Arithemetic Operations on Elliptic Curve Defined over Radix-7 Synmetrical Quaternary Signed- Digit Finite Fields and their application in Secure Communication Systems
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This thesis proposes a Restricted Radix-7 Symmetrical Quaternary Signed Digit Number system (RR7SQSDNS) both as an alternative processing logic threshold system and as a signed digit algebraic structure. The thesis also presents the arithmetic operations on elliptic curves defined over this special type of finite field and develops Restricted Radix-7 Symmetrical Quaternary Signed Digit (RR7SQSD) modular exponentiation scheme that uses a multiply-by-7 addition/subtraction chain to compute the product of very large word length integer operands in data word length constrained compute environments. The multiply-by-7 addition/subtraction chain is also used to develop a one-stop multiply-by-7 point multiplication computation strategy for elliptic curves defined over RR7SQSD finite fields. A Complementary Pass (CP) gate derived 7-valued symmetrical quaternary signed-digit T-gate realized as a basic building block for implementing the SMVL arithmetic unit VLSI circuit operates on RR7SQSD profile voltage signals. The VLSI functional logic circuits were thus synthesized on this basic building blocks level. Multisim Electronic Work Bench was used to analogue simulate the T-gate’s MOSFET circuit. The T-gate’s multiplexing ability, the RR7SQSD full adder and quasi-multiplier circuits’ accuracy were simulated using qbasic language hardware-descriptive-styled source code program with results that confirmed the efficiency of RR7SQSD arithmethic
A Thesis Submitted to the School of Postgraduate Studies, University of Lagos
Logic Circuits , Arthmetic Operations , Digit algebraic structures , Research Subject Categories::MATHEMATICS::Algebra, geometry and mathematical analysis::Algebra and geometry
Daikpor, M.N (2010). Arithemetic Operations on Elliptic Curve Defined over Radix-7 Synmetrical Quaternary Signed- Digit Finite Fields and their application in Secure Communication Systems. A Thesis Submitted to University of Lagos School of Postgraduate Studies Phd Thesis and Dissertation, 366pp.