  In this work, we study interception attacks against a secret sharing protocol
based on Grovers search algorithm. Unlike previous works that only give the
algorithm for two and three participants, we have generalized the algorithm for
any number of participants. Both reflections used in the algorithm are
constructed using a generalized Householder reflection. Our main goal is to
obtain the probability for an eavesdropper to break the secret depending on the
true initial state and the one assumed by the eavesdropper and on the
Householder angle. In cases where there are two and three participants, we give
an exact analytical solution. These formulas are consistent with the numerical
results. We use simulations for the case of between 4 and 7 participants to
extrapolate the analytical formula for any number of participants.
