In this paper, a cryptosystem characterized by chaotic extremum coding and dynamic synchronized random keys is newly proposed. First, a novel chaotic extremum coding algorithm is developed to generate dynamic random numbers with good randomness quality. Meanwhile, the synchronization controllers are recommended to guarantee that the transmitter and receiver can simultaneously generate the same dynamic chaotic extremum-coded random keys (DCECRKs) for encryption and decryption, respectively. The designed DCECRKs are dynamically updated and can solve problems of key distribution and storage in the traditional encryption algorithm. Then, we apply the proposed DCECRKs to encrypt/decrypt image data. We employ the Advanced Encryption Standard Cipher Feedback encryption algorithm, integrated with the DCECRKs, to perform image encryption and decryption. To emphasize the contribution of the proposed DCECRKs and cryptosystem, a series of tests were conducted, including statistical analysis, histogram evaluation, connected component analysis, information entropy measurement, correlation indices assessment, number of pixels change rate, and unified average changing intensity. These results were compared against findings from existing literature, demonstrating that the proposed cryptosystem achieves superior security in image encryption.