This thesis proposes and implements a steganographic method which encrypts the secret message before hiding data to improve the security. The secret message encryption is a sequence of bits obtained from shuffling the bits of the secret message according to the concept of a multiplicative abelian group. We first select a prime number p and convert a secret message into a bit sequence S[i], 1□ S[i]<p, according to ASCII representation of each character, then we choose an integer primitive root g, 1<g<p, such that {gk mod p, for 1□k<p} is the same as {1, 2,…, p-1}, then shuffle the bit sequence S into B such that B[i] = gS[i] mod p. We then replace the k least significant bits of each pixel on a user selected 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 the prime number p are provided.

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