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

TL;DR

This paper proposes a new cryptographic framework based on the continuous logarithm in the complex circle, aiming to enable classical algorithms to be secure against quantum attacks by leveraging spectral properties.

Contribution

It introduces a novel approach using the complex circle's spectral properties to adapt classical cryptographic algorithms for post-quantum security.

Findings

Reintroduction of classical algorithms into post-quantum context

Utilization of spectral properties for cryptographic robustness

Framework adaptable to various cryptographic schemes

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.