Quantum Scrambling as a Cryptographic Resource: From Krylov Complexity to Physical Channel Authentication

We propose that quantum scrambling in many-body quantum channels constitutes a cryptographic resource that enables a fundamentally new class of channel authentication protocols. By synthesizing results from three independent lines of investigation, scrambling irreversibility in closed quantum systems, Krylov complexity-based channel detection, and sidereal filtering validated on real astrophysical data, we establish the following chain of reasoning. First, scrambling in symmetry-broken Heisenberg chains produces a practically irreversible dynamical process, with Poincaré recurrence times scaling as τ_rec ~ (1/ε)2^N - 1. Second, the Lanczos coefficients b_n of the channel Hamiltonian determine the functional form of the channel's temporal autocorrelation through the dynamical susceptibility, yielding a Gaussian template for linearly growing b_n. Third, in simulated experiments using template-matching classifiers applied to scrambling-derived correlation traces, compromised channels can be distinguished from clean channels with an area-under-curve (AUC) value of 0.99 under controlled realistic noise conditions. Fourth, as a proof-of-concept for extracting stable temporal fingerprints from noisy real-world signals, the sidereal filtering layer has been validated on 59,389 pulsar time-of-arrival measurements from the NANOGrav 15-year dataset. We argue that the combination of these results implies that scrambling defines a physical one-way signature: a measurable, predictable, and practically unforgeable channel fingerprint whose security rests on quantum-mechanical irreversibility rather than computational hardness assumptions. This work synthesizes and extends the author's prior publications on sidereal filtering, scrambling dynamics, and the QKD Eve Detector framework, connecting them into a unified cryptographic paradigm.