In today’s digital world, keeping data safe is a top priority. Two common methods used to protect data are steganography and cryptography. Steganography hides secret data within everyday files (like images, GIFs or videos), while cryptography scrambles the data into an unreadable format. This paper introduces a new way to hide data using a technique called Perfect Square Quotient Differencing. Instead of embedding data in a straight sequence, the method hides information in two steps within the components of an image pixel (called the quotient and remainder). In the first step, a perfect square quantization technique is applied to the quotient part. In the second step, the Two Least Significant Bit (2LSB) method is used on the remainder part. A new range-table is also introduced to help determine how much data can be hidden in the first step. This two-step approach allows a large amount of data to be hidden (about 3 bits per pixel on average). The method was tested on many animated color images, and its performance was measured using tools like Peak-Signal-to-Noise-Ratio (PSNR), Mean Square Error (MSE), Universal Image Quality Index (UIQI), and Payload Curve. The results show that this method works better than several modern steganography techniques. Additionally, tests were conducted to ensure the method is secure against potential attacks. This new algorithm could be particularly useful for protecting digital documents stored in cloud-based platforms, offering a robust and efficient way to keep data safe.