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Novel Implementation of Finite Field Multipliers over GF(2m) for Emerging Cryptographic Applications

Shaik, Nazeem Basha
http://rave.ohiolink.edu/etdc/view?acc_num=wright1494255631774212

Abstract Details

2017, Master of Science in Electrical Engineering (MSEE), Wright State University, Electrical Engineering.
Cryptographic and coding theory algorithms use arithmetic operations over nite elds. Finite eld 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, rst 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 di erent irreducible polynomials and addition operations. Desired functionality of the proposed obfuscated structure is achieved through correct input sequence to controller (FSM). This is the rst 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 speci c integration circuits (ASIC) platform and have achieved excellent area-time performance.
Jiafeng Xie, Ph.D. (Advisor)
Henry Chen, Ph.D. (Committee Member)
Yan Zhuang, Ph.D. (Committee Member)
64 p.
Electrical Engineering
All one polynomials; Finite Field; Hardware obfuscation; Pentanomials; Systolic architecture; Trinomials

Recommended Citations

Citations

  • Shaik, N. B. (2017). Novel Implementation of Finite Field Multipliers over GF(2m) for Emerging Cryptographic Applications [Master's thesis, Wright State University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=wright1494255631774212

    APA Style (7th edition)

  • Shaik, Nazeem. Novel Implementation of Finite Field Multipliers over GF(2m) for Emerging Cryptographic Applications. 2017. Wright State University, Master's thesis. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=wright1494255631774212.

    MLA Style (8th edition)

  • Shaik, Nazeem. "Novel Implementation of Finite Field Multipliers over GF(2m) for Emerging Cryptographic Applications." Master's thesis, Wright State University, 2017. http://rave.ohiolink.edu/etdc/view?acc_num=wright1494255631774212

    Chicago Manual of Style (17th edition)

wright1494255631774212
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© 2017, some rights reserved.Creative Commons License Novel Implementation of Finite Field Multipliers over GF(2m) for Emerging Cryptographic Applications by Nazeem Basha Shaik is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License. Based on a work at etd.ohiolink.edu.
This open access ETD is published by Wright State University and OhioLINK.