Analysis of Existing and Proposed 3-Bit and Multi-Bit Multiplier Algorithms for FIR Filters and Adaptive Channel Equalizers on FPGA

Different multiplication algorithms have different performance characteristics. Some are good at speed while others consume less area when implemented on hardware, like Field Programmable Gate Array (FPGA)-the advanced implementation technology for DSP systems. The eminent parallel and sequential multiplication algorithms include Shift and Add, Wallace Tree, Booth, and Array. The multiplier optimization attempts have also been reported in adders used for partial product addition. In this paper, analogous to conventional multipliers, two new multiplication algorithms implemented on FPGA are shown and compared with conventional algorithms as stand-alone and by using them in the implementation of FIR filters and adaptive channel equalizer using the LMS algorithm. The work is carried out on Spartan-6 FPG that may be extended for any type of FPGA. Results are compared in terms of resource utilization, power consumption, and maximum achieved frequency. The results show that for a small length of coefficients like 3-bit, the proposed algorithms work very well in terms of achieved frequency, consumed power, and even resource utilization. Whilst for the length greater than 3-bit, the Pipelined multiplier is much better in frequency than the proposed and conventional ones, and the Booth multiplier consumes fewer resources in terms of lookup tables.

High-Speed and Unified ECC Processor for Generic Weierstrass Curves over GF(p) on FPGA

In this paper, we present a high-speed, unified elliptic curve cryptography (ECC) processor for arbitrary Weierstrass curves over GF(p), which to the best of our knowledge, outperforms other similar works in terms of execution time. Our approach employs the combination of the schoolbook long and Karatsuba multiplication algorithm for the elliptic curve point multiplication (ECPM) to achieve better parallelization while retaining low complexity. In the hardware implementation, the substantial gain in speed is also contributed by our n-bit pipelined Montgomery Modular Multiplier (pMMM), which is constructed from our n-bit pipelined multiplier-accumulators that utilizes digital signal processor (DSP) primitives as digit multipliers. Additionally, we also introduce our unified, pipelined modular adder/subtractor (pMAS) for the underlying field arithmetic, and leverage a more efficient yet compact scheduling of the Montgomery ladder algorithm. The implementation for 256-bit modulus size on the 7-series FPGA: Virtex-7, Kintex-7, and XC7Z020 yields 0.139, 0.138, and 0.206 ms of execution time, respectively. Furthermore, since our pMMM module is generic for any curve in Weierstrass form, we support multi-curve parameters, resulting in a unified ECC architecture. Lastly, our method also works in constant time, making it suitable for applications requiring high speed and SCA-resistant characteristics.

High-Speed and Unified ECC Processor for Generic Weierstrass Curves over GF(p) on FPGA

In this paper, we present a high-speed, unified elliptic curve cryptography (ECC) processor for arbitrary Weierstrass curves over GF(p), which to the best of our knowledge, outperforms other similar works in terms of execution time. Our approach employs the combination of the schoolbook long and Karatsuba multiplication algorithm for the elliptic curve point multiplication (ECPM) to achieve better parallelization while retaining low complexity. In the hardware implementation, the substantial gain in speed is also contributed by our n-bit pipelined Montgomery Modular Multiplier (pMMM), which is constructed from our n-bit pipelined multiplier-accumulators that utilizes DSP primitives as digit multipliers. Additionally, we also introduce our unified, pipelined modular adder/subtractor (pMAS) for the underlying field arithmetic, and leverage a more efficient yet compact scheduling of the Montgomery ladder algorithm. The implementation on the 7-series FPGA: Virtex-7, Kintex-7, and XC7Z020, yields 0.139, 0.138, and 0.206 ms of execution time, respectively. Furthermore, since our pMMM module is generic for any curve in Weierstrass form, we support multi-curve parameters, resulting in a unified ECC architecture. Lastly, our method also works in constant time, making it suitable for applications requiring high speed and SCA-resistant characteristics.

Novel Self-Pipelining Approach for Speed-Power Efficient Reliable Binary Multiplication

Background: The present study explores a novel self-pipelining strategy that can enhance speed-power efficiency as well as the reliability of a binary multiplier as compared to state-of-art register and wavepipelining. Method: Proper synchronization with efficient clocking between the subsequent self-pipelining stages has been assured to design a self-pipelined multiplier. Each self-pipelining stage consists of self-latching leaf cells that are designed, optimized and evaluated by TSMC 0.18μm CMOS technology with 1.8V supply rail and at 25°C temperature. The T-Spice transient response and simulated results for the designed circuits are presented. The proposed idea has been applied to design 4-b×4-b self-pipelined Wallace- tree multiplier. The multiplier was validated for all possible test patterns and the transient response was evaluated. The circuit performance in terms of propagation delay, average power and Power-Delay- Product (PDP) is recorded. Next, the decomposition logic is applied to design a higher-order multiplier (i.e., 8-bit×8-bit and 16-bit×16-bit) based on the proposed strategy using 4-bit×4-bit self-pipelined multiplier. The designed multiplier was also validated through extensive TSpice simulation for all the required test patterns using W-Edit and the evaluated performance is presented. All the designs, optimizations and evaluations performed are based on BSIM3 device parameter of TSMC 0.18μm CMOS technology with 1.8V supply rail at 25°C temperature using S-Edit of Tanner EDA. Results: The reliability was investigated of the proposed 4-b×4-b multiplier in the temperature range - 40°C to 100°C for maximum PDP variation. Conclusion: A benchmarking analysis in terms of speed-power performance with recent competitive design reveals preeminence of the proposed technique.

Design and comparative analysis of inexact speculative adder and multiplier

A Carry look ahead adder is a sort of the summer used in the logic design of the digital systems. The CLA boost up the speed by decreasing the measure of duration needed to calculate the carry bits. The CLA based outline of the inexact speculative adder is pipelined architecture to incorporate couple of logic paths along its basic way and in this manner, improving the recurrence of operation. This paper presents the comparative analysis of the pipelined inexact speculative adder and the general carry look ahead adder and showed that the delay is reduced to 48.27% when compared to carry look ahead adder and also we have designed the pipelined multiplier using the Inexact speculative adders and observed that the delay is reduced to 48.32% when compared to the normal multiplier. This entail Xilinx ISE Design Suite 14.5 Tool.