This paper investigates various current information encryption technologies that are growing quickly, especially different algorithms for encrypting and decrypting unique patterns in image data. The fast Fourier transform (FFT) has emerged as a powerful tool with the potential to significantly impact encryption technology. Current encryption technology is designed to encrypt and decrypt images and is easy to decipher. Hence, this paper presents the proposed encryption and decryption algorithm to improve encryption technology based on an improved Euler integral and FFT; in particular, the algorithm possesses a more complex and multidimensional way to improve encryption technology. The improved algorithm offers the ability to efficiently process and analyze vast amounts of image data. The proposed approach of matching the proposed encryption and decryption algorithms can be applied to cloud computing and quantum computing technology.