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. Moreover, through 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, since they achieve secrecy capacity. Simulation results demonstrate the practical possibility of compromising physical layer security.
翻译:在经典的窃听模式中,爱丽丝希望与鲍勃可靠地沟通,而不会被正在窃听退化频道的Eve听到的Eve听到。实现物理层安全的系统往往依赖于一个错误校正代码,其速率低于Alice和Bob频道的香农能力,因此Bob可以可靠地解码,但是在Alice和Eve频道上方,因此Eve无法可靠地解码。对于有限的区块长度制度,已经提出了数度指标来描述信息泄漏的特征。在这里,我们评估一个新的指标,即成功指数,并展示它可以通过使用随机的Additive Noise Decododing(GRAND)来操作。实现物理层安全度安全度的系统,成功指数是自然的超能力模拟。此外,通过GRAND解析,我们通过直径的解析程序来显示一个真实的解析数据。我们通过直径解的解调数据来评估Everical discodeal,我们通过直径的解析的解析数据,我们能够通过直径的解的解的路径来测量它。