Efficient modular arithmetic units for low power cryptographic applications

The demand for high security in energy constrained devices such as mobiles and PDAs is growing rapidly. This leads to the need for efficient design of cryptographic algorithms which offer data integrity, authentication, non-repudiation and confidentiality of the encrypted data and communication channels. The public key cryptography is an ideal choice for data integrity, authentication and non-repudiation whereas the private key cryptography ensures the confidentiality of the data transmitted. The latter has an extremely high encryption speed but it has certain limitations which make it unsuitable for use in certain applications. Numerous public key cryptographic algorithms are available in the literature which comprise modular arithmetic modules such as modular addition, multiplication, inversion and exponentiation. Recently, numerous cryptographic algorithms have been proposed based on modular arithmetic which are scalable, do word based operations and efficient in various aspects. The modular arithmetic modules play a crucial role in the overall performance of the cryptographic processor. Hence, better results can be obtained by designing efficient arithmetic modules such as modular addition, multiplication, exponentiation and squaring. This thesis is organized into three papers, describes the efficient implementation of modular arithmetic units, application of these modules in International Data Encryption Algorithm (IDEA). Second paper describes the IDEA algorithm implementation using the existing techniques and using the proposed efficient modular units. The third paper describes the fault tolerant design of a modular unit which has online self-checking capability --Abstract, page iv

Design and Implementation of Hybrid Multiplier for DSP Applications

In recent decades, there has been a consistent reduction in feature sizes in integrated circuit (IC) technology, leading to the need for increased placement of functional circuits on each chip. When it comes to the design of digital circuits, there is a significant focus on hybrid logic. Hybrid logic is highly regarded due to its ability to consume less power while achieving higher efficiency. Hybrid logic circuits have similarities to complementary metal-oxide-semiconductor (CMOS) transistors, yet possess a reduced transistor count while offering enhanced performance and reliability capabilities. This study examines the modeling and implementation hybrid multiplier with of help of hybrid adder. The functionality of adder is determined with the help of hybrid logic producing XOR/XNOR functionalities in single circuit.    The proposed hybrid Multiplier, which incorporates a hybrid Adder, has been successfully designed and implemented using CMOS 45nm technology and Mentor Graphics software the hybrid transistor logic multiplier demonstrates a decrease in total delay of 60% compared to CMOS

A Survey on Approximate Multiplier Designs for Energy Efficiency: From Algorithms to Circuits

Given the stringent requirements of energy efficiency for Internet-of-Things edge devices, approximate multipliers, as a basic component of many processors and accelerators, have been constantly proposed and studied for decades, especially in error-resilient applications. The computation error and energy efficiency largely depend on how and where the approximation is introduced into a design. Thus, this article aims to provide a comprehensive review of the approximation techniques in multiplier designs ranging from algorithms and architectures to circuits. We have implemented representative approximate multiplier designs in each category to understand the impact of the design techniques on accuracy and efficiency. The designs can then be effectively deployed in high-level applications, such as machine learning, to gain energy efficiency at the cost of slight accuracy loss.Comment: 38 pages, 37 figure

Designing a Novel High Performance Four-to-Two Compressor Cell Based on CNTFET Technology for Low Voltages

Compressor cell is often placed in critical path of multiplier circuits to perform partial product summation. Therefore it plays a significant role in determining the entire performance of multiplier and digital system. Respecting to the necessity of low power design for portable electronic, designing a low power and high performance compressors seems to be a good solution to overcome of these problems for computations. In this paper a novel high performance four-to-two compressor cell is proposed using Carbon Nanotube Field Effect Transistors (CNTFETs) technology. The new cell is based on Majority Function, NOR, and NAND gates. The main advantage of proposed design in comparison with former cells is the ease of obtaining CARRY output by means of Majority function. Simulations have been done with 32nm technology node using Synopsys HSPICE software. Simulation results confirm the priority of the proposed cell compared to other state-of-the-art four-to-two compressor cells

