Elliptic Curve Modulation (ECM) for Extremely Robust Physical Layer Encryption
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866910957087752192 |
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| author | Oikonomou, Thrassos K. Karagiannidis, George K. |
| author_facet | Oikonomou, Thrassos K. Karagiannidis, George K. |
| contents | This paper introduces Elliptic Curve Modulation (ECM), a novel modulation scheme that can be leveraged to effectively shuffle transmitted data while maintaining symbol error probability (SEP) performance equivalent to unencrypted systems. By utilizing the well-distributed elliptic curve points over the field of large primes, ECM enhances symbol obfuscation, making it a powerful foundation for physical-layer encryption (PLE). Each symbol is mapped from a predefined key while preserving a minimum Euclidean distance constraint, ensuring strong security against adversarial inference without compromising error performance. Building on ECM's strong obfuscation capabilities, we propose ECM with dynamic rotation (ECM-DR) as a practical PLE scheme that achieves near-maximal obfuscation while balancing precomputation complexity. By leveraging a reduced subset of precomputed elliptic curve points and key-based dynamic constellation rotation, ECM-DR ensures that each transmission remains unpredictable, significantly enhancing security compared to traditional PLE schemes without additional computational cost. Security analysis confirms ECM's resilience to brute-force attacks, while numerical results demonstrate its strong obfuscation capabilities. Furthermore, ECM-DR achieves near-maximum information entropy while preserving the SEP performance of unencrypted quadrature amplitude modulation (QAM), offering an extremely robust solution for secure wireless communications. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_14153 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Elliptic Curve Modulation (ECM) for Extremely Robust Physical Layer Encryption Oikonomou, Thrassos K. Karagiannidis, George K. Signal Processing This paper introduces Elliptic Curve Modulation (ECM), a novel modulation scheme that can be leveraged to effectively shuffle transmitted data while maintaining symbol error probability (SEP) performance equivalent to unencrypted systems. By utilizing the well-distributed elliptic curve points over the field of large primes, ECM enhances symbol obfuscation, making it a powerful foundation for physical-layer encryption (PLE). Each symbol is mapped from a predefined key while preserving a minimum Euclidean distance constraint, ensuring strong security against adversarial inference without compromising error performance. Building on ECM's strong obfuscation capabilities, we propose ECM with dynamic rotation (ECM-DR) as a practical PLE scheme that achieves near-maximal obfuscation while balancing precomputation complexity. By leveraging a reduced subset of precomputed elliptic curve points and key-based dynamic constellation rotation, ECM-DR ensures that each transmission remains unpredictable, significantly enhancing security compared to traditional PLE schemes without additional computational cost. Security analysis confirms ECM's resilience to brute-force attacks, while numerical results demonstrate its strong obfuscation capabilities. Furthermore, ECM-DR achieves near-maximum information entropy while preserving the SEP performance of unencrypted quadrature amplitude modulation (QAM), offering an extremely robust solution for secure wireless communications. |
| title | Elliptic Curve Modulation (ECM) for Extremely Robust Physical Layer Encryption |
| topic | Signal Processing |
| url | https://arxiv.org/abs/2505.14153 |