The Thermodynamics of Confidentiality

This work, of a foundational nature, establishes a connection between secure computation and the 2nd principle of thermodynamics. In particular we show that any deterministic computation, where the final state of the system is observable, must dissipate at least W K_B T ln(2). Here W is the information theoretic notion of remaining uncertainty as defined in Quantitative Information Flow, K_B the Boltzmann constant and T the system temperature. By contrast, for probabilistic computations thermodynamic work can be extracted from secure systems: in this case, again using information theoretic results, we provide bounds on the amount of work that can be extracted. Further we show that in deterministic systems the dissipated energy is an upper bound on Smith's remaining vulnerability, by doing so we provide the first thermodynamic interpretation of guess ability. Crucially, unlike much literature on the physics of computation, our focus is not a universal model but a software field of great practical relevance, namely security. We see this work as a genuine scientific advance with the potential to enhance the understanding of both confidentiality and dissipative systems in physics.