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arXiv · 2501.10394

The Continuous Logarithm in the Complex Circle for Post-Quantum Cryptographic Algorithms

Jaafar Gaber
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Abstract

This paper introduces a novel cryptographic approach based on the continuous logarithm in the complex circle, designed to address the challenges posed by quantum computing. By leveraging its multi-valued and spectral properties, this framework enables the reintroduction of classical algorithms (DH, ECDSA, ElGamal, EC) and elliptic curve variants into the post-quantum landscape. Transitioning from classical or elliptic algebraic structures to the geometric and spectral properties of the complex circle, we propose a robust and adaptable foundation for post-quantum cryptography.

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Jaafar Gaber. 2024-12-24. The Continuous Logarithm in the Complex Circle for Post-Quantum Cryptographic Algorithms. https://arxiv.org/abs/2501.10394

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