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

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

4 Simple LSB 0 ( ) ( ) ( ) ( ) ( ) 2 Embedded with 6 (110) ( ) 2 Usually hidden in 1 to 4 bits k = ( ) 2 = (A 6 1) 16

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 LSB with Permutation Cover image Secret message (C 2) 16 = ( ) 2 k = 2 n = 4 Value permutation (0, 1, 2, 3)  (2, 0, 1, 3) k 0 = 1 k 1 = 3 ( ) 2  ( ) 2 value permu  ( ) 2 pos. permu  ( ) 2 i ’ = (1, 0, 3, 2) Stego image

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 Cover image Stego image Value permutation (0, 1, 2, 3)  (2, 0, 1, 3) Cover image Simple LSB Sum of square error = 6 Sum of square error = 7

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 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 Image Hiding by Optimal LSB Substitution and Genetic Algorithm Crossover Mutation Fitness function is the sum of square errors.

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 Reduce complexity Find real optimal solution

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

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 Hiding Data in Images by Simple LSB Substitution Chi-Kwong Chan, L.M. Cheng Pattern Recognition, Vol. 37, 2004, pp

14 Use Modulus Functions Cover pixel ( ) 2 Secret piece (110) 2 ( ) 2 Square error = 5 2 = 25 Consider ( ) 2 + (110) 2 - (1000) 2 = ( ) 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 Comparisons Schemes k Simple LSB GeneticDynamicModulus *

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