Remote points-of-care has recently had a lot of attention for their advantages such as saving lives and cost reduction. The transmitted streams usually contain 1) normal biomedical signals (e.g., electrocardiograms) and 2) highly private information (e.g., patient identity). Despite the obvious advantages, the primary concerns are privacy and authenticity of the transferred data. Therefore, this paper introduces a novel steganographic mechanism that ensures 1) strong privacy preservation of private information by random concealing inside the transferred signals employing a key and 2) evidence of originality for the biomedical signals. To maximize hiding, fast Walsh-Hadamard transform is utilized to transform the signals into a group of coefficients. To ensure the lowest distortion, only less-significant values of coefficients are employed. To strengthen security, the key is utilized in a three-dimensional (3-D) random coefficients' reform to produce a 3-D order employed in the concealing process. The resultant distortion has been thoroughly measured in all stages. After extensive experiments on three types of signals, it has been proved that the algorithm has a little impact on the genuine signals ( 1 %). The security evaluation also confirms that unlawful retrieval of the hidden information within rational time is mightily improbable.