1. Data hiding in Least Significant Bit (LSB) Speaker: Feng Jen-Bang ( 馮振邦 )

2. 2 Outline Data Hiding by LSB Simple LSB LSB with Permutation Find Optimal Solution Use Genetic Algorithm Use Dynamic Algorithm Use Modulus Function Comparisons Comments

3. 3 Data Hiding by LSB Extract does not need cover image Capacity is 1/8 – 1/2 PSNR is about 51 - 31 Embedded by LSB Secret message Cover image Stego image Secret message Extract

4. 4 Simple LSB 0 (0000 0000) 2 128 (1000 0000) 2 129 (1000 0001) 2 135 (1000 0111) 2 155 (10011011) 2 Embedded with 6 (110) 2 158 (10011011) 2 Usually hidden in 1 to 4 bits 0010 1101 0010 1001 0010 1100 0010 1001 k = 3 101001 100001 (1010 0110 0001) 2 = (A 6 1) 16

5. 5 LSB with Permutation Cover pixels: c 0, c 1, …, c n Secret pieces: s 0, s 1, …, s n k bits each Exchange values (0, 1, …, 2 k -1)  (v 0, v 1, …, v 2 k -1 ) Exchange positions Permutation keys: k 0, k 1 k 1 is relatively prime to n

6. 6 LSB with Permutation 0010 1101 0010 1001 0010 1100 0010 1001 Cover image Secret message (C 2) 16 = (1100 0010) 2 k = 2 n = 4 Value permutation (0, 1, 2, 3)  (2, 0, 1, 3) k 0 = 1 k 1 = 3 (1100 0010) 2  (11 00 00 10) 2 value permu  (11 10 10 01) 2 pos. permu  (10 11 01 10) 2 i ’ = (1, 0, 3, 2) 0010 1110 0010 1011 0010 1101 001010 Stego image

7. 7 Finding Optimal Solution Find the optimal solution of value permutation. k 0 and k 1 are keys Too much computation of exhausted method 2 k ! possible permutations 0010 1101 0010 1001 0010 1100 0010 1001 Cover image 0010 1110 0010 1011 0010 1101 001010 Stego image Value permutation (0, 1, 2, 3)  (2, 0, 1, 3) 001011 1000 0010 1100 001010 Cover image Simple LSB Sum of square error 2 2 +1 2 +0 2 +1 2 = 6 Sum of square error 1 2 +2 2 +1 2 +1 2 = 7

8. 8 Image Hiding by Optimal LSB Substitution and Genetic Algorithm Ran-Zan Wang, Chi-Fang Lin, and Ja-Chen Lin Pattern Recognition, Vol. 34, 2001, pp. 671-683 Use genetic algorithm to find nearly optimal solution of value permutations 10 random permus. Crossover Mutation Fitness function 10 pairs Reproduction P=0.1 Nearly optimal Solution

9. 9 Image Hiding by Optimal LSB Substitution and Genetic Algorithm Crossover 0123456702461357 01231357 0123465702461537 02464567 01234567 05234167 Mutation Fitness function is the sum of square errors.

10. 10 Finding Optimal Least Significant Bit Substitution in Image Hiding by Dynamic Programming Strategy Chin-Chen Chang, Ju-Yuan Hsiao, and Chi-Shiang Chan Pattern Recognition, Vol. 36, 2003, pp. 1583-1595 Reduce complexity Find real optimal solution

11. 11 Finding Optimal Least Significant Bit Substitution in Image Hiding by Dynamic Programming Strategy m i,j = sum of square errors that change j to i

12. 12 Finding Optimal Least Significant Bit Substitution in Image Hiding by Dynamic Programming Strategy Optimal permutation (0, 2, 1, 3)

13. 13 Use Modulus Functions A Simple and High-Hiding Capacity Method for Hiding Digit-by-Digit Data in Images Based on Modulus Function Chih-Ching Thien, Ja-Chen Lin. Pattern Recognition, Vol. 36, 2003, pp. 2875-2881 Hiding Data in Images by Simple LSB Substitution Chi-Kwong Chan, L.M. Cheng Pattern Recognition, Vol. 37, 2004, pp. 469-474

14. 14 Use Modulus Functions Cover pixel (1100 1001) 2 Secret piece (110) 2 (1100 1110) 2 Square error = 5 2 = 25 Consider (1100 1000) 2 + (110) 2 - (1000) 2 = (1100 0110) 2 Square error = 3 2 = 9 K = 3 If (r – s) > 2 k-1 c = c + 2 k If (r – s) < 2 k-1 c = c – 2 k r c s

15. 15 Comparisons Schemes k Simple LSB GeneticDynamicModulus 151 24445 46 337*40 43133 34

16. 16 Comments The most simple and easy way A blind method Almost largest capacity Applied wildly