Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Mathematics for industry

International Symposium on Mathematics, Quantum Theory, and Cryptography

Tsuyoshi Takagi, Masato Wakayama, Keisuke Tanaka, Noboru Kunihiro, Kazufumi Kimoto, Yasuhiko Ikematsu

Published Oct 22, 2020• 47 citations
Publisher

Abstract

This book presents the latest research on post-quantum cryptography. It covers the mathematics and quantum theory underlying secure modeling of the post quantum cryptography including e.g. mathematical study of the light-matter interaction models as well as quantum computing
DOI
10.1007/978-981-15-5191-8

Related papers

Modern Cryptography Volume 2

Zhiyong Zheng, Kun Tian, Fengxia Liu

This open access book covers the most cutting-edge and hot research topics and fields of post-quantum cryptography

Financial Mathematics and Fintech•Dec 10, 2022•10 citations

International Symposium on Mathematics, Quantum Theory, and Cryptography

•Jan 1, 2021•0 citations

Post-Quantum Cryptography: Mathematical Foundations of Secure Communication in the Quantum Computing Era

Ilhan Arda Al

Human computer interaction.•Oct 2, 2026•0 citations

O IMPACTO DA COMPUTAÇÃO QUÂNTICA NA CRIPTOGRAFIA MODERNA

Éric D’Andréa Rapatão, Renata Mirella Faria

ABSTRACT Quantum computing represents one of the most significant technological transformations of the 21st century, with the potential to profoundly alter the foundations of information security. This study aims to analyze the impacts of quantum computing on modern cryptographic systems, investigating both the threats posed by quantum algorithms and the protective alternatives currently under development. The research was carried out through a qualitative bibliographic review based on books, scientific articles, and technical publications in the fields of cryptography and quantum computing. The study examined Shor’s and Grover’s algorithms, demonstrating how their mathematical properties undermine classical cryptographic models, particularly public-key systems such as RSA. It also explored post-quantum and quantum cryptographic approaches, highlighting lattice-based solutions and quantum key distribution (QKD). The results indicate that, although quantum computing presents a real threat to digital security, it also drives the emergence of more resilient and innovative cryptographic techniques. It is concluded that the transition to a post-quantum era demands careful planning, international standardization, and continuous investment in research and infrastructure. Key-words: Quantum computing. Modern cryptography. Post-quantum cryptography. Information security.

Revista fisio&terapia.•Nov 13, 2025•0 citations

New Challenges in Post-Quantum Cryptography

Abraham Cano Aguilera, Raphael Frantz, Dimosthenis Iliadis-Apostolidis +8 more

New Challenges in Post-Quantum Cryptography presents a system-level perspective on the transition to post-quantum cryptography. Developed within the MSCA DN-ID QUARC consortium, the book examines how quantum computing challenges the security assumptions underlying modern cryptographic systems and explores the implications for communication networks, computing infrastructures, and digital trust frameworks. The book introduces the foundations of classical and post-quantum cryptography, discusses the quantum threat model, and examines migration strategies, hybrid cryptographic approaches, and crypto-agile system design. Particular attention is given to the deployment of post-quantum cryptography in networking environments, including protocols such as TLS, IPsec, and MACsec, as well as issues related to performance, scalability, hardware acceleration, virtualization, and secure communication infrastructures. Combining theoretical foundations with practical deployment considerations, the book explores how quantum-resilient security can be integrated into modern computing and communication infrastructures.

