1. Reversible Data Embedding Using Difference Expansion IEEE Transactions on Circuits and Systems for Video Technology, Vol. 13, No. 8, Aug. 2003, page(s): 890 -- 896 Authors: Jun Tian Speaker: J.H. Liu

2. Outline  Data Embedding  Reversible Data Hiding  Difference Expansion  Expandable  Changeable  Difference Expansion Decoding  Expandable decoding  Changeable decoding  Conclusions

3. Data Embedding  Reversible data hiding 1

4. Difference Expansion  One of data embedding methods  Basic case:  h = x – y l = ( x + y ) / 2 x=l + h /2 + LSB( h ) y=l - h /2  Hint : There divide(/) is integer divide.  For example, x/y meaning floor(x/y). x =206 y =201 average l = 203 +3-2 If h is odd, bit will lost with h /2. We must return it into x. 2

5. Difference Expansion - method location map L Case1. expandable : h’ = 2× h + b 1  h = x - y Case2. changeable : bitstream C 0 Case3. non-changeable0  bitstream C = collection of LSBs( h )  Expandable : | h’ | = |2x h + b | ≦ min(2(255- l ),2x l -1) Changeable : | h’ | = |2x( h /2)+ b | ≦ min(2(255 -l ),2x l -1) 3

6. Expandable  1 st step: h’ = h x2 + secret bit ( b )  2 nd step: x’ = l + h’ /2 + LSB( h’ ) y’ = l - h’ /2  location map L = 1 x’ =209 y’ =198 l = 203 +6-5 4 206 201 +3-2 b = 1 l =203 h’ =5*2+1=11 x’ =203+11/2+11%2=209 y’ =203-11/2=198

7. Changeable  It is non-expandable  1 st step: h’ = ( h /2)x2 + b  2 nd step: lost bit( c ) = LSB( h )  3 rd step: x’ = l + h’ /2 + LSB( h’ ) y’ = l - h’ /2  location map L = 0 x =246 y =200 l = 223 +23-23 There we will lost the LSB of h. We record the LSBs of h at bitstream C. x’ =247 y’ =200 +24-23 5

8. Expandable decoding  1 st step: get h’ = x’-y’  2 nd step: get b = LSB( h’ )  3 rd step: get h = h’ /2  4 th step: get x = l + h /2 + LSB( h ) y = l - h /2 Note: average l is never changed. x‘ = 209 y‘ = 198 l = 203 +6-5 l =(209+198)/2=203 h’ =209-198=11 b =11%2=1 h =11/2=5 x =203+5/2+5%2 =203+2+1=206 y =203-5/2=201 x = 206 y = 201 l = 203 +3-2 6

9. Changeable decoding  1 st step: get h’ = x’ - y’  2 nd step: get b = LSB( h’ )  3 rd step: get h = h’- b + bitstream( c )  4 th step: get x = l + h /2 + LSB( h ) y = l - h /2 x’ = 247 y’ = 200 l = 223 +24-23 l =(247+200)/2=223 h’ =247-200=47 b =47%2=1 h =47-1+0=46 x =223+(46/2)+46%2 =223+23+0=246 y =223-46/2=200 7 x =246 y =200 l = 223 +23-23

10. Conclusions  Simple and efficient reversible embedding method.  The method of location map L is not good enough. We may improve the method of location map anywise.  The case of changeable is a kind of useless. 8