Quantum Arithmetic Circuits in Public-Key Cryptography

2026-07-13

AI Summary

This work addresses the challenges in scaling quantum arithmetic circuits for public-key cryptanalysis, which are constrained by the no-cloning theorem, limited qubit counts, and circuit depth. To overcome these limitations, the authors propose innovative optimization strategies—including measurement-based uncomputation and conditionally cleaned ancilla qubits—to systematically redesign core quantum operations such as addition, multiplication, and modular exponentiation. By integrating these optimizations with a fault-tolerant runtime model and a rigorous resource estimation framework, the resulting circuits substantially reduce quantum resource overhead while preserving correctness and enhancing scalability. This approach provides an efficient and practical foundation for evaluating the feasibility of quantum cryptanalytic attacks under realistic hardware constraints.

Abstract

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.

Problem

• quantum arithmetic circuits
• public-key cryptanalysis
• no-cloning theorem
• qubit limitations
• circuit depth constraints

Innovation

• quantum arithmetic circuits
• measurement-based uncomputation
• conditionally clean ancilla
• modular exponentiation
• fault-tolerant quantum cryptanalysis