A 2020 Scientific Reports paper by Byoung S. Ham proposes an 'unconditionally secured classical key distribution' (USCKD) protocol: bright coherent light traverses a round-trip double Mach–Zehnder interferometer, Bob and Alice each choose a random phase basis, and the composed unitary transformation makes the shared key deterministic for the legitimate parties while supposedly perfectly random to an eavesdropper — yielding information-theoretic (unconditional) security on conventional, optically amplified fiber at backbone speeds. The author's quantitative security analysis is explicitly deferred — the BER/security discussion closes with 'More detailed analysis is beyond the present scope' — leaving open a rigorous proof against all classes of active attacks, the robustness of the measurement-indistinguishability mechanism under realistic impairments, and whether the claimed network-initialization authentication withstands man-in-the-middle adversaries. No independent security analysis of the protocol is known in the literature. The open problem is the deferred analysis itself: formalize the protocol as a cryptographic key-distribution game against a general eavesdropper and either prove a quantitative information-theoretic bound on Eve's knowledge of the sifted key — reconciling the claim with Shannon-type impossibility results — or exhibit a concrete attack breaking the claimed unconditional security, including the robustness of the security mechanism under realistic channel and device impairments.

Background

Quantum key distribution (QKD) delivers secret keys whose security rests on quantum physics: an eavesdropper measuring nonorthogonal single-photon states unavoidably disturbs them (no-cloning theorem), so intrusion is detectable. In practice QKD suffers from detector loopholes, channel loss, and low key rates, and it is hard to integrate into wavelength-multiplexed optical backbones. The one-time-pad (OTP) cipher — bitwise XOR of the message with a truly random key of the same length — is the only known perfectly secret cipher, but it needs key bits at the message rate, which QKD cannot supply at backbone speeds.

The source paper (Ham, Scientific Reports 10:11687, 2020, DOI 10.1038/s41598-020-68038-7) proposes USCKD to close this gap using bright coherent light on ordinary fiber. The protocol runs over a Mach–Zehnder interferometer (MZI), a two-path interferometer in which a beam splitter divides light into two arms and a second beam splitter recombines it; the relative phase φ\varphi between the arms decides which output port lights up, summarized by a visibility V=(Ij−Ii)/(Ij+Ii)V=(I_j-I_i)/(I_j+I_i) equal to ±1\pm 1 for φ∈{0,π}\varphi\in\{0,\pi\}. Bob encodes a bit in a randomly chosen phase basis φ∈{0,π}\varphi\in\{0,\pi\} over a pair of transmission channels; Alice chooses her own random phase ψ\psi and returns the light through the same channels. The double pass composes the two MZI transformations into the identity when φ=ψ\varphi=\psi and a port-swap inversion when φ≠ψ\varphi\neq\psi, so each party learns deterministically whether the bases matched without announcing their choices; matched bases set a key bit and mismatched instances are reserved for eavesdropping monitoring. Ham attributes unconditional security to two mechanisms: measurement indistinguishability (an eavesdropper tapping the channels supposedly cannot distinguish the superposed paths or phases) and 'deterministic randomness' (the key is deterministic for the parties yet perfectly random for Eve). Against the memory-based attack — Eve records all traffic and later flips a guessed key block coherently — the protocol adds sifting or a per-bit 'network initialization' in which Alice resets the interferometer with a random phase turbulence δ\delta and a short public-announcement sequence; this initialization is also proposed as authentication. Security against the memory attack is quantified as η=2−n\eta=2^{-n} for an nn-bit block (a 128-bit key is called computationally infeasible to guess), and the bit-error-rate budget BER=BERnet+BERcompBER=BER_{net}+BER_{comp} likewise mixes network noise with computational complexity. Compatibility with erbium-doped fiber amplifiers (EDFAs — the optical amplifiers placed every 10–100 km in backbone fiber links), whose phase shift Ham says can be compensated by laser locking, is claimed as a second novelty.

This is where the scientific tension lies. Shannon's classical theorem ('Communication Theory of Secrecy Systems', 1949) shows that perfect secrecy requires a key with entropy equal to the message, and no information-theoretic secret-key agreement is possible over channels an adversary can read without disturbance — e.g., via a passive beam-splitting tap of bright coherent light — unless the legitimate parties hold a physical channel advantage. Ham's security argument stays at the level of interferometric visibility and plausibility, and the paper explicitly defers the rest: the BER/security section ends with 'More detailed analysis is beyond the present scope.' What is missing is a formal, quantitative security treatment of the protocol, or a concrete attack on it.

