Abstract
Algorithms are provided to build a large set of unique complex-valued orthogonal space-time block codes (STBCs) from a known or standard STBC. A physical layer security (PLS) scheme is proposed to take advantage of this set by alternating the STBC in use over a multiple-input single-output (MISO) or multiple-input multiple-output (MIMO) communications link between base station (BS) and user equipment (UE). A practical procedure is proposed and demonstrated to build individual STBCs from the set without use of a lookup table. The sufficient statistic is given and proven to allow for maximal ratio combining (MRC) by the intended receiver for all STBCs in the set. An algorithm is offered for the UE to update the MRC matrix in use as the STBC alternates. Definitions are provided for cryptograms, key residues (KRs), key residue classes (KRCs), and message and cryptogram residue classes pertaining to STBC PLS schemes. These definitions are used to present analysis of the information-theoretic security of the proposed PLS scheme to include message and key equivocation. Theoretical expected bit error rate (BER) for a passive eavesdropper is proven and plotted along with Monte Carlo simulations for confirmation. Discussion of different attack models is provided. Cost and attack complexity are compared between the proposed scheme and two related techniques from the literature.
Highlights
P HYSICAL layer security is currently a major area of research for use with emergent 5G networks and as a potential mitigation strategy towards quantum computing’s expected ability to rapidly break certain types of cryptography [1]–[5]
To better understand the message and cryptogram residue classes pertaining to space-time block codes (STBCs) physical layer security (PLS) schemes, we examine these classes for the Alamouti STBC employing 16-QAM data symbols and only the STBCs from one of its two key residue classes (KRCs)
Execution time for these algorithms may differ greatly depending upon the capabilities of the chosen platform and specific implementation; we present a simplistic complexity cost associated with the proposed PLS scheme based upon average number of operations required to build each STBC to aid in comparison with related works
Summary
P HYSICAL layer security is currently a major area of research for use with emergent 5G networks and as a potential mitigation strategy towards quantum computing’s expected ability to rapidly break certain types of cryptography [1]–[5]. A generalization and extension of this technique was presented in [17] where a pre-shared secret STBC was drawn from a set of complex-valued orthogonal STBCs. This article extends [17] by building a much larger set of STBCs, alternating the STBC after each use, and providing a generic framework for analysis of similar STBC based PLS schemes. To provide new and updated algorithms from [17] to build a much larger set of unique orthogonal STBCs for use with the proposed PLS scheme,. In Appendix D, a theoretical proof is given for Eve’s expected BER
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