[Resource Topic] 2022/156: Cosmic Security: Security Relative to Stateful Natures

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Cosmic Security: Security Relative to Stateful Natures

Authors: Benjamin Chan, Cody Freitag, and Rafael Pass


We define a framework for analyzing the security of cryptographic protocols that makes minimal assumptions about what a “realistic model of computation is”. In particular, whereas classical models assume that the attacker is a (perhaps non-uniform) probabilistic polynomial-time algorithm, and more recent definitional approaches also consider quantum polynomial-time algorithms, we consider an approach that is more agnostic to what computational model is physically realizable. Our notion of cosmic security considers a reduction-based notion of security that models attackers as PPT algorithms having access to some arbitrary unbounded stateful Nature. We also consider a more relaxed notion of cosmic security w.r.t. time-evolving, k-window, Natures that makes restrictions on Nature—roughly speaking, Nature’s behavior may depend on number of messages it has received and the content of the last k(\lambda)-messages (but not on “older” messages). We present both impossibility results and general feasibility results for our notions, indicating to what extent the Church-Turing hypotheses, and variants there-of, are needed for a well-founded theory of Cryptography.

ePrint: https://eprint.iacr.org/2022/156

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