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The integrated circuits are faced with the threats of fault injection attacks (FIAs), which employ the faulty results and differential fault analysis to retrieve the vital information processed by the circuits. Countermeasures should be taken to protect the circuits against FIAs. This paper proposes a security evaluation method to quantitatively analyze the resistance of block ciphers with a Substitution-Permutation Network structure against FIAs from an information-theoretic perspective. A quantitative security factor is defined based on the amount of information leakage. Specifically, an extended cipher model is proposed to numerically analyze the theoretical amount of information leakage, and an efficient approach is proposed to obtain the actual amount of information leakage. Experiments by applying the quantitative evaluation method to AES circuit validate feasibility, efficiency and scalability of the method. The experimental results show that the security factor can quantify the effects of different fault models and countermeasures. 2000 fault injections are sufficient to complete the evaluation under the considered fault models within 10 microseconds. The proposed method can be used during the circuit design stage as well as chip testing stage.