Design of Energy-Efficient Approximate Arithmetic Circuits

Energy consumption has become one of the most critical design challenges in integrated circuit design. Arithmetic computing circuits, in particular array-based arithmetic computing circuits such as adders, multipliers, squarers, have been widely used. In many cases, array-based arithmetic computing circuits consume a significant amount of energy in a chip design. Hence, reduction of energy consumption of array-based arithmetic computing circuits is an important design consideration. To this end, designing low-power arithmetic circuits by intelligently trading off processing precision for energy saving in error-resilient applications such as DSP, machine learning and neuromorphic circuits provides a promising solution to the energy dissipation challenge of such systems. To solve the chip’s energy problem, especially for those applications with inherent error resilience, array-based approximate arithmetic computing (AAAC) circuits that produce errors while having improved energy efficiency have been proposed. Specifically, a number of approximate adders, multipliers and squarers have been presented in the literature. However, the chief limitation of these designs is their un-optimized processing accuracy, which is largely due to the current lack of systemic guidance for array-based AAAC circuit design pertaining to optimal tradeoffs between error, energy and area overhead. Therefore, in this research, our first contribution is to propose a general model for approximate array-based approximate arithmetic computing to guide the minimization of processing error. As part of this model, the Error Compensation Unit (ECU) is identified as a key building block for a wide range of AAAC circuits. We develop theoretical analysis geared towards addressing two critical design problems of the ECU, namely, determination of optimal error compensation values and identification of the optimal error compensation scheme. We demonstrate how this general AAAC model can be leveraged to derive practical design insights that may lead to optimal tradeoffs between accuracy, energy dissipation and area overhead. To further minimize energy consumption, delay and area of AAAC circuits, we perform ECU logic simplification by introducing don't cares. By applying the proposed model, we propose an approximate 16x16 fixed-width Booth multiplier that consumes 44.85% and 28.33% less energy and area compared with theoretically the most accurate fixed-width Booth multiplier when implemented using a 90nm CMOS standard cell library. Furthermore, it reduces average error, max error and mean square error by 11.11%, 28.11% and 25.00%, respectively, when compared with the best reported approximate Booth multiplier and outperforms the best reported approximate design significantly by 19.10% in terms of the energy-delay-mean square error product (EDE_(ms)). Using the same approach, significant energy consumption, area and error reduction is achieved for a squarer unit, with more than 20.00% EDE_(ms) reduction over existing fixed-width squarer designs. To further reduce error and cost by utilizing extra signatures and don't cares, we demonstrate a 16-bit fixed-width squarer that improves the energy-delay-max error (EDE_(max)) by 15.81%

Novel Reversible TSG Gate and Its Application for Designing Components of Primitive Reversible/Quantum ALU

In recent years, reversible logic has emerged as a promising computing paradigm having application in low power CMOS, quantum computing, nanotechnology, and optical computing. The classical set of gates such as AND, OR, and EXOR are not reversible. This paper utilizes a new 4 * 4 reversible gate called TSG gate to build the components of a primitive reversible/quantum ALU. The most significant aspect of the TSG gate is that it can work singly as a reversible full adder, that is reversible full adder can now be implemented with a single gate only. A Novel reversible 4:2 compressor is also designed from the TSG gate which is later used to design a novel 8x8 reversible Wallace tree multiplier. It is proved that the adder, 4:2 compressor and multiplier architectures designed using the TSG gate are better than their counterparts available in literature, in terms of number of reversible gates and garbage outputs. This is perhaps, the first attempt to design a reversible 4:2 compressor and a reversible Wallace tree multiplier as far as existing literature and our knowledge is concerned. Thus, this paper provides an initial threshold to build more complex systems which can execute complicated operations using reversible logic.Comment: 5 Pages; Published in Proceedings of the Fifth IEEE International Conference on Information, Communications and Signal Processing (ICICS 2005), Bangkok, Thailand, 6-9 December 2005,pp.1425-142

Approximate Compressors for Multiplication

At nanometric scales, approximate computing is an attractive prototype used for digital processing. Despite providing less accurate results, approximate computing is preferred over exact computing as it provides a fast & significant output along with low power consumption. Designing of an efficient multiplier has always been a challenge for VLSI designers as multipliers have a large area, long latency consumes considerable power. For this inconvenience compressor with low latency, low power consumption and reduced stages of the product are designed. This paper proposes two methods to design high order compressors (8:4 & 9:4) (i) Using adders (half & full) (ii) Using multiplexers in Cadence VIRTUOSO tool using 45nm technology. Extensive simulation results show that the proposed designs achieve significant accuracy improvement along with power, area, and delay reductions compared to previous compressor designs