This book constitutes the refereed post-conference proceedings of the Fourth International Conference on Number-Theoretic Methods in Cryptology, NuTMiC 2024, held in Szczecin, Poland, during June 24–26, 2024.The 9 full papers and 2 invited papers presented in this book were carefully reviewed and selected from 12 submissions.

.- Invited Talks. .- On the efficient representation of isogenies. .- Elliptic-curves factoring, witnesses and oracles. .- Elliptic Curves in Cryptography. .- On chains of pairing-friendly elliptic curves. .- Faster algorithms for isogeny computations over extensions of finite fields. .- Integral solutions of some systems of polynomial equations and constructing families of pairing-friendly elliptic curves with small ρ-value. .- Number Theory. .- Algebraic Equipage for Learning with Errors in Cyclic Division Algebras. .- From Worst to Average Case to Incremental Search Bounds of the Strong Lucas Test. .- Algebraic Structures and Public-Key Cryptography. .- A New Public Key Cryptosystem Based on the Cubic Pell Curve. .- The Case of Small Prime Numbers Versus the Okamoto-Uchiyama Cryptosystem. .- Compartment-based and Hierarchical Threshold Delegated Verifiable Accountable Subgroup Multi-signatures. .- Towards message recovery in NTRU Encryption with auxiliary data.