Publication Date


Document Type


Committee Members

Zhiqiang Wu (Committee Member), Jiafeng Xie (Advisor), Yan Zhuang (Committee Member)

Degree Name

Master of Science in Electrical Engineering (MSEE)


Finite field multiplication over GF(2^m) is a critical component for elliptic curve cryptography (ECC). National Institute of Standards and Technology (NIST) has recommended five polynomials (two trinomials and three pentanomials) for ECC implementation. Although there are a lot reports available on polynomial basis multipliers, efficient implementation of a design with flexible field-size is quite rare. There is another basis to represent the field called normal basis. Normal basis multiplication over GF(2^m) is widely used in various applications such as elliptic curve cryptography (ECC). As a special class of normal basis with low complexity, Gaussian normal basis (GNB) has received considerable attention recently. In this paper, we first propose a novel low-complexity hybrid-size systolic polynomial basis multiplier based on a proposed novel hybrid-size (for both pentanomial and trinomial) algorithm for efficient systolization of finite field multiplications. Next, we propose a novel decomposition algorithm to develop a digit-level (DL) low critical-path delay and low register-complexity systolic structure for GNB multiplication over GF(2^m). For the hybrid-size systolic polynomial multipliers, both the theoretical and field-programmable gate array (FPGA) implementation show that, our proposed architectures have lower register-complexity than the existing ones. The proposed hybrid-size multiplier can also be extended to other field-size and can be used as a third-party intellectual property (IP) core for various cryptosystems. At the same time, the proposed systolic Gaussian normal basis multipliers can achieve both low critical-path and low register-complexity through the theoretical and application-specific integrated circuit (ASIC) comparisons with the existing GNB multipliers.

Page Count


Department or Program

Department of Electrical Engineering

Year Degree Awarded


Creative Commons License

Creative Commons Attribution-Noncommercial-Share Alike 3.0 License
This work is licensed under a Creative Commons Attribution-Noncommercial-Share Alike 3.0 License.