The　quantum　Fourier　transform,　the　quantum　wavelet　transform,　etc.,　have　been　shown　to　be　a　powerful　tool　in　developing　quantum　algorithms.　However,　in　classical　computing,　there　is　another　kind　of　transforms,　image　scrambling,　which　are　as　useful　as　Fourier　transform,　wavelet　transform,　etc.　The　main　aim　of　image　scrambling,　which　is　generally　used　as　the　preprocessing　or　postprocessing　in　the　confidentiality　storage　and　transmission,　and　image　information　hiding,　was　to　transform　a　meaningful　image　into　a　meaningless　or　disordered　image　in　order　to　enhance　the　image　security.　In　classical　image　processing,　Arnold　and　Fibonacci　image　scrambling　are　often　used.　In　order　to　realize　these　two　image　scrambling　in　quantum　computers,　this　paper　proposes　the　scrambling　quantum　circuits　based　on　the　flexible　representation　for　quantum　images.　The　circuits　take　advantage　of　the　plain　adder　and　adder　modulo　to　factor　the　classical　transformations　into　basic　unitary　operators　such　as　Control-NOT　gates　and　Toffoli　gates.　Theoretical　analysis　indicates　that　the　network　complexity　grows　linearly　with　the　size　of　the　number　to　be　operated.