Design of a novel cryptosystem based on dynamic encryption and decryption by observability

In this paper, a novel symmetric (also known as private-key or secret-key) cryptosystem is proposed. The encryption system of the proposed cryptosystem consists of a masking vector, a linear time-varying system, and a signal generator. The masking vector, the coefficient matrices of the linear system, the time interval over which the system evolves, and the signal generated by the signal generator are the private keys of the cryptosystem. The message to be transmitted is a string of integers which is partitioned to 1- to D-digit integers. Sets of these integers are consecutively buffered in a plaintest vector upon which the encryption system operates. The encryption function consists of the masking of the generated vector and the dynamics (evolution) of the linear system. The decryption system uses keys the same as those of the encryption system. The observability grammian of the linear system is used in the decryption system to recover the plaintext vectors. Furthermore, based on the proposed cryptosystem an extremely secure variable-key cryptosystem is designed. Two examples are given to illustrate the superb performance of the proposed cryptosystems.