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We propose quantum bit-commitment schemes based on quantum one-way permutations. Our schemes reduces exponentially the number of bits which Bob needs to store until the opening phase compared with the classical counterpart. 1Introduction Abit-commitment protocol involves two party: a sender (say Alice) and areceiver (say Bob). Alice has aclassical string inmind, which she wants to communicate to Bob at alater time. In order to guarantee that she will not change hermind in the interim, Alicedoi:10.1007/bf03037308 fatcat:wdl2sqqd3bdc7bjbawnnyqnqom