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Integrity from Algebraic Manipulation Detection in Trusted-Repeater QKD Networks

Ailsa Robertson, Christian Schaffner, Sebastian R. Verschoor

TL;DR

This work tackles the challenge of secure long-distance QKD by addressing integrity guarantees in trusted-repeater networks. It introduces a novel protocol that combines Algebraic Manipulation Detection (AMD) codes with robust secret sharing and multi-path relaying to achieve confidentiality and integrity with Information-Theoretic Security, proven through a sequence of game-based reductions. The authors provide formal security analyses, demonstrate optimal overhead properties, and include an implementation demonstration to illustrate practicality. This approach reduces trust requirements on intermediate nodes and paves the way for scalable, provably secure quantum networks, while outlining clear avenues for extending to dynamic networks and stronger adversary-identification properties.

Abstract

Quantum Key Distribution (QKD) allows secure communication without relying on computational assumptions, but can currently only be deployed over relatively short distances due to hardware constraints. To extend QKD over long distances, networks of trusted repeater nodes can be used, wherein QKD is executed between neighbouring nodes and messages between non-neighbouring nodes are forwarded using a relay protocol. Although these networks are being deployed worldwide, no protocol exists which provides provable guarantees of integrity against manipulation from both external adversaries and corrupted intermediates. In this work, we present the first protocol that provably provides both confidentiality and integrity. Our protocol combines an existing cryptographic technique, Algebraic Manipulation Detection (AMD) codes, with multi-path relaying over trusted repeater networks. This protocol achieves Information Theoretic Security (ITS) against the detection of manipulation, which we prove formally through a sequence of games.

Integrity from Algebraic Manipulation Detection in Trusted-Repeater QKD Networks

TL;DR

This work tackles the challenge of secure long-distance QKD by addressing integrity guarantees in trusted-repeater networks. It introduces a novel protocol that combines Algebraic Manipulation Detection (AMD) codes with robust secret sharing and multi-path relaying to achieve confidentiality and integrity with Information-Theoretic Security, proven through a sequence of game-based reductions. The authors provide formal security analyses, demonstrate optimal overhead properties, and include an implementation demonstration to illustrate practicality. This approach reduces trust requirements on intermediate nodes and paves the way for scalable, provably secure quantum networks, while outlining clear avenues for extending to dynamic networks and stronger adversary-identification properties.

Abstract

Quantum Key Distribution (QKD) allows secure communication without relying on computational assumptions, but can currently only be deployed over relatively short distances due to hardware constraints. To extend QKD over long distances, networks of trusted repeater nodes can be used, wherein QKD is executed between neighbouring nodes and messages between non-neighbouring nodes are forwarded using a relay protocol. Although these networks are being deployed worldwide, no protocol exists which provides provable guarantees of integrity against manipulation from both external adversaries and corrupted intermediates. In this work, we present the first protocol that provably provides both confidentiality and integrity. Our protocol combines an existing cryptographic technique, Algebraic Manipulation Detection (AMD) codes, with multi-path relaying over trusted repeater networks. This protocol achieves Information Theoretic Security (ITS) against the detection of manipulation, which we prove formally through a sequence of games.
Paper Structure (27 sections, 6 theorems, 28 equations, 4 figures, 7 algorithms)

This paper contains 27 sections, 6 theorems, 28 equations, 4 figures, 7 algorithms.

Table of Contents

  1. Introduction
  2. Our contributions
  3. Related Work
  4. SECOQC
  5. Other solutions
  6. Outline
  7. Background
  8. Secret Sharing
  9. Robust secret sharing
  10. Weak robust secret sharing
  11. Algebraic Manipulation Detection (AMD)
  12. Trusted Repeater Networks
  13. Single QKD Links
  14. QKD Networks
  15. Using AMD Codes in Trusted Repeater Networks
  16. ...and 12 more sections

Key Result

lemma 1

In a network with $k$ individual links that are $\varepsilon$-private according to def:statprivacyqsideinfo, the overall state is $k \varepsilon$-private according to def:collectivestatprivacyqsideinfo.

Figures (4)

  • Figure 1:
  • Figure 2: Alice relays message $m$ to Bob on a single path $P_i$ of length $\ell=3$. Encryption on the $j$-th edge is done with an using key $q_{ij}$, resulting in ciphertext $c_{ij}$.
  • Figure 3:
  • Figure 4:

Theorems & Definitions (15)

  • definition 1: Secret-Sharing Scheme
  • definition 2: amd code cdfpw08
  • definition 3: statistical privacy against quantum side information
  • definition 4: collective statistical privacy against quantum side information
  • lemma 1
  • proof : Proof sketch
  • theorem 1: Confidentiality (informal)
  • definition 5: Shift-robustness
  • lemma 2
  • proof
  • ...and 5 more