We present an optical security method for binary data information by using 4-step phase-shifting digital holography and we analyze tolerance error for the decrypted data. 4-step phase-shifting digital holograms are acquired by moving the PZT mirror with equidistant phase steps of ${pi}/2$ in the Mach-Zender type interferometer. The digital hologram in this method is a Fourier transform hologram and is quantized with 256 gray level. The decryption performance of the binary data information is analyzed. One of the most important errors is the quantization error in detecting the hologram intensity on CCD. The greater the number of quantization error pixels and the variation of gray level increase, the more the number of error bits increases for decryption. Computer experiments show the results for encryption and decryption with the proposed method and show the graph to analyze the tolerance of the quantization error in the system.