Reversible data hiding in encrypted images is an effective technology for data hiding and protecting image privacy. Although there are many high-capacity methods have been presented in recent year, most of them need a pre-processing phase to reserve room in the original image before encryption. It may be unpractical, because the image provider has to analyze the content of the image and accomplish additional operations. In this paper, we propose a new robust vacate room after encryption schema based on polynomial arithmetic, which achieves a high embedding capacity with the perfect recovery of the original image. An efficient symmetric encryption method is applied to protect the privacy of the original image. One polynomial is generated by the encryption key and a group of the encrypted pixel, and the secret data is mapped into another polynomial. Through the arithmetic of these two polynomials, we can extract secret data and recover origin image, separately. Experimental results demonstrate that our solution has a stable and good performance on various images (include rough texture image). Compared with some typical methods, the proposed method can get better decrypted image quality with a large embedding capacity.