Publication Date
2016
Document Type
Thesis
Committee Members
Henry Chen (Committee Member), Zhiqiang Wu (Committee Member), Jiafeng Xie (Advisor)
Degree Name
Master of Science in Electrical Engineering (MSEE)
Abstract
All-one-polynomial (AOP)-based systolic multipliers over GF (2m) are usually not con-sidered for practical implementation of cryptosystems such as elliptic curve cryptography (ECC) due to security reasons. Besides that, systolic AOP multipliers usually suer from the problem of high register-complexity, especially in field-programmable gate array (FPGA) platforms where the register resources are not that abundant. In this thesis, however, we have shown that the AOP-based systolic multipliers can easily achieve low register-complexity implementations and the proposed architectures can be employed as computation cores to derive ecient implementations of systolic Montgomery multipli-ers based on trinomials, which are recommended by the National Institute of Standards and Technology (NIST) for cryptosystems. In this paper, first, we propose a novel data broadcasting scheme in which the register-complexity involved within existing AOP-based systolic multipliers is significantly reduced. We have found out that for practical usage, the modified AOP-based systolic structure can be packed as a standard computation core. Next, we propose a novel Montgomery multiplication algorithm that can fully em-ploy the proposed AOP-based computation core. The proposed Montgomery algorithm employs a novel pre-computed-modular (PCM) operation, and the systolic structures based on this algorithm fully inherit the advantages brought from the AOP-based core (low register-complexity, low critical-path delay, and low latency) except some marginal hardware overhead brought by a pre-computation unit. The proposed architectures are then implemented by Xilinx ISE 14.1 and it is shown that compared with the existing designs, the proposed designs achieve at least 70.0% and 47.6% less area-delay product (ADP) and power-delay product (PDP) than the best of competing designs, respectively.
Page Count
60
Department or Program
Department of Electrical Engineering
Year Degree Awarded
2016
Copyright
Copyright 2016, some rights reserved. My ETD may be copied and distributed only for non-commercial purposes and may not be modified. All use must give me credit as the original author.
Creative Commons License
This work is licensed under a Creative Commons Attribution-Noncommercial-No Derivative Works 3.0 License.
