Published May 31, 2026 | Version v1
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Prime-Gap-Based Quantum Indistinguishability: Security Proofs for Prime Harmonic QKD

Authors/Creators

  • 1. ROR icon University of South Florida

Description

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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Preprint: https://eprint.iacr.org/2026/109747 (URL)