High-Performance VLSI Architectures for Lattice-Based Cryptography

Lattice-based cryptography is a cryptographic primitive built upon the hard problems on point lattices. Cryptosystems relying on lattice-based cryptography have attracted huge attention in the last decade since they have post-quantum-resistant security and the remarkable construction of the algorithm. In particular, homomorphic encryption (HE) and post-quantum cryptography (PQC) are the two main applications of lattice-based cryptography. Meanwhile, the efficient hardware implementations for these advanced cryptography schemes are demanding to achieve a high-performance implementation. This dissertation aims to investigate the novel and high-performance very large-scale integration (VLSI) architectures for lattice-based cryptography, including the HE and PQC schemes. This dissertation first presents different architectures for the number-theoretic transform (NTT)-based polynomial multiplication, one of the crucial parts of the fundamental arithmetic for lattice-based HE and PQC schemes. Then a high-speed modular integer multiplier is proposed, particularly for lattice-based cryptography. In addition, a novel modular polynomial multiplier is presented to exploit the fast finite impulse response (FIR) filter architecture to reduce the computational complexity of the schoolbook modular polynomial multiplication for lattice-based PQC scheme. Afterward, an NTT and Chinese remainder theorem (CRT)-based high-speed modular polynomial multiplier is presented for HE schemes whose moduli are large integers

Two-dimensional block processors - structures and implementations

Includes bibliographical references.Two-dimensional (2-D) block processing technique for linear filtering of digital images is introduced. New 2-D block structures are derived for 2-D recursive digital filters realized by difference equations and state-space formulations. Several special cases have also been considered and the relevant 2-D block structures are given. The computational costs of different implementation techniques employing high-speed convolution algorithms such as fast Fourier transform, number theoretic transform and polynomial transform have been studied. A comparison among the relative efficiencies of these implementation schemes is made and a suitable method is then proposed using short convolution algorithm which results in a minimized computational time

FPGA implementations for parallel multidimensional filtering algorithms

PhD ThesisOne and multi dimensional raw data collections introduce noise and artifacts, which need to be recovered from degradations by an automated filtering system before, further machine analysis. The need for automating wide-ranged filtering applications necessitates the design of generic filtering architectures, together with the development of multidimensional and extensive convolution operators. Consequently, the aim of this thesis is to investigate the problem of automated construction of a generic parallel filtering system. Serving this goal, performance-efficient FPGA implementation architectures are developed to realize parallel one/multi-dimensional filtering algorithms. The proposed generic architectures provide a mechanism for fast FPGA prototyping of high performance computations to obtain efficiently implemented performance indices of area, speed, dynamic power, throughput and computation rates, as a complete package. These parallel filtering algorithms and their automated generic architectures tackle the major bottlenecks and limitations of existing multiprocessor systems in wordlength, input data segmentation, boundary conditions as well as inter-processor communications, in order to support high data throughput real-time applications of low-power architectures using a Xilinx Virtex-6 FPGA board. For one-dimensional raw signal filtering case, mathematical model and architectural development of the generalized parallel 1-D filtering algorithms are presented using the 1-D block filtering method. Five generic architectures are implemented on a Virtex-6 ML605 board, evaluated and compared. A complete set of results on area, speed, power, throughput and computation rates are obtained and discussed as performance indices for the 1-D convolution architectures. A successful application of parallel 1-D cross-correlation is demonstrated. For two dimensional greyscale/colour image processing cases, new parallel 2-D/3-D filtering algorithms are presented and mathematically modelled using input decimation and output image reconstruction by interpolation. Ten generic architectures are implemented on the Virtex-6 ML605 board, evaluated and compared. Key results on area, speed, power, throughput and computation rate are obtained and discussed as performance indices for the 2-D convolution architectures. 2-D image reconfigurable processors are developed and implemented using single, dual and quad MAC FIR units. 3-D Colour image processors are devised to act as 3-D colour filtering engines. A 2-D cross-correlator parallel engine is successfully developed as a parallel 2-D matched filtering algorithm for locating any MRI slice within a MRI data stack library. Twelve 3-D MRI filtering operators are plugged in and adapted to be suitable for biomedical imaging, including 3-D edge operators and 3-D noise smoothing operators. Since three dimensional greyscale/colour volumetric image applications are computationally intensive, a new parallel 3-D/4-D filtering algorithm is presented and mathematically modelled using volumetric data image segmentation by decimation and output reconstruction by interpolation, after simultaneously and independently performing 3-D filtering. Eight generic architectures are developed and implemented on the Virtex-6 board, including 3-D spatial and FFT convolution architectures. Fourteen 3-D MRI filtering operators are plugged and adapted for this particular biomedical imaging application, including 3-D edge operators and 3-D noise smoothing operators. Three successful applications are presented in 4-D colour MRI (fMRI) filtering processors, k-space MRI volume data filter and 3-D cross-correlator.IRAQI Government

Fault-tolerant computation using algebraic homomorphisms

Also issued as Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 1992.Includes bibliographical references (p. 193-196).Supported by the Defense Advanced Research Projects Agency, monitored by the U.S. Navy Office of Naval Research. N00014-89-J-1489 Supported by the Charles S. Draper Laboratories. DL-H-418472Paul E. Beckmann

FPGA based Uniform Channelizer Implementation

Channelizers are widely used in modern digital communication systems. Advanced uniform multirate channelization have been theoretically proved to be capable of reducing the computational load, with a better performance. Therefore, in this thesis, we implement these designs on a FPGA board for the sake of the comprehensive evaluation of resource usage, performance and frequency response. The uniform filter-banks are one of the most essential unit in channelization. The Generalised Discrete Fourier Transform Modulated Filter Bank (GDFT-FB), as an important variant of basic a DFT-FB, has been implemented in FPGA and demonstrated with a better computational saving rather than traditional schemes. Moreover the oversampling version is demonstrated to have a better frequency response with an acceptable amount of extra resources. On the other hand, frequency response masking (FRM) techniques is able to reduce the number of coefficients. Therefore, the full FRM GDFT-FB and alternative narrowband FRM GDFT-FB are both implemented in FPGA platform, in order to achieve a better performance and hardware efficiency

Mathematics and Digital Signal Processing

Modern computer technology has opened up new opportunities for the development of digital signal processing methods. The applications of digital signal processing have expanded significantly and today include audio and speech processing, sonar, radar, and other sensor array processing, spectral density estimation, statistical signal processing, digital image processing, signal processing for telecommunications, control systems, biomedical engineering, and seismology, among others. This Special Issue is aimed at wide coverage of the problems of digital signal processing, from mathematical modeling to the implementation of problem-oriented systems. The basis of digital signal processing is digital filtering. Wavelet analysis implements multiscale signal processing and is used to solve applied problems of de-noising and compression. Processing of visual information, including image and video processing and pattern recognition, is actively used in robotic systems and industrial processes control today. Improving digital signal processing circuits and developing new signal processing systems can improve the technical characteristics of many digital devices. The development of new methods of artificial intelligence, including artificial neural networks and brain-computer interfaces, opens up new prospects for the creation of smart technology. This Special Issue contains the latest technological developments in mathematics and digital signal processing. The stated results are of interest to researchers in the field of applied mathematics and developers of modern digital signal processing systems