Secret data in embedded devices can be revealed by injecting computational faults using the fault analysis attacks.The fault analysis researches on a cryptographic implementation by far first assumed a certain fault model, and then discussed the key recovery method under some assumptions. We note that a new remote-fault injection method has emerged, which is threatening in practice. Due to its limited accessibility to cryptographic devices, the remote-fault injection, however, can only inject uncertain faults. In this surroundings, this paper gives a general strategy of the remote-fault attack on the AES block cipher with a data set of faulty ciphertexts generated by uncertain faults. Our method effectively utilizes all the information from various kinds of faults, which is more realistic than previous researches. As a result, we show that it can provide a decent success probability of key identification even when only a few intended faults are available among 32 millions fault injections.