[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-86307-en":3,"doc-seo-86307-105":30,"detail-sidebar-cat-0-en-105":91},{"code":4,"msg":5,"data":6},0,"success",{"doc_id":7,"user_id":8,"nickname":9,"user_avatar":10,"doc_module":4,"category_id":11,"category_name":12,"doc_title":13,"doc_description":14,"doc_content":15,"file_id":16,"file_url":17,"file_type":18,"file_size":19,"view_count":20,"is_deleted":4,"is_public":21,"is_downloadable":21,"audit_status":21,"page_count":22,"language":23,"language_code":24,"site_id":25,"html_lang":24,"table_of_contents":26,"faqs":27,"seo_title":13,"seo_description":14,"update_tm":28,"read_time":29},86307,13056703020460,"Valentina","https://ap-avatar.wpscdn.com/avatar/be000253dac470eee5d?_k=1778207105932848923",8,"Research & Report","Quantum Arithmetic Circuits in Public-Key Cryptography","Quantum computing’s rapid progress is driven by advances in the technology stack, including quantum error correction codes and efficient algorithms. Quantum arithmetic circuits form core building blocks, yet their design is constrained by the no-cloning theorem, qubit limitations, and circuit depth, reducing large-scale practicality. This chapter surveys quantum arithmetic circuits for public-key cryptanalysis, focusing on optimization such as measurement-based uncomputation and conditionally clean ancilla, while reviewing key operations and resource estimation methods.","arXiv :2607 . 11713v1 [ quant-ph] 13 Jul 2026  \nQuantum Arithmetic Circuits in Public-Key Cryptography  \nSiyi Wang 1⋆, Kyungbae Jang2 , Hyunji Kim2 , Anik Basu Bhaumik 1 , Anubhab Baksi3 , Hwajeong Seo2 , and Anupam Chattopadhyay 1  \n1 Nanyang Technological University, Singapore, Singapore  \n2 Hansung University, Seoul, South Korea  \n3 Lunds Universitets, Lund, Sweden  \nAbstract. 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.  \nWe 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.  \nIn brief, this chapter emphasizes strategies for designing resource-efficient quantum arithmetic circuits, providing a basis for realistic evaluations of quantum cryptanalytic capabilities.  \nKeywords: Quantum Computing · Quantum Arithmetic Circuit · Quantum Error Correction · Quantum Cryptanalysis · Public-key Cryptography  \n1 Introduction  \nBy leveraging the principles of quantum mechanics, quantum computing introduces new ways of processing information, with the potential to transform areas such as cryptography and materials science. Breakthroughs in the 1990s, particularly Shor’s factoring algorithm [93] and Grover’s search [42], demonstrated that quantum computers can achieve exponential and quadratic speedups over classical computing for certain problems, especially in cryptanalysis.  \nOne of the most directly impacted areas is public-key cryptography, which underpins secure communication in modern information systems. Schemes such  \n⋆ Corresponding author. Email: [siyi002@e.ntu.edu.sg](siyi002@e.ntu.edu.sg).  \n2 Wang et al.  \nas RSA [83] and elliptic curve cryptography (ECC) derive their security from the hardness of problems like integer factorization and the elliptic curve discrete logarithm problem. However, Shor’s algorithm can efficiently solve both problems on a quantum computer, rendering these widely used public-key systems vulnerable.  \nSpecifically, for the Integer Factorization Problem (IFP) underlying RSA encryption, the most computationally demanding component of Shor’s algorithm is the modular exponentiation. This operation consists of a sequence of modular arithmetic subroutines, such as modular addition and modular multiplication. In contrast, for the Elliptic Curve Discrete Logarithm Problem (ECDLP), which underpins ECC, Shor’s algorithm repeatedly executes point additions over a finite field. The computational complexity is mainly determined by the finite-field arithmetic operations, including modular addition, modular multiplication, and particularly modular division, the latter being the most resource-intensive operation. The efficiency of these basic quantum arithmetic blocks directly affects the scalability and practicality of quantum cryptanalysis. Therefore, optimizing quantum arithmetic circuits has become a critical research focus [108,113], as improvements in these designs can substantially reduce the resource requirements of large-scale quantum algorithms such as Shor’s algorithm.  \n1.1 Quantum Computing Basics  \n1. Quantum bits (Qubits) . It is the basic unit in quantum com","cbCaieMf7KlJ1bTm","https://ap.wps.com/l/cbCaieMf7KlJ1bTm","pdf",625657,4,1,28,"English","en",105,"# Introduction\n## Quantum Computing Basics\n## Evaluation Metrics\n# Quantum Arithmetic Circuits for Public-Key Cryptanalysis","[{\"question\":\"Why are quantum arithmetic circuits important in public-key cryptanalysis?\",\"answer\":\"They are fundamental building blocks for implementing the arithmetic required by quantum algorithms that attack public-key systems, such as modular exponentiation and finite-field operations.\"},{\"question\":\"What challenges make designing quantum arithmetic circuits difficult?\",\"answer\":\"The no-cloning theorem, limited qubit availability, and constraints on circuit depth significantly affect efficiency for large-scale quantum computing.\"},{\"question\":\"Which optimization strategies does the chapter highlight for resource-efficient circuit design?\",\"answer\":\"It emphasizes measurement-based uncomputation and conditionally clean ancilla to improve efficiency and reduce resource 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are quantum arithmetic circuits important in public-key cryptanalysis?","Question",{"text":75,"@type":76},"They are fundamental building blocks for implementing the arithmetic required by quantum algorithms that attack public-key systems, such as modular exponentiation and finite-field operations.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"What challenges make designing quantum arithmetic circuits difficult?",{"text":80,"@type":76},"The no-cloning theorem, limited qubit availability, and constraints on circuit depth significantly affect efficiency for large-scale quantum computing.",{"name":82,"@type":73,"acceptedAnswer":83},"Which optimization strategies does the chapter highlight for resource-efficient circuit design?",{"text":84,"@type":76},"It emphasizes measurement-based uncomputation and conditionally clean ancilla to improve efficiency and reduce resource 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