The Mathematics of Cryptography & Data Compression

Abstract

This honors thesis focuses on Cryptography, Data Compression, and the link between the two in modern applications. Beginning with the notion that a link could exist due to the similar structure of the general methods, chapters individually explore the processes. An analysis of classical cryptography starts in the classical age and describes methods used until World War II. Shifting to modern computer implementations, the call for National standards introduced a new generation of consumer computer based cryptographic methods that needed to be strong enough for world-wide use. Switching focus to data compression, compression methods from the 1950s through current day are explored and demonstrated. Ultimately, the original question is answered by accepting that a link does exist, but not in the form of a combination it was originally thought to be. Rather, when used in series: compression then encryption, the compression adds to the overall security of the data and yields a smaller encrypted file.