MATHEMATICAL MODELING AND SYNTHESIS OF REVERSIBLE CRYPTOGRAPHIC LOGIC

Reversible logic has emerged as a pivotal area of study in the realm of computing, primarily due to its potential for energy efficient computation. Reversible cryptographic logic is an important area in applications such as signal processing, nanotechnology, bio-information, low power and lightweight applications and cyber security. The area and power constraints are as well taken into account of cryptographic protocol. In addition, intruders and hackers may snoop or modify identified data sent over the channel. Reversible cryptographic logic can be installed to prevent this situation. For this there is a need to study with optimal metrics viz. quantum cost, area, and performance. The feedback shift register is used for encryption and decryption techniques in a symmetrical way. This paper presents a comprehensive mathematical modeling framework for reversible logic circuits, focusing on the fundamental principles that govern their operation. We explore various reversible gate designs, analyze their operational efficiencies, and derive mathematical expressions that describe their behavior. By employing tools from combinatorial optimization and linear algebra, we investigate the trade-offs between circuit complexity and energy consumption. The modeling framework is validated through simulation results, which illustrate the advantages of reversible logic over traditional irreversible circuits in specific applications. Our findings highlight the significance of reversible logic in advancing quantum computing, low power digital systems and sustainable computing paradigms.