Mpofu, Kelvin TMthunzi-Kufa, PatienceCarpentieri, BShams, M2026-02-272026-02-272025-11DOI: 10.5772/intechopen.1012847http://hdl.handle.net/10204/14713As quantum computing continues its rapid progression, traditional cryptographic schemes based on the hardness of integer factorization and discrete logarithms, such as RSA and ECC, face obsolescence. This chapter explores the number theoretic underpinnings of Post-Quantum Cryptography (PQC), surveying emerging quantum-resistant protocols including lattice-based, code-based, multivariate polynomial, and isogeny-based cryptography. We analyze the mathematical assumptions behind their security, the role of hard problems in number theory (e.g., shortest vector problem, syndrome decoding, supersingular isogeny graphs), and the computational implications of these approaches. Furthermore, the chapter discusses the transition from classical cryptography to PQC within the NIST standardization process and how these cryptographic primitives align with the modern number theoretic and algorithmic challenges. Designed for both researchers and educators, this chapter aims to bridge theory and practice while emphasizing the continuing centrality of number theory in shaping the future of secure communication in the quantum era.FulltextenPost-quantum cryptographyLattice-based cryptographyIsogeny-based cryptographyCode-based cryptographyMultivariate cryptographyQuantum-resistant algorithmsNumber theoryQuantum computingCryptanalysisComputational hardnessPublic-key infrastructurePKIShor’s algorithmNIST standardizationBook Chaptern/a