Implementation of Steganography Using LSB Replacement and Number Theory

Abstract

This thesis implements a steganographic method which encrypts the secret message by exponential and modular operations before hiding data to improve the security. For the cover image, we also do an affine transform based on the locations of pixels before embedding the bits. The secret message encryption is a sequence of bits obtained from shuffling the bits of the secret message according to the concept of an exponential and modular arithmetic. We first select a prime number p and convert a secret message into many sets of a bit sequence S[i], 1 S[i]<p, according to ASCII representation of each character, we can choose a primitive root g, 1<g<p, such that {gk mod p, for 1k<p} is the same as {1,2,3,…,p-1}, then shuffle the bit sequence S into B such that B[i] = gS[i] mod p. On the other hand, we do an affine transform on a cover image, then we replace the k least significant bits of each pixel on the affine transformed cover-image with B. The extraction of the secret message is based on solving a discrete logarithm problem which is regarded as a difficult problem when p is large. Experiments with different cover images, secret messages, and prime number p are provided.