You can concatenate a gif and a zip (the information you want to hide) into one file. Gifs are read from the start of the file, while zips are read from the end of the file.
To create such a file in linux:
$ cat file1.gif >> outfile.gif
$ cat file2.zip >> outfile.gif
The resulting file should have the size of file1.gif and file2.zip together and should be openable by any gif viewer and zip file handler.
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