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Increasing Interference Detection in Quantum Cryptography using the Quantum Fourier Transform

Nicholas J. C. Papadopoulos, Kirby Linvill

TL;DR

The paper tackles vulnerability of QKD to partial information leakage and many-copies attacks by proposing memory-free QFT-based protocols: a two-pass QKD and a QFT-based three-pass direct encryption scheme. It provides a concrete encoding/decoding framework using phase scrambling and the quantum Fourier transform, along with a probabilistic formalism to compute eavesdropper-detection probabilities under various verification schemes. The results show that QFT-based verification can yield higher detection probabilities than BB84, even when verification schemes are public, and offer flexible design choices (compartmentalization) to tailor security to application needs. The work offers practical, memory-free implementations and a quantitative toolkit (including equations like $P_e(V,B)=1-\prod_{t\in V} \Pr_c(t,B)$) to guide protocol designers in selecting and analyzing robust eavesdropping-detection schemes for quantum communication.

Abstract

Quantum key distribution (QKD) and quantum message encryption protocols promise a secure way to distribute information while detecting eavesdropping. However, current protocols may suffer from significantly reduced eavesdropping protection when only a subset of qubits are observed by an attacker. In this paper, we present two quantum cryptographic protocols leveraging the quantum Fourier transform (QFT) and show their higher effectiveness even when an attacker measures only a subset of the transmitted qubits. The foremost of these protocols is a novel QKD method that leverages this effectiveness of the QFT while being more practical than previously proposed QFT-based protocols, most notably by not relying on quantum memory. We additionally show how existing quantum encryption methods can be augmented with a QFT-based approach to improve eavesdropping detection. Finally, we provide equations to analyze different QFT-based detection schemes within these protocols so that protocol designers can make custom schemes for their purpose.

Increasing Interference Detection in Quantum Cryptography using the Quantum Fourier Transform

TL;DR

The paper tackles vulnerability of QKD to partial information leakage and many-copies attacks by proposing memory-free QFT-based protocols: a two-pass QKD and a QFT-based three-pass direct encryption scheme. It provides a concrete encoding/decoding framework using phase scrambling and the quantum Fourier transform, along with a probabilistic formalism to compute eavesdropper-detection probabilities under various verification schemes. The results show that QFT-based verification can yield higher detection probabilities than BB84, even when verification schemes are public, and offer flexible design choices (compartmentalization) to tailor security to application needs. The work offers practical, memory-free implementations and a quantitative toolkit (including equations like ) to guide protocol designers in selecting and analyzing robust eavesdropping-detection schemes for quantum communication.

Abstract

Quantum key distribution (QKD) and quantum message encryption protocols promise a secure way to distribute information while detecting eavesdropping. However, current protocols may suffer from significantly reduced eavesdropping protection when only a subset of qubits are observed by an attacker. In this paper, we present two quantum cryptographic protocols leveraging the quantum Fourier transform (QFT) and show their higher effectiveness even when an attacker measures only a subset of the transmitted qubits. The foremost of these protocols is a novel QKD method that leverages this effectiveness of the QFT while being more practical than previously proposed QFT-based protocols, most notably by not relying on quantum memory. We additionally show how existing quantum encryption methods can be augmented with a QFT-based approach to improve eavesdropping detection. Finally, we provide equations to analyze different QFT-based detection schemes within these protocols so that protocol designers can make custom schemes for their purpose.
Paper Structure (15 sections, 1 theorem, 12 equations, 4 figures, 1 table)

This paper contains 15 sections, 1 theorem, 12 equations, 4 figures, 1 table.

Table of Contents

  1. Introduction
  2. Related Work
  3. Background: Notable Attacks on QKD Protocols
  4. Partial Information Leakage
  5. The Many-Copies Attack
  6. Memory-free Quantum Cryptographic Protocols using the QFT
  7. Quantum Key Distribution Protocol
  8. Interference Resistance
  9. Direct Message Encryption
  10. Probability of Interference Detection
  11. Probability of measuring correctly due to a phase error
  12. Rotation effect from previous qubits
  13. Probablity of measuring a qubit correctly
  14. Analysis of Verification Schemes
  15. Analogous Verification Scheme to BB84

Key Result

lemma thmcounterlemma

The probability of detection for our protocol is at least as great as that for BB84: $\Pr_{e,BB84}(V, B) \leq \Pr_{e,QFT}(V, B)$

Figures (4)

  • Figure 1: Example partial leakage from the BB84 protocol. Eve only measures some of the qubits Alice sends to Bob. She measures none of the verification qubits and therefore has no chance of detection.
  • Figure 2: The circuit for the quantum portion of the QFT-based QKD protocol presented in this paper.
  • Figure 3: The circuit for direct message encryption using the QFT.
  • Figure 4: Example verification schemes. Each square represents a transmitted qubit. Qubits marked with $v$ are used for verification, and qubits marked with $E$ are qubits that Eve measured. Qubits marked with $QFT$ denote compartments of QFT encoding. (a) BB84 with random verification qubit placement and Eve measuring all qubits. (b) Two-pass, QFT-based QKD with random verification qubit placement and Eve measuring all qubits. (c) Compartmentalized two-pass, QFT-based QKD with one verification qubit per key qubit. (d) Uncompartmentalized two-pass, QFT-based QKD with one verification qubit per key qubit. (e) Compartmentalized two-pass, QFT-based QKD with two verification qubits per key qubit. (f) Uncompartmentalized two-pass, QFT-based QKD with two verification qubits per key qubit. Eve is assumed to only measure key qubits in (c)-(f).

Theorems & Definitions (2)

  • lemma thmcounterlemma
  • proof : Proof sketch