Novel Implementation of Finite Field Multipliers over GF(2m) for Emerging Cryptographic Applications
Publication Date
2017
Document Type
Thesis
Committee Members
Henry Chen (Committee Member), Jiafeng Xie (Advisor), Yan Zhuang (Committee Member)
Degree Name
Master of Science in Electrical Engineering (MSEE)
Abstract
Cryptographic and coding theory algorithms use arithmetic operations over finite fields. Finite field multiplications over GF(2m) are critical components for these systems. Well known irreducible polynomials are all-one-polynomials (AOP), equally spaced polynomial (ESP), trinomial and pentanomial. Due to its simple structure, AOP based multiplica- tion is easy to implement and hence the AOP based multiplication of variable length can be used as a standard computation core. In this thesis, first of all, we employ low register complexity AOP based systolic multiplication core to propose multiplication over GF(2m) based on NIST recommended pentanomials. The proposed parallel and serial ar- chitectures use pre-computation (PC) modules to compute bits involve in multiplication and re-combination (RC) modules to combine computed bits from PC to form vectors which will reduce the multiplication complexity. The corresponding architecture based on the proposed algorithm is then synthesized by Xilinx ISE 14.1 on a Virtex 5 FPGA device and it is observed that the proposed structures has lower area-delay complexity than the best of existing designs. Second, we propose a novel obfuscation mechanism to equip multiplication over different irreducible polynomials and addition operations. Desired functionality of the proposed obfuscated structure is achieved through correct input sequence to controller (FSM). This is the first architecture proposed which can implement four types of polynomial multiplications and additions with obfuscated man- ner. The proposed architecture is synthesized and implemented in application specific integration circuits (ASIC) platform and have achieved excellent area-time performance.
Page Count
64
Department or Program
Department of Electrical Engineering
Year Degree Awarded
2017
Copyright
Copyright 2017, some rights reserved. My ETD may be copied and distributed only for non-commercial purposes and may be modified only if the modified version is distributed with these same permissions. 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.
