Quantum cryptography is commonly used to generate fresh secure keys with quantum signal transmission for instant use between two parties. However, research shows that the relatively low key generation rate hinders its practical use where a symmetric cryptography component consumes the shared key. That is, the security of the symmetric cryptography demands frequent rate of key updates, which leads to a higher consumption of the internal one-time-pad communication bandwidth, since it requires the length of the key to be as long as that of the secret. In order to alleviate these issues, we develop a matrix algorithm for fast and simple high-capacity quantum cryptography. Our scheme can achieve secure private communication with fresh keys generated from Fibonacci- and Lucas- valued orbital angular momentum (OAM) states for the seed to construct recursive Fibonacci and Lucas matrices. Moreover, the proposed matrix algorithm for quantum cryptography can ultimately be simplified to matrix multiplication, which is implemented and optimized in modern computers. Most importantly, considerably information capacity can be improved effectively and efficiently by the recursive property of Fibonacci and Lucas matrices, thereby avoiding the restriction of physical conditions, such as the communication bandwidth.