Geometric Steganography via Angular Encoding of Color Vectors in Cover Images

We present a steganographic method that embeds textual messages into existing cover images by rotating the color vectors of selected pixels to target directions in the RG plane, leaving pixel magnitudes and the B channel unchanged. Each of 37 character tokens is assigned a unique angular sector of approximately 9.73°; encoding a token rotates the (R-128, G-128) vector of the corresponding cover pixel into that sector while preserving the vector's original Euclidean length. We give a complete implementation, derive the quantization error bounds that govern decoding accuracy, and evaluate the scheme with respect to three criteria: decoding fidelity, perceptual distortion (PSNR and per-pixel Euclidean distance), and statistical detectability via angle-histogram and polar-distribution analysis. The encoding introduces a characteristic 37-spoke angular signature absent from natural images and detectable by straightforward statistical tests. Two principled extensions are proposed to address this: a differential scheme that accumulates angular increments and eliminates the fixed-spoke signature, and a spherical generalization that exploits all three color channels to increase capacity and reduce detectability.