Impossibility of Growing Quantum Bit Commitments

Abstract

Quantum key distribution (QKD) is often, more correctly, called key growing. Given a short key as a seed, QKD enables two parties, connected by an insecure quantum channel, to generate a secret key of arbitrary length. Conversely, no key agreement is possible without access to an initial key. Here, we consider another fundamental cryptographic task, commitments. While, similar to key agreement, commitments cannot be realized from scratch, we ask whether they may be grown. That is, given the ability to commit to a fixed number of bits, is there a way to augment this to commitments to strings of arbitrary length? Using recently developed information-theoretic techniques, we answer this question to the negative.

10 pages, minor changes

References in corpus (3)

• Composability in quantum cryptography
• Unconditionally Secure Bit Commitment with Flying Qudits
• Security of quantum bit string commitment depends on the information measure

Cited by in corpus (19)

• Quantum Information Processing with Finite Resources -- Mathematical Foundations
• Quantum Cryptography Beyond Quantum Key Distribution
• A largely self-contained and complete security proof for quantum key distribution
• Chain Rules for Smooth Min- and Max-Entropies
• Experimental bit commitment based on quantum communication and special relativity
• Practical relativistic bit commitment
• Improved DIQKD protocols with finite-size analysis
• Secure bit commitment from relativistic constraints
• Postselection technique for optical Quantum Key Distribution with improved de Finetti reductions
• Experimental quantum key distribution certified by Bell's theorem
• Computational Notions of Quantum Min-Entropy
• On the Efficiency of Classical and Quantum Secure Function Evaluation
• (Quantum) Min-Entropy Resources
• Erasable Bit Commitment from Temporary Quantum Trust
• Nonexistence of a universal quantum machine to examine the precision of unknown quantum states
• Asymptotically secure All-or-nothing Quantum Oblivious Transfer
• Impossibility of Quantum Private Queries
• Computational Monogamy of Entanglement and Non-Interactive Quantum Key Distribution
• On the Security of Password-Authenticated Quantum Key Exchange