In this work, we consider the general problem of distributed detection in the presence of Byzantines using wireless sensor networks. Instead of attempting to mitigate Byzantine attacks as a system designer, we investigate the issue from the perspective of a Byzantine attacker. The probability for each individual sensor to be compromised (compromising probability) required to blind the system operation is adopted as the attack measure. Under the system setting that the fusion center (FC) declares the most likely hypothesis to be true based on the M-ary data from N local sensors, a Byzantine attack policy that can blind the FC with the minimum compromising probability for each individual sensor is derived under the assumption that the Byzantine attacker knows the statistics of the local outputs. The closed-form expression for a blind-achieving Byzantine transition probability that is used to alter the statistics of the local outputs of compromised sensors is also established. Our results indicate that the statistics of the local outputs is essential for the minimization of an attacker's effort.