Realizing arbitrary-precision modular multiplication with a fixed-precision multiplier datapath

Within the context of cryptographic hardware, the term scalability refers to the ability to process operands of any size, regardless of the precision of the underlying data path or registers. In this paper we present a simple yet effective technique for increasing the scalability of a fixed-precision Montgomery multiplier. Our idea is to extend the datapath of a Montgomery multiplier in such a way that it can also perform an ordinary multiplication of two n-bit operands (without modular reduction), yielding a 2n-bit result. This conventional (nxn->2n)-bit multiplication is then used as a “sub-routine” to realize arbitrary-precision Montgomery multiplication according to standard software algorithms such as Coarsely Integrated Operand Scanning (CIOS). We show that performing a 2n-bit modular multiplication on an n-bit multiplier can be done in 5n clock cycles, whereby we assume that the n-bit modular multiplication takes n cycles. Extending a Montgomery multiplier for this extra functionality requires just some minor modifications of the datapath and entails a slight increase in silicon area

Customisable arithmetic hardware designs

Imperial Users onl

Designing Flexible, Energy Efficient and Secure Wireless Solutions for the Internet of Things

The Internet of Things (IoT) is an emerging concept where ubiquitous physical objects (things) consisting of sensor, transceiver, processing hardware and software are interconnected via the Internet. The information collected by individual IoT nodes is shared among other often heterogeneous devices and over the Internet. This dissertation presents flexible, energy efficient and secure wireless solutions in the IoT application domain. System design and architecture designs are discussed envisioning a near-future world where wireless communication among heterogeneous IoT devices are seamlessly enabled. Firstly, an energy-autonomous wireless communication system for ultra-small, ultra-low power IoT platforms is presented. To achieve orders of magnitude energy efficiency improvement, a comprehensive system-level framework that jointly optimizes various system parameters is developed. A new synchronization protocol and modulation schemes are specified for energy-scarce ultra-small IoT nodes. The dynamic link adaptation is proposed to guarantee the ultra-small node to always operate in the most energy efficiency mode, given an operating scenario. The outcome is a truly energy-optimized wireless communication system to enable various new applications such as implanted smart-dust devices. Secondly, a configurable Software Defined Radio (SDR) baseband processor is designed and shown to be an efficient platform on which to execute several IoT wireless standards. It is a custom SIMD execution model coupled with a scalar unit and several architectural optimizations: streaming registers, variable bitwidth, dedicated ALUs, and an optimized reduction network. Voltage scaling and clock gating are employed to further reduce the power, with a more than a 100% time margin reserved for reliable operation in the near-threshold region. Two upper bound systems are evaluated. A comprehensive power/area estimation indicates that the overhead of realizing SDR flexibility is insignificant. The benefit of baseband SDR is quantified and evaluated. To further augment the benefits of a flexible baseband solution and to address the security issue of IoT connectivity, a light-weight Galois Field (GF) processor is proposed. This processor enables both energy-efficient block coding and symmetric/asymmetric cryptography kernel processing for a wide range of GF sizes (2^m, m = 2, 3, ..., 233) and arbitrary irreducible polynomials. Program directed connections among primitive GF arithmetic units enable dynamically configured parallelism to efficiently perform either four-way SIMD GF operations, including multiplicative inverse, or a long bit-width GF product in a single cycle. This demonstrates the feasibility of a unified architecture to enable error correction coding flexibility and secure wireless communication in the low power IoT domain.PHDComputer Science & EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttps://deepblue.lib.umich.edu/bitstream/2027.42/137164/1/yajchen_1.pd

