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<p>In this paper, we propose a novel physical-layer encryption scheme that integrates space–time spreading into polarization-division-multiplexed coherent optical systems. To strengthen key confidentiality, the method first employs the Kronecker product of Jones matrices to generate spatially spread keys that are mutually coupled across the in-phase and quadrature components of both polarization axes, thereby expanding the key space and suppressing vulnerabilities arising from partial key leakage. Subsequently, by applying time spreading based on the chromatic-dispersion transfer function, the spread keys evolve into continuous Gaussian-like sequences, a phenomenon that is theoretically explained by the superposition of discrete spreading and additive noise under the central limit theorem. This two-stage spatiotemporal spreading enables symbol-level masking, effectively distributing encrypted constellation points and substantially increasing the difficulty of unauthorized reconstruction. Comprehensive numerical simulations using Nyquist-shaped DP-<i>M</i>-QAM waveforms (<i>M</i> = 4, 16, 64) confirm that legitimate receivers can accurately regenerate and subtract the spatiotemporally spread keys, achieving bit-error-rate and normalized generalized mutual information performance equivalent to those of systems without encryption. In contrast, eavesdroppers—assumed to have full access to encrypted symbols—experience an SNR penalty of approximately 3 dB at the FEC threshold due to unknown-key-induced noise, indicating a clear, quantifiable security margin at the physical layer. Furthermore, spatially spread keys were validated using the NIST SP 800 − 22 randomness test suite, verifying their statistical soundness across multiple key-generation parameter domains. These results demonstrate that the proposed approach provides a practical, low-latency, and low-overhead physical-layer encryption mechanism that is compatible with modern coherent transceivers. The scheme offers a promising pathway to enhance the confidentiality of next-generation optical networks supporting data-center interconnects, 5G/6G infrastructure, and massively scalable cloud services.</p>

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Secure key generation via Jones matrix Kronecker product and time-spreading for polarization-multiplexed optical signals

  • 期刊论文

  • 发表日期：

    2026年3月30日

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  • Reika Suketomo,
  • Takahiro Kodama

摘要

In this paper, we propose a novel physical-layer encryption scheme that integrates space–time spreading into polarization-division-multiplexed coherent optical systems. To strengthen key confidentiality, the method first employs the Kronecker product of Jones matrices to generate spatially spread keys that are mutually coupled across the in-phase and quadrature components of both polarization axes, thereby expanding the key space and suppressing vulnerabilities arising from partial key leakage. Subsequently, by applying time spreading based on the chromatic-dispersion transfer function, the spread keys evolve into continuous Gaussian-like sequences, a phenomenon that is theoretically explained by the superposition of discrete spreading and additive noise under the central limit theorem. This two-stage spatiotemporal spreading enables symbol-level masking, effectively distributing encrypted constellation points and substantially increasing the difficulty of unauthorized reconstruction. Comprehensive numerical simulations using Nyquist-shaped DP-M-QAM waveforms (M = 4, 16, 64) confirm that legitimate receivers can accurately regenerate and subtract the spatiotemporally spread keys, achieving bit-error-rate and normalized generalized mutual information performance equivalent to those of systems without encryption. In contrast, eavesdroppers—assumed to have full access to encrypted symbols—experience an SNR penalty of approximately 3 dB at the FEC threshold due to unknown-key-induced noise, indicating a clear, quantifiable security margin at the physical layer. Furthermore, spatially spread keys were validated using the NIST SP 800 − 22 randomness test suite, verifying their statistical soundness across multiple key-generation parameter domains. These results demonstrate that the proposed approach provides a practical, low-latency, and low-overhead physical-layer encryption mechanism that is compatible with modern coherent transceivers. The scheme offers a promising pathway to enhance the confidentiality of next-generation optical networks supporting data-center interconnects, 5G/6G infrastructure, and massively scalable cloud services.