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NEW MISSION AND OPPORTUNITY FOR MATHEMATICS RESEARCHERS: CRYPTOGRAPHY IN THE QUANTUM ERA.

Lidong Chen, Dustin Moody

Published Jan 1, 2020• 0 citations
OpenAlex

Abstract

This article introduces the NIST post-quantum cryptography standardization process. We highlight the challenges, discuss the mathematical problems in the proposed post-quantum cryptographic algorithms and the opportunities for mathematics researchers to contribute.

Related papers

New mission and opportunity for mathematics researchers: cryptography in the quantum era

Lidong Chen, Dustin Moody

This article introduces the NIST post-quantum cryptography standardization process. We highlight the challenges, discuss the mathematical problems in the proposed post-quantum cryptographic algorithms and the opportunities for mathematics researchers to contribute.

Advances in Mathematics of Communications•Sep 19, 2019•4 citations

Illuminating the Path of Post-Quantum Cryptographic Protocols: A Survey of some Recent Literatures

Alvary Kefas Kwala, Alpna Mishra, Shri Kant

Abstract The imminent threat posed by quantum computers to modern public key cryptography has spurred the development of post-quantum cryptography (PQC) algorithms. Over the last two decades, the field of PQC research has thrived, yielding a diverse range of algorithms resilient against quantum attacks. These PQC algorithms are undergoing selection and standardization by prominent bodies ; such as National Institute of Standards and Technology (NIST). However, the challenge remains substantial, given the monumental task of migrating numerous new devices to PQC algorithms. This complex, multi-decade transition from classical cryptography to PQC, necessitates careful survey of research articles to consider the current post quantum cryptographic schemes, and key protective strategies against quantum threats, implementation feasibility, compliance and challenges of implementations. This will provide insight and future directions for new researchers and organizations. .

•Nov 6, 2023•0 citations

Post-Quantum Cryptography: Evaluating and Standardizing Quantum-Resistant Algorithms

Godwin Olaoye

The advent of quantum computing poses a significant threat to current cryptographic systems, particularly public-key algorithms such as RSA and ECC, which are vulnerable to quantum attacks like Shor's algorithm. Post-Quantum Cryptography (PQC) aims to develop and standardize quantum-resistant cryptographic algorithms to secure digital communications in the quantum era. This paper examines the current landscape of PQC, focusing on the evaluation and standardization efforts led by organizations such as the National Institute of Standards and Technology (NIST). We analyze the major families of quantum-resistant algorithms, including lattice-based, hash-based, code-based, multivariate, and isogeny-based cryptography, discussing their security guarantees, performance trade-offs, and implementation challenges. Furthermore, we review NIST's PQC standardization process, highlighting selected finalists and alternate candidates, and explore the ongoing transition challenges in adopting these algorithms across industries. Finally, we discuss future directions for PQC research, including hybrid cryptographic systems and the need for continued cryptanalysis to ensure long-term security. This work provides a comprehensive overview of the progress and challenges in deploying quantum-resistant cryptography to safeguard against emerging quantum threats.

•Apr 9, 2025•0 citations

Post-Quantum Cryptography for Navigating Challenges and Exploring Opportunities

Tejinder Sharma, Shivangi, Rishab Sharma

The rise of quantum computing poses a significant threat to the security of such classical cryptographic systems, as they inherently depend on the computational difficulty of problems such as integer factorization and discrete logarithm. Examining Theoretical Foundations of Post-Quantum Cryptography: Challenges and Opportunities for Building Secure Cryptographic Protocols in the PostQuantum World This paper aims to explore how quantum computers will affect the current state of cryptography, contributing towards the ongoing discussion to upgrade our cryptographic systems' foundations in the face of potential quantum attacks and assessing the efforts for developing quantum-resilient algorithms. Quantum computers promise unprecedented computation power by harnessing the strange properties of quantum mechanics. While quantum algorithms still pose a significant threat to conventional cryptography, the emergence of post-quantum algorithms offer hope to secure our data in the quantum era

International Journal of Research and Review in Applied Science Humanities and Technology•Jan 30, 2025•3 citations

Post-Quantum Cryptography: Current Developments, Challenges, and Future Directions

Wiliam Fernando

Quantum computing poses a significant threat to existing cryptosystems, as Shor's and Grover's algorithms efficiently solve the underlying mathematical problems of classical cryptographic algorithms. Post-Quantum Cryptography (PQC) provides a proactive response to this emerging threat, enabling resilience against quantum attacks. Researchers have extensively explored various mathematical structures believed to be resilient against quantum attacks across several PQC families. The NIST PQC standardisation project demonstrates the global need to integrate PQC into existing digital systems, even before the quantum era. Practical use cases of PQC schemes in various areas, along with the associated challenges, have been thoroughly studied to understand future research directions that must be followed for the better optimisation of real-world PQC implementation in a quantum-safe future.

