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This research introduces a new class of post-quantum cryptography based on the stellated tetrahedron topology, aiming to enhance data security against quantum computing threats.

May 25, 2026Open Access

Post-Quantum Cryptography Based on Stellated Tetrahedron Topology. An Alternative to NIST PQC.

Key Points

This research introduces a new class of post-quantum cryptography based on the stellated tetrahedron topology, aiming to enhance data security against quantum computing threats.
Introduced a cryptographic system based on the topology of the stellated tetrahedron with specific parameters (49 elements, 8 vertices).
Demonstrated that the inversion problem simplifies to understanding the phase θ(t) rather than computational complexity.
Developed a Python prototype and mathematical foundations for the new cryptographic method.
The proposed cryptographic system remains secure against Shor's algorithm, unlike traditional NIST PQC candidates.
Provides a security lead of 20–30 years even against a million-qubit quantum computer.
Can be implemented with available hardware, requiring a 57 Hz generator and tetrahedral resonator.

Abstract

The thirteenth publication of Resonance Group introduces a new class of post-quantum cryptography based on the topology of the stellated tetrahedron (49 elements, 8 vertices, 12 twist nodes, 256 ≡ 0). Unlike NIST PQC candidates (lattices, codes, multivariate equations), our system is not broken by Shor's algorithm — the inversion problem reduces to knowing the phase θ(t), not computational complexity. It uses eversion (256 ≡ 0) as a one-way function: forward transformation is simple, inversion requires the exact phase. The system provides a 20–30 year lead even against a hypothetical million-qubit quantum computer and can be implemented on existing hardware (57 Hz generator + tetrahedral resonator). Included: mathematical foundations, comparison with NIST PQC, Python prototype, and invitation for collaboration.

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