Gaussian Image Steganography via Parameter-Domain Keyed Embeddings

2D Gaussian-based image representation is becoming increasingly popular, and our work proposes a new approach to steganography by embedding information within Gaussian parameters rather than image pixels. We first fit the parameters of this representation to the target image and employ a secret key to select a subset of these parameters for fine-tuning, allowing us to embed an 8-bit message while maintaining high visual fidelity in the reconstructed image. Thirty fitting experiments on three synthetic images show that the correct key can recover the message without error, while decoding with incorrect keys yields a Bit Error Rate (BER) of 0.543, close to random guessing. Compared with random selection using the key, selecting the least-disturbing edits recovers the message more reliably (one-sided p=0.031), and the average PSNR cost is only 0.091 dB in visual quality. The embedding method transfers to 112 natural images at 256×256 using 4,096 Gaussians. The correct-key BER is 0.000, and decoding under a wrong key stays close to random guessing at 0.520. Our method embeds the payload through three Gaussian parameter types: log-anisotropy, opacity, and color luminance. In a separate nine-fit reduced setting, color luminance is removed, so the payload uses two instead of three parameter types, a 33.3% reduction; all 256 Gaussians remain in the fitted representation. The correct key still recovers the message without error. However, wrong-key BER rises from 0.514 to 0.571, moving farther from random guessing (0.5).