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Advances in Mathematics of Communications

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

Lidong Chen, Dustin Moody

Published Sep 19, 2019• 4 citations
Publisher

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.
DOI
10.3934/amc.2020013

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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
The security of current public-key cryptosystems relies on the hardness of factoring large integers or solving discrete logarithm problems. However, these mathematical problems can be solved in polynomial time using a quantum computer. This vulnerability has prompted research into post-quantum cryptography using alternative mathematical problems that are secure in the era of quantum computers. In this regard, the National Institute of Standards and Technology (NIST) began to standardize post-quantum cryptography in 2016. In this expository article, we give an overview of recent research on post-quantum cryptography. In particular, we describe the construction and security of multivariate polynomial cryptosystems and lattice-based cryptosystems, which are the main candidates of post-quantum cryptography.
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.