•Jan 1, 2026•0 citations

The Mathematical Foundation of Post-Quantum Cryptography

Chuanming Zong

In 1994, P. Shor discovered quantum algorithms that can break both the RSA cryptosystem and the ElGamal cryptosystem. In 2007, a Canadian company D-Wave demonstrated the first quantum computer. These events and quick further developments have brought a crisis to secret communication. In 2022, the National Institute of Standards and Technology (NIST) announced 4 candidates-CRYSTALS-Kyber, CRYSTALS-Dilithium, Falcon, and Sphincs+-for post-quantum cryptography standards. The first 3 are based on lattice theory and the last on Hash functions. In 2024, NIST announced 3 standards: FIPS 203 based on CRYSTALS-Kyber, FIPS 204 based on CRYSTALS-Dilithium, and FIPS 205 based on Sphincs+. The fourth standard based on Falcon is on the way. It is well known that the security of the lattice-based cryptosystems relies on the hardness of the shortest vector problem (SVP), the closest vector problem (CVP), and their generalizations. In fact, the SVP is a ball packing problem and the CVP is a ball covering problem. Furthermore, both SVP and CVP are equivalent to arithmetic problems for positive definite quadratic forms. There are several books and survey papers dealing with the computational complexity of the lattice-based cryptography for classical computers. However, there is no review article to demonstrate the mathematical foundation of the complexity theory. This paper will briefly introduce post-quantum cryptography and demonstrate its mathematical roots in ball packing, ball covering, and positive definite quadratic forms.

arXiv:2404.19186•Research•Jan 1, 2025•5 citations
ABSTRACT Quantum computing represents one of the most significant technological transformations of the 21st century, with the potential to profoundly alter the foundations of information security. This study aims to analyze the impacts of quantum computing on modern cryptographic systems, investigating both the threats posed by quantum algorithms and the protective alternatives currently under development. The research was carried out through a qualitative bibliographic review based on books, scientific articles, and technical publications in the fields of cryptography and quantum computing. The study examined Shor’s and Grover’s algorithms, demonstrating how their mathematical properties undermine classical cryptographic models, particularly public-key systems such as RSA. It also explored post-quantum and quantum cryptographic approaches, highlighting lattice-based solutions and quantum key distribution (QKD). The results indicate that, although quantum computing presents a real threat to digital security, it also drives the emergence of more resilient and innovative cryptographic techniques. It is concluded that the transition to a post-quantum era demands careful planning, international standardization, and continuous investment in research and infrastructure. Key-words: Quantum computing. Modern cryptography. Post-quantum cryptography. Information security.
New Challenges in Post-Quantum Cryptography presents a system-level perspective on the transition to post-quantum cryptography. Developed within the MSCA DN-ID QUARC consortium, the book examines how quantum computing challenges the security assumptions underlying modern cryptographic systems and explores the implications for communication networks, computing infrastructures, and digital trust frameworks. The book introduces the foundations of classical and post-quantum cryptography, discusses the quantum threat model, and examines migration strategies, hybrid cryptographic approaches, and crypto-agile system design. Particular attention is given to the deployment of post-quantum cryptography in networking environments, including protocols such as TLS, IPsec, and MACsec, as well as issues related to performance, scalability, hardware acceleration, virtualization, and secure communication infrastructures. Combining theoretical foundations with practical deployment considerations, the book explores how quantum-resilient security can be integrated into modern computing and communication infrastructures.
In 1994, P. Shor discovered quantum algorithms that can break both the RSA cryptosystem and the ElGamal cryptosystem. In 2007, a Canadian company D-Wave demonstrated the first quantum computer. These events and quick further developments have brought a crisis to secret communication. In 2022, the National Institute of Standards and Technology (NIST) announced 4 candidates-CRYSTALS-Kyber, CRYSTALS-Dilithium, Falcon, and Sphincs+-for post-quantum cryptography standards. The first 3 are based on lattice theory and the last on Hash functions. In 2024, NIST announced 3 standards: FIPS 203 based on CRYSTALS-Kyber, FIPS 204 based on CRYSTALS-Dilithium, and FIPS 205 based on Sphincs+. The fourth standard based on Falcon is on the way. It is well known that the security of the lattice-based cryptosystems relies on the hardness of the shortest vector problem (SVP), the closest vector problem (CVP), and their generalizations. In fact, the SVP is a ball packing problem and the CVP is a ball covering problem. Furthermore, both SVP and CVP are equivalent to arithmetic problems for positive definite quadratic forms. There are several books and survey papers dealing with the computational complexity of the lattice-based cryptography for classical computers. However, there is no review article to demonstrate the mathematical foundation of the complexity theory. This paper will briefly introduce post-quantum cryptography and demonstrate its mathematical roots in ball packing, ball covering, and positive definite quadratic forms.