Encrypt, Decode: The Role of Math in Information Security Throughout History

Daniel Panario, School of Mathematics and Statistics

For centuries, mathematics has provided methods and ideas to hide information. These mathematical methods enable us today to communicate with some degree of security and privacy.

In this talk, we visit a few key ideas used many times along history to encrypt messages. The basic fundamental primitives employed are substitutions and transpositions. We exemplify both the cryptographic methods used as well as the mathematical ideas required for some of these methods. Examples will be drawn from the Roman empire, the middle ages and the renaissance period.

The mathematics employed until the 19th century was relatively simple. In the 20th century, with the advent of computers, the required level of mathematics intensified. We conclude the talk by briefly commenting on current used cryptographical methods, introduced in the 1970’s, and on potential future developments for the area for the 21st century.