Prime-Gap-Based Quantum Indistinguishability: Security Proofs for Prime Harmonic QKD

We prove the first closed-form security parameter for Prime Harmonic Modulation QKD: F_k = cos^2(pi*g_k / (2*p_k*p_{k+1})), where g_k is the prime gap. Under the Cramér conjecture, adjacent-state adversary advantage vanishes superpolynomially. The adaptive prime ladder provides post-quantum forward secrecy. First QKD security proof tied to prime number theory. Patent: PCT/US25/39370. Note: Also available on IACR ePrint: https://eprint.iacr.org/2026/109747

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Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-05-31
DOI
https://doi.org/10.5281/zenodo.20477227
Primary Topic
Coding theory and cryptography
Type
preprint
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preprint

Prime-Gap-Based Quantum Indistinguishability: Security Proofs for Prime Harmonic QKD

Will Daoud
Zenodo (CERN European Organization for Nuclear Research)
Coding theory and cryptography
preprint

Prime-Gap-Based Quantum Indistinguishability: Security Proofs for Prime Harmonic QKD

Will Daoud
preprint en

Abstract

We prove the first closed-form security parameter for Prime Harmonic Modulation QKD: F_k = cos^2(pi*g_k / (2*p_k*p_{k+1})), where g_k is the prime gap. Under the Cramér conjecture, adjacent-state adversary advantage vanishes superpolynomially. The adaptive prime ladder provides post-quantum forward secrecy. First QKD security proof tied to prime number theory. Patent: PCT/US25/39370. Note: Also available on IACR ePrint: https://eprint.iacr.org/2026/109747

Zenodo (CERN European Organization for Nuclear Research)
University of South Florida (US)
Coding theory and cryptography
DOIOpen Access PDFOpenAlex
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Prime-Gap-Based Quantum Indistinguishability: Security Proofs for Prime Harmonic QKD — Will Daoud · Zenodo (CERN European Organization for Nuclear Research) (2026) | TGRS Research Map | TGRS