Data hiding in Least Significant Bit (LSB)

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

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

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

Simple LSB 0 (0000 0000)2 155 (10011011)2 128 (1000 0000)2 Embedded with 6 (110)2 129 (1000 0001)2 158 (10011011)2 135 (1000 0111)2 Usually hidden in 1 to 4 bits 0010 1101 0010 1001 101 001 k = 3 (1010 0110 0001)2 = (A 6 1)16 0010 1100 0010 1001 100 001

LSB with Permutation • Cover pixels: c0, c1, …, cn • Secret pieces: s0, s1, …, sn • k bits each • Exchange values • (0, 1, …, 2k-1)  (v0, v1, …, v2k-1) • Exchange positions • Permutation keys: k0, k1 • k1 is relatively prime to n

LSB with Permutation • (1100 0010)2 •  (11 00 00 10)2 • value permu  (11 10 10 01)2 pos. permu  (10 11 01 10)2 Secret message (C 2)16 = (1100 0010)2 0010 1101 0010 1001 k = 2 n = 4 0010 1100 0010 1001 Cover image Value permutation (0, 1, 2, 3)  (2, 0, 1, 3) k0 = 1 k1 = 3 0010 1110 0010 1011 0010 1101 0010 1010 Stego image i ’ = (1, 0, 3, 2)

Finding Optimal Solution • Find the optimal solution of value permutation. • k0 and k1 are keys • Too much computation of exhausted method • 2k! possible permutations Value permutation (0, 1, 2, 3)  (2, 0, 1, 3) Simple LSB 0010 1101 0010 1001 0010 1111 0010 1000 0010 1110 0010 1011 0010 1100 0010 1001 0010 1100 0010 1010 0010 1101 0010 1010 Cover image Cover image Stego image Sum of square error 22+12+02+12= 6 Sum of squareerror 12+22+12+12= 7

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 Crossover 10 pairs Fitness function Nearly optimal Solution 10 random permus. P=0.1 Mutation Reproduction

Image Hiding by Optimal LSB Substitution and Genetic Algorithm 0 1 2 3 4 5 6 7 0 2 4 6 1 3 5 7 Crossover 0 1 2 3 1 3 5 7 0 2 4 6 4 5 6 7 0 1 2 3 4 6 5 7 0 2 4 6 1 5 3 7 0 1 2 3 4 5 6 7 Fitness function is the sum of square errors. Mutation 0 5 2 3 4 1 6 7

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

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

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

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

Use Modulus Functions Cover pixel (1100 1001)2 Secret piece (110)2 K = 3 s r If (r–s) > 2k-1 c = c + 2k If (r–s) < 2k-1 c = c– 2k c (1100 1110)2 Square error = 52 = 25 Consider (1100 1000)2 + (110)2 - (1000)2 = (1100 0110)2 Square error = 32 = 9

Comparisons

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

Data hiding in Least Significant Bit (LSB)