Based on controlled order rearrange encryption (CORE) for quantum key distribution using EPR pairs [Fu.G. Deng, G.L. Long, Phys. Rev. A 68, 042315 (2003)], we propose generalized controlled order rearrangement encryption (GCORE) protocols of N qubits and N qutrits, and concretely display them in cases using 3-qubit, 2-qutrit maximally entangled basis states. We further show that our protocols will become safer with an increase in dimensions and number of particles. Moreover, we carry out the security analysis using quantum covariant cloning machine. Although the applications of the generalized scheme need to be further studied, GCORE has many distinct features such as large capacity and high efficiency.