Security analysis on asymmetric optical cryptosystem based on interference and equal modulus decomposition

In this paper, the security of an optical cryptosystem based on interference and equal modulus decomposition (EMD) has been evaluated. The security strength of the asymmetric cryptosystem has been enhanced by combining interference and EMD to generate four phase-only masks (POMs). Compared to the previous interference- or EMD-based cryptosystems where only one POM is the private key, the number of private keys in this system increases (i.e., four POMs) consequently increasing the key space of the cryptosystem. Moreover, due to additional private keys as unknown parameters in iterative procedures, this cryptosystem with silhouette removal is immune to special attacks which the EMD-based cryptosystems are vulnerable to. It seems that the security strength of the optical cryptosystem based on interference and EMD has been improved; however, we have noticed that the two POMs used as private key are still related to the ciphertexts and can be potentially utilized to attack the cryptosystem. According to the POMs generation principle, a relationship between private keys and ciphertexts could be derived and used as additional constraints to investigate the iterative attacks. Based on this finding, new iterative ciphertext-only attacks with different constraints have been proposed to crack the cryptosystem. In addition, we found that the POMs P₂(u, v) and P₄(u, v) which are used as private keys have low key sensitivity, which may lead to information leak. Numerical simulations have been carried out to validate the feasibility and effectiveness of the proposed attacks.