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Number theory is a branch of pure mathematics that focuses on the properties and relationships of integers, especially prime numbers, divisibility, and modular arithmetic. It forms the mathematical backbone of modern cryptography, where secure communication relies on hard mathematical problems such as integer factorization and discrete logarithms. Cryptographic foundations use these concepts to design algorithms for encryption, digital signatures, and secure data exchange, ensuring confidentiality, integrity, and authentication in digital systems. For example, widely used cryptographic schemes like RSA and elliptic curve cryptography are built directly on number-theoretic principles, demonstrating how abstract mathematical ideas can have powerful real-world applications in protecting information in areas such as online banking, communication networks, and cybersecurity.
This lecture is part of CYB204 Applied mathematics in cyber in the Cyber Security department. The course has 15 recorded lectures across 5 series, all free to watch.