Mathematical Basis of Cryptography and its Applications in Nigerian Mobile Banking Security

This study examines the mathematical foundations of modern cryptographic systems and their applications to the security architecture of mobile banking platforms operated by Nigerian commercial banks. The rapid growth of mobile banking in Nigeria, driven by increasing smartphone penetration and the Central Bank of Nigeria's financial inclusion agenda, has expanded the attack surface for cyber threats targeting financial transactions. The study reviews the number-theoretic underpinnings of RSA encryption, including modular arithmetic, Euler's totient function, and the computational difficulty of integer factorisation, alongside the algebraic geometry foundations of elliptic curve cryptography. Using publicly available technical documentation and published cybersecurity audit reports from Nigerian financial technology firms, the study maps the deployment of these cryptographic primitives in transaction authentication, data encryption, and digital signature schemes used by leading Nigerian mobile banking applications. A comparative analysis of the cryptographic standards adopted by five major Nigerian banks is conducted, with particular attention to key length adequacy and compliance with guidelines issued by the Central Bank of Nigeria. Results indicate partial adoption of elliptic curve cryptography, which offers equivalent security to RSA at shorter key lengths, suggesting scope for improvement in computational efficiency and resistance to emerging quantum computing threats. Keywords: cryptography, RSA encryption, elliptic curve cryptography, mobile banking, Nigeria