Quantum bit escrow

Abstract

Uncondit ionally secure bit commi tmen t and coin flipping are known to be impossible in the classical world. Bit commitment is known to be impossible also in the quan tum world. We introduce a related new primitive quantum bit escrow. In this primitive Alice commits to a bit b to Bob. The commi tment is bindingin the sense tha t if Alice is asked to reveal the bit, Alice can not bias her commi tmen t wi thout having a good probability of being detected cheating. The commitment is sealing in the sense tha t if Bob learns information about the encoded bit, then if later on he is asked to prove he was playing honestly, he is detected cheating with a good probability. Rigorously proving the correctness of quan tum cryptographic protocols has proved to be a difficult task. We develop techniques to prove quant i ta t ive s ta tements about the binding and sealing propert ies of the quan tum bit escrow protocol. A related primitive we construct is a quan tum biased coin flipping protocol where no player can control the game, i.e., even an all-powerful cheating player must lose with some constant probability, which stands in sharp contrast to the classical world where such protocols are impossible. *This research was supported in part by a U.C. president 's postdoctoral fellowship and NSF Grant CCR-9800024. *Supported in part by David Zuckerman's David and Lucile Packard Fellowship for Science and Engineering and NSF NYI Grant No. CCR-9457799. *This research was supported in part by NSF Grant CCR9800024, and a 3SEP grant. §This research was supported in part by D A R P A and NSF under CCR-9627819, by NSF under CCR-9820855, and by a Visiting Professorship sponsored by the Research Miller Inst i tute at Berkeley. Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the lull citation on the first page. To copy otherwise, to republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. STOC 2000 Portland Oregon USA Copyright ACM 2000 1-58113-184-4/00/5...$5.00 General Terms Quan tum cryptography, bit commi tmen t Quan tum coin tossing, Quan tum