title: 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 in the negative.
authors.affiliation: Computer Science Department, ETH Zurich, 8092 Zurich, Switzerland.
authors.forename: Severin
authors.initials: S
authors.lastname: Winkler
authors.forename: Marco
authors.initials: M
authors.lastname: Tomamichel
authors.forename: Stefan
authors.initials: S
authors.lastname: Hengl
authors.forename: Renato
authors.initials: R
authors.lastname: Renner