The security strength of an interference-based optical image cryptosystem with a designed amplitude modulator (AM) is evaluated. Compared to previous improved interference-based cryptosystems in which iterative or post-processing algorithms are involved, to remove the silhouette problem, a pre-designed AM is placed at the image plane to modulate the plaintext directly, which eliminates this drawback. Moreover, the AM is used as an additional private key, which enlarges the key space and further enhances the security system. However, we have noticed that one of the designed parameters in the AM has a low key sensitivity, which is fault-tolerant and is not required for precise reconstruction. Additionally, the AM is plaintext-independent, which means that the AM can be recovered first by using a pair of chosen plaintexts and the corresponding ciphertext. Based on these findings, we propose a hybrid algorithm that includes two chosen-plaintext attacks (CPAs) and a ciphertext-only attack (COA) to break the enhanced cryptosystem. Specially, CPAs with an impulse function and an arbitrarily given plaintext are proposed to retrieve two parameters in the AM. With the retrieved AM, information on the plaintext can be recovered from the corresponding ciphertext by two kinds of COAs without any knowledge of the private keys. To the best of our knowledge, this is the first time that the interference-based cryptosystem with a designed AM has been cracked successfully, which may provide potential evidence for further security improvements. Numerical simulations are carried out to validate the feasibility of the proposed attacks.