Gauss once said "Mathematics is the queen of sciences, and number-theory the queen of mathematics," because he saw number-theory as the most pure form of mathematics with no real world applications. However, with the rise of the internet at the end of the 20th century number-theory found a very relevant application: cryptography, the science of communicating secretly. Until the rise of the internet, cryptography was mainly of interest for espionage and military purposes. However, with e-commerce and online privacy the technology has become exceedingly useful for the general population. Accordingly academic, commercial, and military research and development in this field has rapidly grown in the last 30 years. Modern crypto systems are based on number-theory, abstract algebra, and computational complexity theory. This talk will give a basic introduction to modern cryptography and will not assume any prior knowledge of abstract algebra, number theory, or computational complexity. This talk provides specific examples of uses of mathematics in key agreement Schemes and random number generation.