  We study the security of quantum string commitment (QSC) protocols with group
covariant encoding scheme. First we consider a class of QSC protocol, which is
general enough to incorporate all the QSC protocols given in the preceding
literatures. Then among those protocols, we consider group covariant protocols
and show that the exact upperbound on the binding condition can be calculated.
Next using this result, we prove that for every irreducible representation of a
finite group, there always exists a corresponding nontrivial QSC protocol which
reaches a level of security impossible to achieve classically.
