This dissertation addresses information security application advancement through designing and analyzing quantum circuit approaches. It focuses on both non-parametric circuit and parameterized quantum circuits (PQCs) models, addressing information security challenges across three main contribution areas. First, it introduces a numerical analysis approach to design a quantum multiplier based on the Toom-Cook 20.5-way method utilizing unbalanced Toom multiplication techniques to build multiplication with time-space efficient multiplication for cryptographic computations. Second, the research presents a depth-optimized elliptic curve point multiplication (ECPM) circuit designed for Shor-based quantum cryptanalysis circuits in binary field elliptic curves. By minimizing quantum cost and optimizing ECPM circuit depth, the proposed approach enhances computational efficiency, providing a robust foundation for cryptographic algorithms security evaluation, in particular, elaborating on the quantum attacks (e.g., cryptanalysis) aspect in information security. Thirdly, we investigate hybrid classical-quantum approaches for steganalysis by integrating PQCs with classical neural networks, aiming to improve the accuracy of classifiers in detecting concealed information within digital images, addressing steganalysis accuracy improvement challenges in information security.