# Elliptic Curve Modulation (ECM) for Extremely Robust Physical Layer Encryption

Source: [Elliptic Curve Modulation (ECM) for Extremely Robust Physical Layer Encryption](<https://www.sota2.com/research/paper/68fa80591e209131cea9cc24>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-10-26T06:59:24.854Z

Authors: Thrassos K. Oikonomou, George K. Karagiannidis

Published: 2025-05-20T10:02:13.000Z

## Abstract

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.

## Recorded benchmark results

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## Original sources and implementation

[Original paper](<https://arxiv.org/abs/2505.14153>)

[PDF](<https://arxiv.org/pdf/2505.14153.pdf>)