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

Security of a Grover's Algorithm-based secret sharing protocol, generalized for an arbitrary number of participants, against interception attacks