In this paper, a new encryption scheme based on irrational numbers is implemented for the security of medical images in health information systems. It is a mutually authenticated scheme which is secure against all known standard attacks. The main feature of this scheme is that it is robust and the key is dynamic for each image transmission. This new scheme employs the linear transformation to shuffle the positions of image-pixels and uses the XOR-mod operation to confuse the relationship between the plainimage and cipher-image. The theoretical and statistical tests are carried out with detailed examinations, demonstrating the high level security of the new scheme.