  We propose an efficient quantum protocol performing quantum bit commitment,
which is a simple cryptographic primitive involved with two parties, called a
committer and a verifier. Our protocol is non-interactive, uses no supplemental
shared information, and achieves computational concealing and statistical
binding under a natural complexity-theoretical assumption. An earlier protocol
in the literature relies on the existence of an efficient quantum one-way
function. Our protocol, on the contrary, exploits a seemingly weaker assumption
on computational difficulty of distinguishing two specific ensembles of reduced
quantum states. This assumption is guaranteed by, for example, computational
hardness of solving the graph automorphism problem efficiently on a quantum
computer.
