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In this paper, some modifications are introduced to the Original Hartley Transform (OHT) in an attempt to increase the resistance of the OHT against the cropping attack. The unique frequency pattern of the OHT triggered the proposed modifications, where the coefficients of the transformation kernel matrix are swapped to meet the requirements of the new transform. The Modified Hartley Transform (MHT) can be utilized in many signal and image applications; however, in this paper the main focus is on the cropping and filtering applications only. Two applications of the MHT are also presented in this paper. The first (major) application is a new form of the Naturalness Preserving Transform (NPT) based on the MHT for hiding distinctive ownership identification information into sensitive data (i.e., remote sensing data). The new MHT-based NPT is more resilient to the cropping attack. Experimental results in this paper emphasize the capability of the MHT-based NPT to invisibly hide a digital signature into a host data, which also can be used for a secure data (image) transmission. The second (minor) application is a Cross-Like Shape L-Pass Filter (CLSLPF), which is mainly developed to suit the unique frequency pattern of the new MHT. This type of filter preserves the minimum number of the frequency components which holds the highest percentage of the input signal's energy. Experimental results are provided for comparison between the proposed CLSLPF and Butterworth low pass filter with a main focus on the total energy of the preserved frequency components.