The embedding process for most of the state‐of‐the‐art adaptive steganographic methods (not easily detectable) such as highly undetectable steganography (HUGO), edge adaptive image steganography (EA), and Adaptive ±1 Steganography in Extended Noisy Regions, is contingent upon the neighboring pixel values to prevent discovery by steganalysis methods. Hence, the calculation of the possible embedding rate must be suspended until the embedding process is performed pixel by pixel, in sequence. If, however, the cover image is JPEG‐compressed, an error image can be considered as an embedding map implying where and to what extent secret bits can be embedded. In this paper, we present a modular steganography using error images. It is demonstrated that the detectability level of the resulting stego images is lower than that of state‐of‐the‐art schemes and the proposed method executes 2.32 times faster than HUGO. Further, to improve the time performance, a block‐wise parallel algorithm is presented where a single thread is assigned to each block of pixels. Because of the independent behavior of the embedding method and unlike the other methods, it is proved that each block of pixels can be embedded independently. The effectiveness of this parallel approach is analyzed and verified to execute approximately 55 times faster than serial execution. Copyright © 2014 John Wiley & Sons, Ltd.