Collision is a phenomenon in which two distinct inputs produce an identical output, so if an attacker finds the encryption keys in such a way that when it is applied to an encrypted image, it produces an arbitrary image instead of original one. We propose collision in an asymmetric cryptosystem based on a phase-truncated Fresnel transform. For encryption, instead of using conventional random-phase masks, structured phase masks with desired construction parameters are used. The decryption keys are generated using the amplitude and phase truncation. An attacker generates an arbitrary (collision) image from the encrypted image using a modified Gerchberg-Saxton phase retrieval algorithm. Two different users, authorized and unauthorized user (attacker), can claim the retrieved image as the original data. The authorized user uses the correct decryption keys and retrieves the original image, while an unauthorized user uses the generated keys and retrieves the collision image. In order to verify the authenticity of the retrieved data, a joint transform correlator is used. A sharp auto-correlation peak is obtained when an image retrieved by authorized user is matched with the encrypted image. However, cross-correlation is obtained when an encrypted image is matched with the collision image. Results of computer simulation support the idea of the proposed collision.
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