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This paper presents a comprehensive analysis of differential fault analysis (DFA) attacks on the Advanced Encryption Standard (AES) from an information-theoretic perspective. Injecting faults into cryptosystems is categorized as an active at tack where attackers induce an error in operations to retrieve the secret internal information, e.g., the secret key of ciphers. Here, we consider DFA attacks as equivalent to a special kind of passive attack where attackers can obtain leaked information without measurement noise. The DFA attacks are regarded as a conversion process from the leaked information to the secret key. Each fault model defines an upper bound for the amount of leaked information. The optimal DFA attacks should be able to exploit fully the leaked information in order to retrieve the secret key with a practical level of complexity. This paper discusses a new DFA methodology to achieve the optimal DFA attack by deriving the amount of the leaked information for various fault models from an information-theoretic perspective. We review several previous DFA at tacks on AES variants to check the optimality of their attacks. We also propose improved DFA attacks on AES-192 and AES-256 that reach the theoretical limits.