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 onestop 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 arithmetic.
Naseimo, D (2021). Arithmetic Operations On Elliptic Curve Defined Over Radix-7 Symmetrical Quaternary Signed -Digit Finite Fields And Their Application In Secure Communication Systems.. Afribary. Retrieved from https://afribary.com/works/arithmetic-operations-on-elliptic-curve-defined-over-radix-7-symmetrical-quaternary-signed-digit-finite-fields-and-their-application-in-secure-communication-systems
Naseimo, DAIKPOR "Arithmetic Operations On Elliptic Curve Defined Over Radix-7 Symmetrical Quaternary Signed -Digit Finite Fields And Their Application In Secure Communication Systems." Afribary. Afribary, 29 Apr. 2021, https://afribary.com/works/arithmetic-operations-on-elliptic-curve-defined-over-radix-7-symmetrical-quaternary-signed-digit-finite-fields-and-their-application-in-secure-communication-systems. Accessed 02 May. 2024.
Naseimo, DAIKPOR . "Arithmetic Operations On Elliptic Curve Defined Over Radix-7 Symmetrical Quaternary Signed -Digit Finite Fields And Their Application In Secure Communication Systems.". Afribary, Afribary, 29 Apr. 2021. Web. 02 May. 2024. < https://afribary.com/works/arithmetic-operations-on-elliptic-curve-defined-over-radix-7-symmetrical-quaternary-signed-digit-finite-fields-and-their-application-in-secure-communication-systems >.
Naseimo, DAIKPOR . "Arithmetic Operations On Elliptic Curve Defined Over Radix-7 Symmetrical Quaternary Signed -Digit Finite Fields And Their Application In Secure Communication Systems." Afribary (2021). Accessed May 02, 2024. https://afribary.com/works/arithmetic-operations-on-elliptic-curve-defined-over-radix-7-symmetrical-quaternary-signed-digit-finite-fields-and-their-application-in-secure-communication-systems