Recently, data hiding and encryption methods have been very important for transmitting information to the relevant people correctly and reliably. Although each newly developed computer-aided data hiding and encryption method is stronger than previous methods, there may be security gaps or speed factors in future use. Therefore, faster and more secure encryption methods are needed. Chaotic systems can be used for high-performance random number generators because their frequency spectrum is wide. Moreover, they show extreme sensitivity to the initial conditions and eliminate the need for large sized keying. This means that a faster and more secure encryption can be made with random numbers generated from a chaotic system. All of these features make chaotic systems stand out in data hiding and encryption applications. Chaos-based image encryption and decryption applications were performed differently than in traditional encryption algorithms in the literature. For the application, a three-dimensional chaotic system was discretized by the Runge–Kutta-4 method, and random numbers were generated. These random numbers were tested by the statistical NIST-800-22 tests, the international top random standard, and their suitability was determined. With the random numbers that passed the tests successfully, the image was successfully encrypted and sent via e-mail; then the encrypted image was decrypted back to the original image by the receiver. Finally, an electronic circuit realization of the chaotic encryption approach was depicted using LabVIEW to confirm the operability of the application.