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

TL;DR

This paper presents Elliptic Curve Modulation (ECM), a new physical layer encryption method that offers high security and maintains error performance, using elliptic curve points for data obfuscation and dynamic constellation rotation.

Contribution

The paper introduces ECM and ECM-DR, novel modulation schemes leveraging elliptic curves for secure, robust physical layer encryption with minimal computational overhead.

Findings

ECM achieves strong data obfuscation with SEP performance similar to unencrypted systems.

ECM-DR provides near-maximal security through dynamic rotation and reduced precomputation.

Security analysis confirms ECM's resilience to brute-force attacks.

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.