Quantum computing has advanced rapidly in recent decades, driven by developments across the technology stack, including quantum error-correcting codes and efficient quantum algorithms. Among these, quantum arithmetic circuits serve as fundamental building blocks for various promising algorithms. Despite their crucial role, the design of quantum arithmetic circuits faces challenges arising from the no-cloning theorem, qubit limitations, and circuit depth constraints, which significantly impact the efficiency of large-scale quantum computing. We provide an overview of quantum arithmetic circuits in the context of public-key cryptanalysis, with particular emphasis on optimization strategies such as measurement-based uncomputation and conditionally clean ancilla. We review state-of-the-art designs for essential arithmetic operations in public-key cryptanalysis such as addition, multiplication, and modular exponentiation. We also present an overview of the techniques used for fault-tolerant runtime and resource estimation in quantum cryptanalysis. In brief, this chapter emphasizes strategies for designing resource-efficient quantum arithmetic circuits, providing a basis for realistic evaluations of quantum cryptanalytic capabilities.
Emergence of fault-tolerant quantum computers (FTQC) brings about promise of harnessing the power of quantum computing at larger scale. At the same time, as quantum computers are expected to process more sensitive information, there is a need to understand the security issues in fault-tolerant quantum computers, and develop defenses for attacks that may compromise confidentiality or integrity of the data processed by FTQC. While noisy intermediate-scale quantum (NISQ) computers have already been studied from the security perspective, understanding security issues with FTQC is still an open research question. To address the missing research gap, this work presents the first exploration of possible security vulnerabilities of FTQC. The work presents analysis of possible threat models and outlines potential vulnerabilities of FTQC. Understanding the landscape of the threats can help lead to development of safer FTQC design at both software and hardware levels.