Encryption scheme based on the automorphism group of the Ree function field

Internet of things (IoT) is a growing technology with a big market and impact to our lives. It can ease various different tasks for us. Meanwhile, IoT has many serious security threats, like data breaches, side-channel attacks, and virus and data authentication. Our present classical cryptography, like the Rivest-Shamir-Adleman (RSA) algorithm, work well under the classical computers. However, the technology is slowly shifting towards quantum computing, which has immense processing power and is more than enough to break the current cryptographic primitives in affordable time. So, it is required to design quantum cryptographic algorithms to prevent our systems from security breaches even before quantum computers will be available for commercial purposes on the market. In this paper, we describe a new implementation of MST3 cryptosystems based on the group of automorphisms of the field of the Pu function. The main difference of the presented implementation is the extension of the logarithmic signature and, as a consequence, the presence of multi-stage recovery of message parts from the ciphertext. The presented implementation of the cryptosystem is more reliable. The cryptanalysis complexity and message size for encryption are square times larger than the MST3 cryptosystem in the Suzuki group. This approach shows advantages and it is a quantum safe for the IoT use.