Increasing rendering performance of graphics hardware

Graphics Processing Unit (GPU) performance is increasing faster than central processing unit (CPU) performance. This growth is driven by performance improvements that can be divided into the following three categories: algorithmic improvements, architectural improvements, and circuit-level improvements. In this dissertation I present techniques that improve the rendering performance of graphics hardware measured in speed, power consumption or image quality in each of these three areas. At the algorithmic level, I introduce a method for using graphics hardware to rapidly and efficiently generate summed-area tables, which are data structures that hold pre-computed two-dimensional integrals of subsets of a given image, and present several novel rendering techniques that take advantage of summed-area tables to produce dynamic, high-quality images at interactive frame rates. These techniques improve the visual quality of images rendered on current commodity GPUs without requiring modifications to the underlying hardware or architecture. At the architectural level, I propose modifications to the architecture of current GPUs that add conditional streaming capabilities. I describe a novel GPU-based ray-tracing algorithm that takes advantage of conditional output streams to reduce the memory bandwidth requirements by over an order of magnitude times when compared to previous techniques. At the circuit level, I propose a compute-on-demand paradigm for the design of high-speed and energy-efficient graphics components. The goal of the compute-on-demand paradigm is to only perform computation at the bit-level when needed. The compute-on-demand paradigm exploits the data-dependent nature of computation, and thereby obtains speed and energy improvements by optimizing designs for the common case. This approach is illustrated with the design of a high-speed Z-comparator that is implemented using asynchronous logic. Asynchronous or "clockless" circuits were chosen for my implementations since they allow for data-dependent completion times and reduced power consumption by disabling inactive components. The resulting circuit-level implementation runs over 1.5 times faster while on dissipating 25% the energy of a comparable synchronous comparator for the average case. Also at the circuit-level, I introduce a novel implementation of counterflow pipelining, which allows two streams of data to flow in opposite directions within the same pipeline without the need for complex arbitration. The advantages of this implementation are demonstrated by the design of a high-speed asynchronous Booth multiplier. While both the comparator and the multiplier are useful components of a graphics pipeline, the objective of this work was to propose the new design paradigm as a promising alternative to current graphics hardware design practices

Energy efficient hardware acceleration of multimedia processing tools

The world of mobile devices is experiencing an ongoing trend of feature enhancement and generalpurpose multimedia platform convergence. This trend poses many grand challenges, the most pressing being their limited battery life as a consequence of delivering computationally demanding features. The envisaged mobile application features can be considered to be accelerated by a set of underpinning hardware blocks Based on the survey that this thesis presents on modem video compression standards and their associated enabling technologies, it is concluded that tight energy and throughput constraints can still be effectively tackled at algorithmic level in order to design re-usable optimised hardware acceleration cores. To prove these conclusions, the work m this thesis is focused on two of the basic enabling technologies that support mobile video applications, namely the Shape Adaptive Discrete Cosine Transform (SA-DCT) and its inverse, the SA-IDCT. The hardware architectures presented in this work have been designed with energy efficiency in mind. This goal is achieved by employing high level techniques such as redundant computation elimination, parallelism and low switching computation structures. Both architectures compare favourably against the relevant pnor art in the literature. The SA-DCT/IDCT technologies are instances of a more general computation - namely, both are Constant Matrix Multiplication (CMM) operations. Thus, this thesis also proposes an algorithm for the efficient hardware design of any general CMM-based enabling technology. The proposed algorithm leverages the effective solution search capability of genetic programming. A bonus feature of the proposed modelling approach is that it is further amenable to hardware acceleration. Another bonus feature is an early exit mechanism that achieves large search space reductions .Results show an improvement on state of the art algorithms with future potential for even greater savings

Adiabatic Circuits for Power-Constrained Cryptographic Computations

This thesis tackles the need for ultra-low power operation in power-constrained cryptographic computations. An example of such an application could be smartcards. One of the techniques which has proven to have the potential of rendering ultra-low power operation is ‘Adiabatic Logic Technique’. However, the adiabatic circuits has associated challenges due to high energy dissipation of the Power-Clock Generator (PCG) and complexity of the multi-phase power-clocking scheme. Energy efficiency of the adiabatic system is often degraded due to the high energy dissipation of the PCG. In this thesis, nstep charging strategy using tank capacitors is considered for the power-clock generation and several design rules and trade-offs between the circuit complexity and energy efficiency of the PCG using n-step charging circuits have been proposed. Since pipelining is inherent in adiabatic logic design, careful selection of architecture is essential, as otherwise overhead in terms of area and energy due to synchronization buffers is induced specifically, in the case of adiabatic designs using 4-phase power-clocking scheme. Several architectures for the Montgomery multiplier using adiabatic logic technique are implemented and compared. An architecture which constitutes an appropriate trade-off between energy efficiency and throughput is proposed along with its methodology. Also, a strategy to reduce the overhead due to synchronization buffers is proposed. A modification in the Montgomery multiplication algorithm is proposed. Furthermore, a problem due to the application of power-clock gating in cascade stages of adiabatic logic is identified. The problem degrades the energy savings that would otherwise be obtained by the application of power-clock gating. A solution to this problem is proposed. Cryptographic implementations also present an obvious target for Power Analysis Attacks (PAA). There are several existing secure adiabatic logic designs which are proposed as a countermeasure against PAA. Shortcomings of the existing logic designs are identified, and two novel secure adiabatic logic designs are proposed as the countermeasures against PAA and improvement over the existing logic designs

