One-Time Pad, Arithmetic Coding and Logic Gates: An unifying theme using Dynamical Systems

In this letter, we prove that the perfectly secure One-Time Pad (OTP) encryption can be seen as finding the initial condition on the binary map under a random switch based on the perfectly random pad. This turns out to be a special case of Grangetto’s randomized arithmetic coding performed on the Binary Map. Furthermore, we derive the set of possible perfect secrecy systems using such an approach. Since OTP encryption is an XOR operation, we thus have a dynamical systems implementation of the XOR gate. We show similar implementations for other gates such as NOR, NAND, OR, XNOR, AND and NOT. The dynamical systems framework unifies the three areas to which Shannon made foundational contributions: lossless compression (Source Coding), perfect encryption (Cryptography), and design of logic gates (Computation). 1 Shannon’s Legacy: Coding, Cryptography and Computation Claude Shannon was one of the most important figures in the information revolution of the last century. He made foundational contributions to Coding, Cryptography and Computation. His master’s thesis used Boolean algebra to analyze and synthesize switching and computer circuits [1]. In 1948, he formulated a mathematical theory of communication where among other things, he was the first to define Entropy as the fundamental limit of noiseless lossless source coding [2]. In the following year, he proved the perfect secrecy