Abstract

There exists a deeply intertwined relation between cryptography and probability theory. Most fundamental concepts in cryptography, like cryptographic security, are based on probabilistic reasoning. This paper will explore concepts related to Chernoff bounds in cryptanalysis, pseudo-random number generation, entropy and information-theoretic security, and statistical randomness tests, through the use of rigorous de!nitions, theorems, and proofs. We conclude by exploring a historical case study of Andrew Gleason’s tail-bound attack on the Japanese “Coral” cipher during World War II, as well as some modern-day applications of probability theory in cryptography.