in reducing resource requirements at the cost of a moderate overhead on speed. This implementation is proposed to make NN applications viable in terms of cost and speed for online applications. An NN-based flux estimator is implemented in FPGA and the results obtained are presented.

FPGA (Field Programmable Gate Arrays) implementation of an off-line handwritten digit recognition system based on elastic meshing directional feature extraction and integrated neural network classifier is proposed in this paper. Elastic meshing directional feature extraction is used to extract the feature of normalized 32*16 handwritten digit images. Integrated neural network classifier with BP (back-propagation) learning algorithm is designed as classifier. The pipeline technology and multi-buffer technology are used in the FPGA implementation of elastic meshing directional feature extraction. FPGA implementation architecture of neural network computing unit and integrated neural network classifier is proposed in this paper. Experiment shows that compared with software-based implementation, FPGA-based system can greatly speed up off-line handwritten digit recognition and is suitable for application in some real-time situations where high process speed and portability are required.

Characterisation of the standard deviation of a time‐series signal has uncommon, yet widespread applications. The usual requirement for a representation of signal standard deviation in real‐time implies a high computation speed. A method based on a field programmable gate array (FPGA) implementation is presented. The technique is benchmarked against conventional computational approaches and shows a single windowed standard deviation update calculation of a 16 bit sample can be achieved in 11 ns on a modern CPU. The FPGA implementation is found to be superior to all other approaches examined with an operation time of below 10 ns, and thus provides a useful tool for the real‐time measurement of the standard deviation of signals above 100 MHz.

This paper deals with Field Programmable Gate Array (FPGA) implementation design of a Predistorter real-time processing. The corresponding Baseband Digital Predistortion (DPD) is based on Memory Polynomial (MP) modelling of a UHF 8 MHz LDMOS Power Amplifier (PA). The PA MP model coefficients are estimated based on Least Square Estimation (LSE) algorithm. The proposed DPD design is using Look Up Table (LUT) for the Predistorter unit and the Indirect Learning Architecture (ILA) approach for estimating the coefficients of the predistorter. Implementation test results for the UHF LDMOS PA with DVB-T modulated signals showed good linearization performances with the adjacent channel power ratio (ACPR) reaching −46 dB.