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Generalized Quantum-assisted Digital Signature

Alberto Tarable, Rudi Paolo Paganelli, Elisabetta Storelli, Alberto Gatto, Marco Ferrari

TL;DR

This work addresses the challenge of IT-secure digital signatures by leveraging QKD-derived keys to support a quantum-assisted framework. It generalizes prior QaDS to GQaDS, introduces Carter-Wegman MACs to drastically shorten signatures, and develops a semi-analytical optimization of protocol parameters that balance forgery and repudiation risks, including a deterministic variant when a second verifier is trusted. The authors derive nuanced, regime-dependent expressions for repudiation and forging probabilities and show how to tune parameters (such as the fraction of shared key blocks and thresholds) to meet stringent security targets (e.g., $P_R<10^{-24}$ and $P_F<10^{-40}$) with realistic key lengths. The Carter-Wegman MAC implementation reduces signature length while preserving IT security, and the deterministic GQaDS variant further lowers requirements by enabling parallel verification and arbitration. Overall, GQaDS offers a practically realizable, QKD-backed digital signature paradigm with scalable security guarantees and flexible deployment options including a highly compact deterministic mode.

Abstract

This paper introduces Generalized Quantum-assisted Digital Signature (GQaDS), an improved version of a recently proposed scheme whose information theoretic security is inherited by adopting QKD keys for digital signature purposes. Its security against forging is computed considering a trial-and-error approach taken by the malicious forger and GQaDS parameters are optimized via an analytical approach balancing between forgery and repudiation probabilities. The hash functions of the previous implementation are replaced with Carter-Wegman Message Authentication Codes (MACs), strengthening the scheme security and reducing the signature length. For particular scenarios where the second verifier has a safe reputation, a simplified version of GQaDS, namely deterministic GQaDS, can further reduce the required signature length, keeping the desired security strength.

Generalized Quantum-assisted Digital Signature

TL;DR

This work addresses the challenge of IT-secure digital signatures by leveraging QKD-derived keys to support a quantum-assisted framework. It generalizes prior QaDS to GQaDS, introduces Carter-Wegman MACs to drastically shorten signatures, and develops a semi-analytical optimization of protocol parameters that balance forgery and repudiation risks, including a deterministic variant when a second verifier is trusted. The authors derive nuanced, regime-dependent expressions for repudiation and forging probabilities and show how to tune parameters (such as the fraction of shared key blocks and thresholds) to meet stringent security targets (e.g., and ) with realistic key lengths. The Carter-Wegman MAC implementation reduces signature length while preserving IT security, and the deterministic GQaDS variant further lowers requirements by enabling parallel verification and arbitration. Overall, GQaDS offers a practically realizable, QKD-backed digital signature paradigm with scalable security guarantees and flexible deployment options including a highly compact deterministic mode.

Abstract

This paper introduces Generalized Quantum-assisted Digital Signature (GQaDS), an improved version of a recently proposed scheme whose information theoretic security is inherited by adopting QKD keys for digital signature purposes. Its security against forging is computed considering a trial-and-error approach taken by the malicious forger and GQaDS parameters are optimized via an analytical approach balancing between forgery and repudiation probabilities. The hash functions of the previous implementation are replaced with Carter-Wegman Message Authentication Codes (MACs), strengthening the scheme security and reducing the signature length. For particular scenarios where the second verifier has a safe reputation, a simplified version of GQaDS, namely deterministic GQaDS, can further reduce the required signature length, keeping the desired security strength.
Paper Structure (17 sections, 1 theorem, 19 equations, 7 figures, 1 table)

This paper contains 17 sections, 1 theorem, 19 equations, 7 figures, 1 table.

Table of Contents

  1. Introduction
  2. A Feasible Hybrid Quantum-assisted Digital Signature (QaDS)
  3. QaDS security evaluations
  4. Repudiation proof
  5. Integrity and Hash function features
  6. Forgery proof and key block guessing
  7. Balancing security against forgery and repudiation
  8. Repudiation probability
  9. Forging probability
  10. Optimization of $\gamma$ with fixed $n$ and $r$
  11. Optimization of GQaDS parameters with fixed key length
  12. Asymmetric constraints on forgery and repudiation
  13. GQaDS
  14. Parameter definition
  15. Carter-Wegman MAC
  16. ...and 2 more sections

Key Result

Proposition 3.1

The computation complexity of Bob's forging is

Figures (7)

  • Figure 1: $\beta^*(\gamma)$ and $z_R\left(\beta^*(\gamma),\gamma\right)$ according to \ref{['eq:beta_star']} and \ref{['eq:zeta_star']}.
  • Figure 2: The optimal value of $\gamma$ as a function of $n$, $\gamma^*$ as defined in \ref{['eq:PF_app']}, for $r = 82$.
  • Figure 3: The lowest achieved value of $\max\{P_R, P_F\}$ as a function of $n$, for $r = 82$.
  • Figure 4: $\gamma^*$ versus $n_{\mathrm{opt}}$ for the set of key lengths $\{L_i\}_{i=1}^{11}$.
  • Figure 5: $\max\{P_F,P_R\}$ versus $n_{\mathrm{opt}}$ for the set of key lengths $\{L_i\}_{i=1}^{11}$.
  • ...and 2 more figures

Theorems & Definitions (1)

  • Proposition 3.1