Number Theory and Cryptography

(4 Credits)

Cryptology existed since the ancient times with the art of ciphers and codes and has now evolved to become a branch of mathematics and computer science that develops the tools and the algorithms underpinning its two divisions: cryptography (development of protocols for the security, authentication and safety of communication) and cryptanalysis (the science of breaking cryptosystems). Before the modern era, cryptography was concerned solely with data confidentiality. For that purpose, classical cryptosystems involving symmetric-key algorithms have been developed. In recent decades, the field has been revolutionized with the invention of asymmetric-key encryption algorithms such as public-key ciphers and later expanded beyond confidentiality concerns to include techniques for user authentication, data integrity checking, data origin authentication, digital signatures, interactive proofs, and secure computation, amongst others. Modern cryptography hence relied on a great deal of fascinating mathematics arising from elementary number theory and the more recent advances expanded to include arithmetic algebraic geometry and algebraic number theory.