In 2014, a new fault analysis called blind fault attack (BFA) was proposed, in which attackers can only obtain the number of different faulty outputs without knowing the public data. The original BFA requires 480,000 fault injections to recover a 128-bit AES key. This work attempts to reduce the number of fault injections under the same attack assumptions. We analyze BFA from an information theoretical perspective and introduce a new probability-based distinguisher. Three approaches are proposed for different attack scenarios. The best one realized a 66.8% reduction of the number of fault injections on AES