Complexity-Style Resources in Cryptography

Abstract: Previously, the author has developed a framework within which to quantify and compare the resources consumed during computational-especially unconventional computational-processes (adding to the familiar resources of run-time and memory space such non-standard resources as precision and energy); it is natural and beneficial in this framework to employ various complexity-theoretic tools and techniques. Here, we seek an analogous treatment not of computational processes but of cryptographic protocols and similar, so as to be able to apply the existing arsenal of complexity-theoretic methods in new ways, in the derivation and verification of protocols in a wider, cryptographic context. Accordingly, we advocate a framework in which one may view as resources the costs-which may be related to computation, communication, information (including side-channel information) or availability of primitives, for example-incurred when executing cryptographic protocols, coin-tossing schemes, etc. The ultimate aim is to formulate as a resource, and be able to analyse complexity-theoretically, the security of these protocols and schemes.