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On Split-State Quantum Tamper Detection and Non-Malleability

Thiago Bergamaschi, Naresh Goud Boddu

TL;DR

The paper advances quantum tamper-detection by showing that a multipartite quantum encoding across at least $3$ shares enables tamper-detection against split-state tampering with bounded entanglement, a feat impossible for classical codes. It provides a concrete 3-split tamper-detection code with constant rate and inverse-subexponential error in the bounded-storage regime, built from quantum-secure non-malleable extractors and unitary 2-designs. Beyond the code itself, the authors develop a blueprint to turn these codes into tamper-detecting secret sharing schemes and establish links to quantum encryption/authentication, highlighting how tamper-detection naturally implies a form of encryption of shares. They also connect their constructions to leakage-resilient secret sharing and to non-malleable quantum encryption notions, yielding a framework that unifies tamper-resilience, secret sharing, and encryption in the quantum setting. The work raises open questions about optimal capacity, LOCC tamper-detection, and extensions to quantum secrets, while providing concrete building blocks for tamper-detecting quantum cryptographic primitives with practical rate and security guarantees.

Abstract

Tamper-detection codes (TDCs) are fundamental objects at the intersection of cryptography and coding theory. A TDC encodes messages in such a manner that tampering the codeword causes the decoder to either output the original message, or reject it. In this work, we study quantum analogs of one of the most well-studied adversarial tampering models: the so-called $t$-split-state tampering model, where the codeword is divided into $t$ shares, and each share is tampered with "locally". It is impossible to achieve tamper detection in the split-state model using classical codewords. Nevertheless, we demonstrate that the situation changes significantly if the message can be encoded into a multipartite quantum state, entangled across the $t$ shares. Concretely, we define a family of quantum TDCs defined on any $t\geq 3$ shares, which can detect arbitrary split-state tampering so long as the adversaries are unentangled, or even limited to a finite amount of pre-shared entanglement. Previously, this was only known in the limit of asymptotically large $t$. As our flagship application, we show how to augment threshold secret sharing schemes with similar tamper-detecting guarantees. We complement our results by establishing connections between quantum TDCs and quantum encryption schemes.

On Split-State Quantum Tamper Detection and Non-Malleability

TL;DR

The paper advances quantum tamper-detection by showing that a multipartite quantum encoding across at least shares enables tamper-detection against split-state tampering with bounded entanglement, a feat impossible for classical codes. It provides a concrete 3-split tamper-detection code with constant rate and inverse-subexponential error in the bounded-storage regime, built from quantum-secure non-malleable extractors and unitary 2-designs. Beyond the code itself, the authors develop a blueprint to turn these codes into tamper-detecting secret sharing schemes and establish links to quantum encryption/authentication, highlighting how tamper-detection naturally implies a form of encryption of shares. They also connect their constructions to leakage-resilient secret sharing and to non-malleable quantum encryption notions, yielding a framework that unifies tamper-resilience, secret sharing, and encryption in the quantum setting. The work raises open questions about optimal capacity, LOCC tamper-detection, and extensions to quantum secrets, while providing concrete building blocks for tamper-detecting quantum cryptographic primitives with practical rate and security guarantees.

Abstract

Tamper-detection codes (TDCs) are fundamental objects at the intersection of cryptography and coding theory. A TDC encodes messages in such a manner that tampering the codeword causes the decoder to either output the original message, or reject it. In this work, we study quantum analogs of one of the most well-studied adversarial tampering models: the so-called -split-state tampering model, where the codeword is divided into shares, and each share is tampered with "locally". It is impossible to achieve tamper detection in the split-state model using classical codewords. Nevertheless, we demonstrate that the situation changes significantly if the message can be encoded into a multipartite quantum state, entangled across the shares. Concretely, we define a family of quantum TDCs defined on any shares, which can detect arbitrary split-state tampering so long as the adversaries are unentangled, or even limited to a finite amount of pre-shared entanglement. Previously, this was only known in the limit of asymptotically large . As our flagship application, we show how to augment threshold secret sharing schemes with similar tamper-detecting guarantees. We complement our results by establishing connections between quantum TDCs and quantum encryption schemes.
Paper Structure (339 sections, 290 theorems, 700 equations, 55 figures, 3 tables, 44 algorithms)

This paper contains 339 sections, 290 theorems, 700 equations, 55 figures, 3 tables, 44 algorithms.

Table of Contents

  1. Introduction
  2. Summary of contributions
  3. Main Code Construction.
  4. Applications to Tamper-Resilient Secret Sharing.
  5. Connections to Quantum Encryption Schemes.
  6. Related Work
  7. Our Techniques
  8. Non-Malleability implies Quantum Tamper Detection
  9. Tamper-Detection Codes in the Bounded Storage Model
  10. Tamper-Detecting Secret Sharing Schemes against Lo
  11. Discussion
  12. Preliminaries
  13. Quantum and Classical Information Theory
  14. Basic General Notation
  15. Quantum States and Registers
  16. ...and 324 more sections

Key Result

theorem thmcountertheorem

For every $n\in \mathbb{N}$, $\gamma\in (0, \frac{1}{20})$, there exists a quantum tamper detection code secure against the 3-split-state tampering model $\mathsf{LO}_{\Theta(\gamma n)}^3$, of blocklength $n$, rate $\frac{1}{11} - \gamma$, and error $2^{-n^{\Omega(1)}}$.

Figures (55)

  • Figure 1: The Quantum Split-State Tampering Model, $t=3$Boddu2023SplitState. A (possibly entangled) message $M$ is encoded, and subsequently tampered with using quantum channels $U, V, W$, jointly with an entangled state on registers $E_1, E_2, E_3$.
  • Figure 2: Quantum TDC against $\mathsf{LO}^{t+1}$.
  • Figure 3: A "Tamper-Detecting" Secret Sharing Scheme
  • Figure 4: Clifford Twirling with Side Information.
  • Figure 5: $t$-split-state tampering model for $t=3$.
  • ...and 50 more figures

Theorems & Definitions (585)

  • theorem thmcountertheorem: 3-Split Tamper Detection Codes
  • theorem thmcountertheorem: Tamper-Detecting Quantum Secret Sharing
  • theorem thmcountertheorem: Tamper-Detection Codes Encrypt their Shares
  • definition thmcounterdefinition: Quantum Non-Malleable Codes Boddu2023SplitState
  • definition thmcounterdefinition: Schatten $p$-norm
  • definition thmcounterdefinition: Trace distance
  • definition thmcounterdefinition
  • definition thmcounterdefinition: Conditioning
  • definition thmcounterdefinition
  • definition thmcounterdefinition: The Schmidt Number, Terhal1999SchmidtNF
  • ...and 575 more