# Physical layer insecurity

In the classic wiretap model, Alice wishes to reliably communicate to Bob without being overheard by Eve who is eavesdropping over a degraded channel. Systems for achieving that physical layer security often rely on an error correction code whose rate is below the Shannon capacity of Alice and Bob's channel, so Bob can reliably decode, but above Alice and Eve's, so Eve cannot reliably decode. For the finite block length regime, several metrics have been proposed to characterise information leakage. Here we assess a new metric, the success exponent, and demonstrate it can be operationalized through the use of Guessing Random Additive Noise Decoding (GRAND) to compromise the physical-layer security of any moderate length code. Success exponents are the natural beyond-capacity analogue of error exponents that characterise the probability that a maximum likelihood decoding is correct when the code-rate is above Shannon capacity, which is exponentially decaying in the code-length. Success exponents can be used to approximately evaluate the frequency with which Eve's decoding is correct in beyond-capacity channel conditions. Through the use of GRAND, we demonstrate that Eve can constrain her decoding procedure so that when she does identify a decoding, it is correct with high likelihood, significantly compromising Alice and Bob's communication by truthfully revealing a proportion of it. We provide general mathematical expressions for the determination of success exponents as well as for the evaluation of Eve's query number threshold, using the binary symmetric channel as a worked example. As GRAND algorithms are code-book agnostic and can decode any code structure, we provide empirical results for Random Linear Codes as exemplars. Simulation results demonstrate the practical possibility of compromising physical layer security.

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