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Related Experiment Video

Updated: May 29, 2026

Generation and Coherent Control of Pulsed Quantum Frequency Combs
06:42

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Published on: June 8, 2018

Impossibility of growing quantum bit commitments.

Severin Winkler1, Marco Tomamichel, Stefan Hengl

  • 1Computer Science Department, ETH Zurich, 8092 Zurich, Switzerland.

Physical Review Letters
|September 21, 2011
PubMed
Summary
This summary is machine-generated.

Commitments, a cryptographic task, cannot be "grown" from a fixed number of bits to arbitrary lengths, unlike quantum key distribution (QKD). This study demonstrates that extending limited commitments to unlimited ones is impossible using information-theoretic methods.

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Area of Science:

  • Cryptography
  • Quantum Information Theory
  • Theoretical Computer Science

Background:

  • Quantum key distribution (QKD), or key growing, enables generating long secret keys from a short seed over insecure quantum channels.
  • Cryptographic primitives like key agreement require an initial key, and cannot be realized from scratch.
  • The concept of 'growing' cryptographic primitives, analogous to key growing in QKD, is explored.

Purpose of the Study:

  • To investigate whether cryptographic commitments can be 'grown' to arbitrary lengths from a fixed initial commitment.
  • To determine if a limited commitment capability can be extended to handle arbitrary-length strings.
  • To apply information-theoretic techniques to fundamental cryptographic tasks.

Main Methods:

  • Utilizing recently developed information-theoretic techniques.
  • Analyzing the theoretical possibility of augmenting fixed-length commitments to arbitrary-length commitments.
  • Formal cryptographic analysis of commitment schemes.

Main Results:

  • The study answers the question of whether commitments can be grown in the negative.
  • It is impossible to augment a fixed number of commitment bits to commitments of arbitrary length.
  • Information-theoretic methods confirm the limitations of extending commitment schemes.

Conclusions:

  • Cryptographic commitments cannot be 'grown' to arbitrary lengths from a fixed initial commitment.
  • Unlike key growing in QKD, commitment schemes have fundamental limitations in scalability.
  • The findings highlight the distinct theoretical properties of different cryptographic primitives.