Chaotic Cryptography with Modified Inclusion Method and Indirect Coupled Chaotic Synchronisation

This work proposes a chaotic cryptographic system based on a modified inclusion method in combination with indirect coupled synchronisation to create a chaotic private key. A Rossler type chaotic oscillator is used to embed an encrypted message in its dynamics as well as to drive the piece-wise linear function of a Chua type system, used to create a chaotic key to encrypt the embedded message. In the receiver side a Rossler high gain observer is used to synchronise with the transmitter as well as to drive a second Chua oscillator to decrypt the message. A bidirectional link is applied to remove the nonlinear term in transmitter-receiver error dynamics analysis. Information retrieval is achieved when encrypted message amplification factors and gain matrix values are correctly tuned; leading to a transfer function between error dynamics and encrypted message equal to unity. In this way encrypted message is retrieved with straight forward error dynamics subtraction, avoiding left invertibility problem. Message is finally obtained with key chaotic decryption from a second receiver-driven Chua oscillator. All results presented are based on software simulation in an ideal communication channel.