Biblio

The purpose of this research is to propose a new mathematical model, designed to evaluate the security of cryptosystems. This model is a mixture of ideas from two basic mathematical theories, information theory and game theory. The role of information theory is assigning the model with security criteria of the cryptosystems. The role of game theory was to produce the value of the game which is representing the outcome of these criteria, which finally refers to cryptosystem's security. The proposed model support an accurate and mathematical way to evaluate the security of cryptosystems by unifying the criteria resulted from information theory and produce a unique reasonable value.

This paper proposes a new cryptosystem that combines Diffie-Hellman protocol implemented with hyperelliptic curves over a Galois field GF(2n) with Tree Parity Machine synchronization for a Visible Light Communication indoor channel. The proposed cryptosystem security focuses on overcoming a weakness of neuronal synchronization; specifically, the stimulus vector that is public, which allows an attacker to try to synchronize with one of the participants of the synchronization. Real data receptions of the Visible Light Communication channel are included. In addition, there is an improvement of 115% over a range of 100 $łeq$ tsync$łeq$ 400 of the average synchronization time t\_sync, compared to the classic Tree Parity Machine synchronization.