Path of Science•Jun 30, 2025•2 citations

CRYPTOGRAPHIC SECURITY IN THE ERA OF QUANTUM COMPUTERS: THE CONCEPT AND DEVELOPMENT PROSPECTS OF POST-QUANTUM CRYPTOGRAPHY

Dilnoz Muhamediyeva, Farhad Tagaev

This article analyzes the threats to the security of modern cryptographic systems posed by the development of quantum computers, as well as the emergence of the concept of post-quantum cryptography as a solution to these problems. The study demonstrates that classical public-key cryptosystems, particularly RSA, DSA, and elliptic curve-based algorithms, can be broken using quantum algorithms. At the same time, new cryptographic systems based on hash functions, codes, lattices, and multivariate quadratic equations are considered a promising direction. The main challenges related to the efficiency, reliability, and applicability of post-quantum cryptography are also highlighted. As a result, the necessity of developing new cryptographic standards to ensure future information security is demonstrated.

•May 3, 2026•0 citations
Abstract The imminent threat posed by quantum computers to modern public key cryptography has spurred the development of post-quantum cryptography (PQC) algorithms. Over the last two decades, the field of PQC research has thrived, yielding a diverse range of algorithms resilient against quantum attacks. These PQC algorithms are undergoing selection and standardization by prominent bodies ; such as National Institute of Standards and Technology (NIST). However, the challenge remains substantial, given the monumental task of migrating numerous new devices to PQC algorithms. This complex, multi-decade transition from classical cryptography to PQC, necessitates careful survey of research articles to consider the current post quantum cryptographic schemes, and key protective strategies against quantum threats, implementation feasibility, compliance and challenges of implementations. This will provide insight and future directions for new researchers and organizations. .
The advent of quantum computing poses a significant threat to current cryptographic systems, particularly public-key algorithms such as RSA and ECC, which are vulnerable to quantum attacks like Shor's algorithm. Post-Quantum Cryptography (PQC) aims to develop and standardize quantum-resistant cryptographic algorithms to secure digital communications in the quantum era. This paper examines the current landscape of PQC, focusing on the evaluation and standardization efforts led by organizations such as the National Institute of Standards and Technology (NIST). We analyze the major families of quantum-resistant algorithms, including lattice-based, hash-based, code-based, multivariate, and isogeny-based cryptography, discussing their security guarantees, performance trade-offs, and implementation challenges. Furthermore, we review NIST's PQC standardization process, highlighting selected finalists and alternate candidates, and explore the ongoing transition challenges in adopting these algorithms across industries. Finally, we discuss future directions for PQC research, including hybrid cryptographic systems and the need for continued cryptanalysis to ensure long-term security. This work provides a comprehensive overview of the progress and challenges in deploying quantum-resistant cryptography to safeguard against emerging quantum threats.
The rise of quantum computing poses a significant threat to the security of such classical cryptographic systems, as they inherently depend on the computational difficulty of problems such as integer factorization and discrete logarithm. Examining Theoretical Foundations of Post-Quantum Cryptography: Challenges and Opportunities for Building Secure Cryptographic Protocols in the PostQuantum World This paper aims to explore how quantum computers will affect the current state of cryptography, contributing towards the ongoing discussion to upgrade our cryptographic systems' foundations in the face of potential quantum attacks and assessing the efforts for developing quantum-resilient algorithms. Quantum computers promise unprecedented computation power by harnessing the strange properties of quantum mechanics. While quantum algorithms still pose a significant threat to conventional cryptography, the emergence of post-quantum algorithms offer hope to secure our data in the quantum era
Quantum computing poses a significant threat to existing cryptosystems, as Shor's and Grover's algorithms efficiently solve the underlying mathematical problems of classical cryptographic algorithms. Post-Quantum Cryptography (PQC) provides a proactive response to this emerging threat, enabling resilience against quantum attacks. Researchers have extensively explored various mathematical structures believed to be resilient against quantum attacks across several PQC families. The NIST PQC standardisation project demonstrates the global need to integrate PQC into existing digital systems, even before the quantum era. Practical use cases of PQC schemes in various areas, along with the associated challenges, have been thoroughly studied to understand future research directions that must be followed for the better optimisation of real-world PQC implementation in a quantum-safe future.
This article analyzes the threats to the security of modern cryptographic systems posed by the development of quantum computers, as well as the emergence of the concept of post-quantum cryptography as a solution to these problems. The study demonstrates that classical public-key cryptosystems, particularly RSA, DSA, and elliptic curve-based algorithms, can be broken using quantum algorithms. At the same time, new cryptographic systems based on hash functions, codes, lattices, and multivariate quadratic equations are considered a promising direction. The main challenges related to the efficiency, reliability, and applicability of post-quantum cryptography are also highlighted. As a result, the necessity of developing new cryptographic standards to ensure future information security is demonstrated.