Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

How to Sign Quantum Messages

Mohammed Barhoush, Louis Salvail

TL;DR

This work overturns the conventional wisdom that signing quantum information is impossible by introducing three complementary frameworks: (i) time-dependent (TD) signatures that either rely on time-lock puzzles or on dynamic verification keys, (ii) TD-DVK signatures that derive time-evolving keys from pq-OWFs to achieve public verifiability without TLPs, and (iii) signing in the bounded quantum storage model (BQSM) to obtain information-theoretic security. It then leverages these TD primitives to construct public-key quantum encryption with authenticated quantum public keys and to realize public-key quantum money, including fully offline options under standard assumptions. A central theme is using time as a cryptographic resource to circumvent the impossibility of signing quantum data, enabling a suite of applications from QPKE with tamper-resistant quantum keys to TD quantum money. The results demonstrate the versatility of time-dependent cryptographic techniques and suggest broader implications for quantum-safe public-key infrastructures and monetization of quantum states. Together, the constructions provide foundational tools for authenticating and deploying quantum information over insecure channels while maintaining public verifiability and practicality under well-established assumptions such as pq-OWFs and TLPs.

Abstract

Signing quantum messages has long been considered impossible even under computational assumptions. In this work, we challenge this notion and provide three innovative approaches to sign quantum messages that are the first to ensure authenticity with public verifiability. Our contributions can be summarized as follows: 1) We introduce the concept of time-dependent (TD) signatures, where the signature of a quantum message depends on the time of signing and the verification process depends on the time of the signature reception. We construct this primitive assuming the existence of post-quantum secure one-way functions (pq-OWFs) and time-lock puzzles (TLPs). 2) By utilizing verification keys that evolve over time, we eliminate the need for TLPs in our construction. This leads to TD signatures from pq-OWFs with dynamic verification keys. 3) We then consider the bounded quantum storage model, where adversaries are limited with respect to their quantum memories. We show that quantum messages can be signed with information-theoretic security in this model. Moreover, we leverage TD signatures to achieve the following objectives, relying solely on pq-OWFs: (a) We design a public key encryption scheme featuring authenticated quantum public keys that resist adversarial tampering. (b) We present a novel TD public-key quantum money scheme.

How to Sign Quantum Messages

TL;DR

This work overturns the conventional wisdom that signing quantum information is impossible by introducing three complementary frameworks: (i) time-dependent (TD) signatures that either rely on time-lock puzzles or on dynamic verification keys, (ii) TD-DVK signatures that derive time-evolving keys from pq-OWFs to achieve public verifiability without TLPs, and (iii) signing in the bounded quantum storage model (BQSM) to obtain information-theoretic security. It then leverages these TD primitives to construct public-key quantum encryption with authenticated quantum public keys and to realize public-key quantum money, including fully offline options under standard assumptions. A central theme is using time as a cryptographic resource to circumvent the impossibility of signing quantum data, enabling a suite of applications from QPKE with tamper-resistant quantum keys to TD quantum money. The results demonstrate the versatility of time-dependent cryptographic techniques and suggest broader implications for quantum-safe public-key infrastructures and monetization of quantum states. Together, the constructions provide foundational tools for authenticating and deploying quantum information over insecure channels while maintaining public verifiability and practicality under well-established assumptions such as pq-OWFs and TLPs.

Abstract

Signing quantum messages has long been considered impossible even under computational assumptions. In this work, we challenge this notion and provide three innovative approaches to sign quantum messages that are the first to ensure authenticity with public verifiability. Our contributions can be summarized as follows: 1) We introduce the concept of time-dependent (TD) signatures, where the signature of a quantum message depends on the time of signing and the verification process depends on the time of the signature reception. We construct this primitive assuming the existence of post-quantum secure one-way functions (pq-OWFs) and time-lock puzzles (TLPs). 2) By utilizing verification keys that evolve over time, we eliminate the need for TLPs in our construction. This leads to TD signatures from pq-OWFs with dynamic verification keys. 3) We then consider the bounded quantum storage model, where adversaries are limited with respect to their quantum memories. We show that quantum messages can be signed with information-theoretic security in this model. Moreover, we leverage TD signatures to achieve the following objectives, relying solely on pq-OWFs: (a) We design a public key encryption scheme featuring authenticated quantum public keys that resist adversarial tampering. (b) We present a novel TD public-key quantum money scheme.
Paper Structure (40 sections, 18 theorems, 26 equations)

This paper contains 40 sections, 18 theorems, 26 equations.

Table of Contents

  1. Introduction
  2. Summary of Results
  3. Future Work
  4. Related Work
  5. Related Work
  6. Technical Overview
  7. Time-Dependent Signatures.
  8. The Issue with $\textsf{TLP}$s.
  9. Time-Dependent Signatures with Dynamic Verification Keys.
  10. Application: Public-Key Quantum Money.
  11. Application: Encryption with Authenticated Public Keys.
  12. Preliminaries
  13. Notation
  14. Algebra
  15. Min-Entropy
  16. ...and 25 more sections

Key Result

lemma 1

Let $M$ be an arbitrary $\ell \times n$ binary matrix. Let $A$ be an algorithm that is given as input: $(a_1,b_1),...,(a_{m},b_{m})$ and $(\hat{a}_1,\hat{b}_1),...,(\hat{a}_{p},\hat{b}_{p})$ where $a_i, \hat{a}_i \in \{0,1\}^n$, $b_i,\hat{b}_i\in \{0,1\}^{\ell}$, $m<n$, $p$ is a polynomial in $\ell$

Theorems & Definitions (64)

  • definition 1: Time-Dependent Signatures
  • definition 2: Time-Lock Puzzles (Informal)
  • lemma 1: BS23
  • definition 3: Conditional Min-Entropy
  • definition 4: Smooth Min-Entropy
  • lemma 2: Chain Rule for Min-Entropy RK04
  • definition 5
  • theorem 1: Privacy Amplification RK04
  • theorem 2: Monogamy of Entanglement, Theorem 3 in TFKW13
  • definition 6: Post-Quantum Secure Pseudorandom Function
  • ...and 54 more