Embedded encryption devices and smart sensors are vulnerable to physical attacks. Due to the continuous shrinking of chip size, laser injection, particle radiation and electromagnetic transient injection are possible methods that introduce transient multiple faults. In the fault analysis stage, the adversary is unclear about the actual number of faults injected. Typically, the single-nibble fault analysis encounters difficulties. Therefore, in this paper, we propose novel ciphertext-only impossible differentials that can analyze the number of random faults to six nibbles. We use the impossible differentials to exclude the secret key that definitely does not exist, and then gradually obtain the unique secret key through inverse difference equations. Using software simulation, we conducted 32,000 random multiple fault attacks on Midori. The experiments were carried out to verify the theoretical model of multiple fault attacks. We obtain the relationship between fault injection and information content. To reduce the number of fault attacks, we further optimized the fault attack method. The secret key can be obtained at least 11 times. The proposed ciphertext-only impossible differential analysis provides an effective method for random multiple faults analysis, which would be helpful for improving the security of block ciphers.