International Association for Cryptologic Research

International Association
for Cryptologic Research


Paper: A Tight High-Order Entropic Quantum Uncertainty Relation With Applications

Ivan Damgård
Serge Fehr
Renato Renner
Louis Salvail
Christian Schaffner
Search ePrint
Search Google
Abstract: We derive a new entropic quantum uncertainty relation involving min-entropy. The relation is tight and can be applied in various quantum-cryptographic settings. Protocols for quantum 1-out-of-2 Oblivious Transfer and quantum Bit Commitment are presented and the uncertainty relation is used to prove the security of these protocols in the bounded-quantum-storage model according to new strong security definitions. As another application, we consider the realistic setting of Quantum Key Distribution (QKD) against quantum-memory-bounded eavesdroppers. The uncertainty relation allows to prove the security of QKD protocols in this setting while tolerating considerably higher error rates compared to the standard model with unbounded adversaries. For instance, for the six-state protocol with one-way communication, a bit-flip error rate of up to 17% can be tolerated (compared to 13% in the standard model). Our uncertainty relation also yields a lower bound on the min-entropy key uncertainty against known-plaintext attacks when quantum ciphers are composed. Previously, the key uncertainty of these ciphers was only known with respect to Shannon entropy.
  title={A Tight High-Order Entropic Quantum Uncertainty Relation With Applications},
  booktitle={IACR Eprint archive},
  keywords={foundations / quantum cryptography, uncertainty relation, bounded-quantum-storage model},
  note={Full version of CRYPTO 2007 paper. 13746 received 20 Aug 2007},
  author={Ivan Damgård and Serge Fehr and Renato Renner and Louis Salvail and Christian Schaffner},