# Hamming Code Strategy for Medical Image Sharing
## 2 Related Works  
Image sharing has been studied extensively over the last decade. Most are rooted in the secret sharing concept. The very first secret sharing schemes were proposed by both [PERSON] and [PERSON] back in 1979 [16; 17]. These schemes solve the problem of sharing a secret key among many participants. The trivial solution for secret key sharing is to provide each participant with a copy of the said key. However, the security of the secret key is not assured if only one copy is compromised. The solution is to split the secret into smaller pieces and give each participant a piece. The original secret will be fully reconstructed when all the required pieces are summoned.  
[PERSON]'s scheme [17] is a \((k,n)\) threshold secret sharing scheme that divides the secret into pieces and requires at least pieces out of to reconstruct the secret. Because the scheme is based on Lagrange's interpolation modulo as the prime number, its direct application to greyscale images would introduce distortion to the reconstructed images as a result of truncating the pixels whose values are greater than the aforementioned prime number (in practice, they are truncated by 250). In 2002, [PERSON] and [PERSON] [18] proposed a solution for that problem allowing image sharing without loss. Their method is to preprocess the original image to normalize all the pixels to the range of 0 to 250 so that they can use interpolation modulo 251 to produce shadows. In addition, the shadows constructed this way are smaller in size compared to their original images. In 2006, [PERSON] and [PERSON] [19] employed both the interpolation and Huffman coding to produce even smaller shadows. Later, [PERSON] and [PERSON] [20] proposed a scheme that can be used to reduce the size of shadow images by half. The advantage of the smaller size of shadow images is obvious--the smaller the size, the less storage is required, especially when the shadows are kept on portable storage devices like USB drives. For colour images, [PERSON] et al. [21] developed a colour image sharing scheme based on the gradual search algorithm [22] and [PERSON]'s secret sharing [17]. Randomization was introduced into shadows to raise the security level. In 2009, [PERSON] et al. [23] combined neural network and visual secret sharing to devise an image sharing platform for true-colour secret images.  
Over the years, researches have incorporated data hiding, steganography and image authentication techniques into image sharing methods [24; 25; 26; 27; 28; 29; 30; 31]. Data hiding and steganography techniques help conceal shadows in benign cover images that can go unnoticed by adversaries. After being reconstructed, the recovered image can be verified using image authentication techniques.  
Recently, medical applications hugely reap the benefits of image sharing researches. Many medical image sharing schemes have been proposed [32; 33; 34; 35]. In 2011, [PERSON] et al. [35] proposed a sharing scheme for storing medical images and EPRs (electronic patients' records) based on [PERSON]'s secret sharing scheme. Besides EPR hiding and confidentiality, this scheme also ensures the authenticity of the recovered images. In 2013, [PERSON] et al. [33] employed cryptographic encryption to securely share medical images in cloud storage, in which a system with three levels of security was provided to facilitate the communications between doctors and cloud service providers. Later, in 2014, [PERSON] and [PERSON] [32] combined [PERSON]'s secret sharing with DNA cryptography to share medical images. They hid EPRs into medical images using DNA hiding techniques and used Huffman coding to compress the images before constructing shadows using [PERSON]'s technique. Also in 2014, [PERSON] et al. [34] utilized a visual sharing technique to divide medical images into meaningless shares. One of the advantages of this scheme is its simplicity, stacking the shares immediately to reveal the original medical image.