Research On Neural Cryptosystem Of Complex-Valued And Quaternion-Valued Tree Parity Machine

With the development of computer,the traditional cryptography based on mathematical problems will be attacked by brute force.The neural network with neural synchronization provides a new idea for key exchange in cryptography.The neural cryptography based on tree parity machine(TPM)can learn from each other much faster than the sample generated by one-way learning from other networks to achieve synchronization.It can distinguish active participants from passive participants.In order to enhance the synchronization efficiency and solve the synchronization judgment problem of the neural cryptography based on complex-valued tree parity machine,we propose the complex-valued queue learning rules and a complex-valued neural synchronization judgment algorithm.In order to enhance the safety of the model we propose a neural cryptography model based on quaternion-valued tree parity machine.Then we propose the suggestions about using the quaternion multiplication table operation rules.The main work is summarized as follows.(1)In order to enhance the synchronization efficiency of the existing neural cryptography based on complex-valued tree parity machine(CVTPM),we propose complex-valued queue learning rules.By changing the learning scale of the traditional complex-valued learning rules,complex-valued new queue learning rules are proposed,by which the iteration number can be reduced and the synchronization process can be speeded up,thus improving the synchronization efficiency.(2)In order to solve the synchronization judgment problem of the existing neural cryptography based on CVTPM,we propose a complex-valued neural synchronization judgment algorithm.Not only the HASH value of the current hidden neurons,but also that of the past hidden neurons,is considered in the algorithm design.Next,we set the maximum times that the real part and imaginary part of the hidden neurons’ states are consecutively equal as a judgement indicator,by which the accurate synchronization time point can be captured,and an improved successful rate of synchronization judgment can be achieved.(3)In order to improve the security of the model based on complex-valued tree parity machine,we extend it to the quaternion field and propose a neural cryptography model based on quaternion-valued tree parity machine(QVTPM).Then the security analysis is carried out to prove its security theoretically.Finally,the security of QVTPM neural cryptography model is verified by comparative experiments.On the basis of the proposed neural cryptography model based on quaternion-valued tree parity machine,the influence of quaternion multiplication table operation rules on it is considered.Then comparison experiments on synchronization success rate,average iteration number,simple attack and geometric attack,respectively,are conducted,which show that both the synchronization efficiency and security can be improved.(4)To solve a class of special equations in the split domain,we derived the expression of the least squares η-Hermitian solution with the least norm for the split quaternion matrix equation AXB +CYD =E.It provides ideas for quaternion-valued tree parity machine using the quaternion multiplication table operation rules.