Abstract
We study semantically secure communication over state dependent (SD) wiretap channels (WTCs) with non-causal channel state information (CSI) at the encoder. This model subsumes all other instances of CSI availability as special cases, and calls for an efficient utilization of the state sequence both for reliability and security purposes. A lower bound on the secrecy-capacity, that improves upon the previously best known result by Chen and Han Vinck, is derived based on a novel superposition coding scheme. The improvement over the Chen and Han Vinck result is strict for some SD-WTCs. Specializing the lower bound to the case where CSI is also available to the decoder reveals that it is at least as good as the achievable formula by Chia and El-Gamal, which is already known to outperform the adaptation of the Chen and Han Vinck code to the encoder and decoder CSI scenario. The results are derived under the strict semantic security metric that requires negligible information leakage for all message distributions. The proof of achievability relies on a stronger version of the soft-covering lemma for superposition codes. The lower bound is shown to be tight for a class of reversely less-noisy SD-WTCs, thus characterizing the fundamental limit of reliable a secure communication. An explicit coding scheme that includes a key extraction phase via the random state sequence is also proposed.
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Notes
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More specifically, asymmetric ciphers that rely on the hardness of integer factorization or discrete logarithms can be completely broken using QCs via Shor’s algorithm (or a variant thereof) [3, 4]. Symmetric encryption, on the other hand, would be weakened by QC attacks but could regain its strength by increasing the size of the key [5]. This essentially follows since a QC can search through a space of size \(2^n\) in time \(2^{\frac{n}{2}}\), so by doubling the size of the key a symmetric cryptosystem would offer the same protection versus a QC attack, as the original system did versus a classic attack.
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Goldfeld, Z., Cuff, P., Permuter, H.H. (2017). Physical Layer Security over Wiretap Channels with Random Parameters. In: Dolev, S., Lodha, S. (eds) Cyber Security Cryptography and Machine Learning. CSCML 2017. Lecture Notes in Computer Science(), vol 10332. Springer, Cham. https://doi.org/10.1007/978-3-319-60080-2_11
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DOI: https://doi.org/10.1007/978-3-319-60080-2_11
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