Doctor of Philosophy

dissertationWith the spread of internet and mobile devices, transferring information safely and securely has become more important than ever. Finite fields have widespread applications in such domains, such as in cryptography, error correction codes, among many others. In most finite field applications, the field size - and therefore the bit-width of the operands - can be very large. The high complexity of arithmetic operations over such large fields requires circuits to be (semi-) custom designed. This raises the potential for errors/bugs in the implementation, which can be maliciously exploited and can compromise the security of such systems. Formal verification of finite field arithmetic circuits has therefore become an imperative. This dissertation targets the problem of formal verification of hardware implementations of combinational arithmetic circuits over finite fields of the type F2k . Two specific problems are addressed: i) verifying the correctness of a custom-designed arithmetic circuit implementation against a given word-level polynomial specification over F2k ; and ii) gate-level equivalence checking of two different arithmetic circuit implementations. This dissertation proposes polynomial abstractions over finite fields to model and represent the circuit constraints. Subsequently, decision procedures based on modern computer algebra techniques - notably, Gr¨obner bases-related theory and technology - are engineered to solve the verification problem efficiently. The arithmetic circuit is modeled as a polynomial system in the ring F2k [x1, x2, · · · , xd], and computer algebrabased results (Hilbert's Nullstellensatz) over finite fields are exploited for verification. Using our approach, experiments are performed on a variety of custom-designed finite field arithmetic benchmark circuits. The results are also compared against contemporary methods, based on SAT and SMT solvers, BDDs, and AIG-based methods. Our tools can verify the correctness of, and detect bugs in, up to 163-bit circuits in F2163 , whereas contemporary approaches are infeasible beyond 48-bit circuits

Rethinking FPGA Architectures for Deep Neural Network applications

The prominence of machine learning-powered solutions instituted an unprecedented trend of integration into virtually all applications with a broad range of deployment constraints from tiny embedded systems to large-scale warehouse computing machines. While recent research confirms the edges of using contemporary FPGAs to deploy or accelerate machine learning applications, especially where the latency and energy consumption are strictly limited, their pre-machine learning optimised architectures remain a barrier to the overall efficiency and performance. Realizing this shortcoming, this thesis demonstrates an architectural study aiming at solutions that enable hidden potentials in the FPGA technology, primarily for machine learning algorithms. Particularly, it shows how slight alterations to the state-of-the-art architectures could significantly enhance the FPGAs toward becoming more machine learning-friendly while maintaining the near-promised performance for the rest of the applications. Eventually, it presents a novel systematic approach to deriving new block architectures guided by designing limitations and machine learning algorithm characteristics through benchmarking. First, through three modifications to Xilinx DSP48E2 blocks, an enhanced digital signal processing (DSP) block for important computations in embedded deep neural network (DNN) accelerators is described. Then, two tiers of modifications to FPGA logic cell architecture are explained that deliver a variety of performance and utilisation benefits with only minor area overheads. Eventually, with the goal of exploring this new design space in a methodical manner, a problem formulation involving computing nested loops over multiply-accumulate (MAC) operations is first proposed. A quantitative methodology for deriving efficient coarse-grained compute block architectures from benchmarks is then suggested together with a family of new embedded blocks, called MLBlocks

Image Processing Using FPGAs

This book presents a selection of papers representing current research on using field programmable gate arrays (FPGAs) for realising image processing algorithms. These papers are reprints of papers selected for a Special Issue of the Journal of Imaging on image processing using FPGAs. A diverse range of topics is covered, including parallel soft processors, memory management, image filters, segmentation, clustering, image analysis, and image compression. Applications include traffic sign recognition for autonomous driving, cell detection for histopathology, and video compression. Collectively, they represent the current state-of-the-art on image processing using FPGAs