Problem Statement

Determine, by rigorous quantitative analysis, whether the unconditional-security claim of the USCKD protocol of Ham (Scientific Reports 10:11687, 2020) is correct — the analysis its author explicitly deferred as beyond the paper's scope. Concretely:

  1. Formalize the round-trip double-MZI protocol — Bob's random phase basis φ∈{0,π}\varphi\in\{0,\pi\}, Alice's random phase ψ∈{0,π}\psi\in\{0,\pi\}, the double unitary transformation (identity iff φ=ψ\varphi=\psi, inversion otherwise), the resulting key-setting and sifting rule, and the network-initialization procedure with its public announcements (Tables 1–3 of the source paper) — as a key-distribution task against a general eavesdropper with physical access to the paired transmission channels.

  2. Either prove a quantitative information-theoretic security bound on the sifted key — e.g., Eve's distinguishing advantage or per-block guessing probability as a function of block length nn and channel parameters, consistent with the claimed η=2−n\eta=2^{-n} — covering at minimum passive beam-splitting taps of the bright coherent light, store-and-process (memory-based) attacks on key blocks, coherent intercept-resend, and man-in-the-middle manipulation of the network-initialization sequence; or exhibit a concrete, physically implementable attack that violates the claimed bound. An affirmative proof must identify the physical asymmetry that prevents Eve from copying the bright signals, thereby reconciling the claim with Shannon's theorem that perfectly secret key agreement is impossible over channels an adversary reads without disturbance.

  3. Establish whether the measurement-indistinguishability mechanism on which the security claim rests survives realistic channel and device impairments — environmental phase noise, EDFA-amplified links, finite detector sensitivity, nonideal beam splitters, polarization effects — to the degree the security argument requires, quantitatively (visibility/BER degradation and its effect on Eve's information).

  4. Make explicit what authentication assumption the initialization-based authentication relies on, and whether it withstands active adversaries.

A resolution requires item 1 and either branch of item 2 (proof or break); items 3 and 4 remain components of the same security determination, required only insofar as the chosen branch depends on them, jointly supporting the single objective of establishing or refuting the protocol's unconditional security.

References

  1. Byoung S. Ham, 'Unconditionally secured classical cryptography using quantum superposition and unitary transformation', Scientific Reports 10, 11687 (2020). DOI: 10.1038/s41598-020-68038-7, https://doi.org/10.1038/s41598-020-68038-7
  2. Byoung S. Ham, 'Addressable optical key distribution for unconditionally secured cryptography using phase-controlled quantum superposition', arXiv:1807.08126 (2018), https://arxiv.org/abs/1807.08126
  3. Byoung S. Ham, 'Phase noise-immune unconditionally secured classical key distribution using doubly coupled Mach–Zehnder interferometer', arXiv:2009.02665 (2020), https://arxiv.org/abs/2009.02665
  4. Byoung S. Ham, 'Analysis of phase noise effects in a coupled Mach–Zehnder interferometer for a much stabilized free-space optical link', Scientific Reports 11 (2021). DOI: 10.1038/s41598-021-81522-y, https://doi.org/10.1038/s41598-021-81522-y
  5. Byoung S. Ham, 'Experimental demonstrations of unconditional security in a purely classical regime', Scientific Reports 11 (2021). DOI: 10.1038/s41598-021-83724-w, https://doi.org/10.1038/s41598-021-83724-w
  6. Byoung S. Ham, 'Network-Compatible Unconditionally Secured Classical Key Distribution via Quantum Superposition-Induced Deterministic Randomness', Cryptography 6(1), 4 (2022). DOI: 10.3390/cryptography6010004, https://doi.org/10.3390/cryptography6010004
  7. Byoung S. Ham, 'Investigation of unconditionally secured classical key distribution via a free space', 2022 13th International Conference on ICT Convergence (ICTC) (2022). DOI: 10.1109/ICTC55196.2022.9952944, https://doi.org/10.1109/ICTC55196.2022.9952944
  8. C. E. Shannon, 'Communication Theory of Secrecy Systems', Bell System Technical Journal 28 (1949). DOI: 10.1002/j.1538-7305.1949.tb00928.x, https://doi.org/10.1002/j.1538-7305.1949.tb00928.x
  9. Akinsanmi S. Ige, David Cavalluzzi, Ivan B. Djordjevic, Keith Runge, Pierre A. Deymier, 'Information encoding and encryption in acoustic analogues of qubits', Scientific Reports 14 (2024). DOI: 10.1038/s41598-024-65800-z, https://doi.org/10.1038/s41598-024-65800-z