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arXiv:2202.05314 · IEEE International Symposium on Information Theory (ISIT)

Mosaics of Combinatorial Designs for Semantic Security on Quantum Wiretap Channels

Holger Boche, Minglai Cai, Moritz Wiese

Published Jun 26, 2022• 4 citations
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Abstract

We study semantic security for classical-quantum channels. Our security functions are functional forms of mosaics of combinatorial designs. We extend methods in [25] from classical channels to classical-quantum channels to demonstrate that mosaics of designs ensure semantic security for classical-quantum channels, and are also capacity achieving coding schemes. An advantage of these modular wiretap codes is that we provide explicit code constructions that can be implemented in practice for every channel, given an arbitrary public code.

DOI
10.1109/isit50566.2022.9834543

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We study semantic security for classical-quantum channels. Our security functions are functional forms of mosaics of combinatorial designs. We extend methods in [25] from classical channels to classical-quantum channels to demonstrate that mosaics of designs ensure semantic security for classical-quantum channels, and are also capacity achieving coding schemes. An advantage of these modular wiretap codes is that we provide explicit code constructions that can be implemented in practice for every channel, given an arbitrary public code.
We consider the problem of semantic security via classical-quantum and quantum wiretap channels and use explicit constructions to transform a non-secure code into a semantically secure code, achieving capacity by means of biregular irreducible functions. Explicit parameters in finite regimes can be extracted from theorems. We also generalize the semantic security capacity theorem, which shows that a strongly secure code guarantees a semantically secure code with the same secrecy rate, to any quantum channel, including the infinite-dimensional and non-Gaussian ones.
With the advent of quantum key distribution (QKD) systems, perfect (i.e. information-theoretic) security can now be achieved for distribution of a cryptographic key. QKD systems and similar protocols use classical error-correcting codes for both error correction (for the honest parties to correct errors) and privacy amplification (to make an eavesdropper fully ignorant). From a coding perspective, a good model for such a setting is the wire tap channel system introduced by Wyner in 1975. In this paper, we study fundamental limits and coding methods for wire tap channel systems. We provide a novel proof for the secrecy capacity theorem for wire tap channels and show how capacity achieving codes can be used to achieve the secrecy capacity for any wiretap channel. We also consider binary erasure channel and binary symmetric channel special cases for the wiretap channel system and propose specific practical codes. In some cases our designs achieve the secrecy capacity and in others the codes provide complete security at rates below secrecy capacity in some specific cases.
With the advent of quantum key distribution (QKD) systems, perfect (i.e. information-theoretic) security can now be achieved for distribution of a cryptographic key. QKD systems and similar protocols use classical errorcorrecting codes for both error correction (for the honest p arties to correct errors) and privacy amplification (to make an eavesdropper fully ignorant). From a coding perspective, a good model for such a setting is the wire tap channel introduced by Wyner in 1975. In this paper, we study fundamental limits and coding methods for wire tap channels. We provide a novel proof for the secrecy capacity theorem for wire tap channels and show how capacity achieving codes can be used to achieve the secrecy capacity for any wiretap channel. We also consider binary erasure channel and binary symmetric channel special cases for the wiretap channel and propose specific practical codes. In some cases our designs achieve the secrecy capacity and in others the codes provide complete security at rates below secrecy capacity in some specific cases.
Transmissions over the wiretap channel have been studied for a long time from the information theory standpoint. This has allowed to assess the secrecy performance against eavesdropping while ensuring reliable transmission towards the legitimate receiver. However, most previous studies rely on a number of assumptions which are far from practical wireless communications, like infinite length codewords, random coding, discrete channels or continuous channels with Gaussian signaling. In this paper, we show how the level of security at the physical layer can be assessed from the information theoretic standpoint while taking into account the constraints of practical transmissions over realistic wireless wiretap channels, i.e., by considering practical codes with finite length, discrete modulation formats and continuous channels with fading. For this purpose, we consider the notion of mutual information security, which is provably equivalent to semantic security. Our target is to show that classical and already implemented coding and modulation schemes can be used to achieve some level of security at the physical layer, opposed to approaches resorting to completely new designs tailored to secure transmissions. To corroborate this thesis, we consider some coding and modulation schemes compliant with the IEEE 802.16e (WiMax) standard and show how they can be used to achieve some given security level.
We propose a new proof method for direct coding theorems for wiretap channels where the eavesdropper has access to a quantum version of the transmitted signal on an infinite dimensional Hilbert space. This method yields errors that decay exponentially with increasing block lengths. Moreover, it provides a guarantee of a quantum version of semantic security, which is an established concept in classical cryptography and physical layer security. Semantic security has strong operational implications meaning essentially that the eavesdropper cannot use its quantum observation to gather any meaningful information about the transmitted signal. Therefore, it complements existing works which either do not prove the exponential error decay or use weaker notions of security. The main part of this proof method is a direct coding result on channel resolvability which states that there is only a doubly exponentially small probability that a standard random codebook does not solve the channel resolvability problem for the classical-quantum channel.