Randomness appears in cryptography in various forms, ranging from the selection of cryptographic keys to the imperative that both ciphertexts and public keys remain indistinguishable from uniformly chosen elements. The former has been extensively studied over the years, standardized by NIST through a series of recommendations on the construction and analysis of Random Number Generators (RNG), and explored from both an algebraic and information-theoretical perspective.
The latter is a timely subject, as some vulnerabilities in recently proposed post-quantum key-encapsulation mechanisms and digital signatures have been initially identified in terms of the distinguishability of keys or ciphertext from random. In this presentation, we will begin with basic concepts of randomness, Coding Theory, and Discrete Fourier Analysis. These concepts will ultimately be utilized to illustrate a connection between the properties of codes and the entropy of random processes employed in Cryptography.