A New Digital Image Steganography Approach Based on The Galois Field GF(pm) Using Graph and Auto

Abstract

In this paper, we introduce concepts of optimal and near optimal secret data hiding schemes. We present a new digital image steganography approach based on the Galois field () m GF p using graph and automata to design the data hiding scheme of the general form 2 (, , log) mn k N p     for binary, gray and palette images with the given assumptions, where , , , k m n N are positive integers and p is prime, show the sufficient conditions for the existence and prove the existence of some optimal and near optimal secret data hiding schemes. These results are derived from the concept of the maximal secret data ratio of embedded bits, the module approach and the fastest optimal parity assignment method proposed by Huy et al. in 2011 and 2013. An application of the schemes to the process of hiding a finite sequence of secret data in an image is also considered. Security analyses and experimental results confirm that our approach can create steganographic schemes which achieve high efficiency in embedding capacity, visual quality, speed as well as security, which are key properties of steganography.

A Novel Cryptosystem Based on Steganography and Automata Technique for Searchable Encryption

“…We organize the rest of this paper as follows. In Section 2, we recall some terminologies, definitions and results in [24,27,28,29]. Section 3 proposes algorithms used by users and servers in SSE, we first construct a novel cryptosystem based on the data hiding scheme in [27], apply this cryptosystem to the process of encrypting and decrypting a secret data sequence and some security analyses are also discussed in Subsection 3.1.…”

“…In Section 2, we recall some terminologies, definitions and results in [24,27,28,29]. Section 3 proposes algorithms used by users and servers in SSE, we first construct a novel cryptosystem based on the data hiding scheme in [27], apply this cryptosystem to the process of encrypting and decrypting a secret data sequence and some security analyses are also discussed in Subsection 3.1. We then use the automata approach in our previous researches [28,29] to design exact and approximate pattern matching algorithms on secrete data encrypted by our cryptosystem in Subsection 3.2.…”

“…In this section, we will attempt to recall terminologies, definitions and results in [24,27,28,29], which are really needed in order to present our new results clearly and logically, as well as help readers follow our paper's content easily. Now, we start with our near optimal data hiding scheme (2,9,8) proposed in [27], one of our data hiding schemes based on the Galois field 2 (2 ) GF , constructed from the polynomial ring Z2[x] [24]. This scheme is a core material for constructing our new cryptosystem.…”

“…While data hiding is used to hide data in digital media such as image, audio, video files, etc. It can be classified into steganography that protects secret data by hiding the existence of them and watermarking that prevents digital media by embedding watermarks in them [6,34,27].…”

“…In our approach, we use the data hiding scheme (2,9,8) that is block based method in spatial domain, where 9 is the number of pixels in any image block, 8 is the number of secret bits which can be embedded in a block by changing colors of at most 2 pixels in the block. This scheme is near optimal for gray and palette images with high efficiency in embedding capacity, speed, security as well as visual quality, which are main properties of data hiding schemes [27]. Since our cryptosystem is designed to solve the problem of pattern matching on encrypted data and for an assumption that secret data is a string over the alphabet of size 256, the cryptosystem allows to encrypt letters of the secret data one by one.…”