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1st class

The terminology used here will follow the guides given in [33]:

It is known as embedded information or hidden information, the

information which is secretly sent.

The audio track, image, video, text, or in essence, the data among

which the information is to be embedded, receives the name of carrier or

cover. Depending on the specific kind of cover, one can also say cover

audio, cover image, etc.

The object resulting of the insertion of the information to embed into

the carrier is called stego-object. As before, the terms stego-audio, stego-

image, etc. can also be used.

The key (which may have been) used in the process is known as stego-

key, although when the context does not give place to doubts, just key

can be used.

---Steganography(stego) is hide secrets

----A steganographic method consists of an embedding algorithmand an extraction algorithm.

---The embedding algorithm describes how to hide a message intothe cover object.

----The extraction algorithm illustrates how to extract themessage from the stego object.

----To reduce distortion on a cover object based on a tree structure is called tree

based parity check (TBPC)

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-------- The toggle criteria of a node in the TBPC method can be relaxed

by the strategy of majority vote.

---------Our strategy inherits the efficiency of the TBPC method and

produces a stego object with least distortion under the tree based parity

check model.

-------The embedding efficiency is defined to be the number of hidden

message bits per embedding modification.

-------Higher embedding efficiency implies better undetectability for

steganographic methods.-------The lower embedding efficiency is defined to be the ratio of the

number of hidden message bits to the maximum embedding

modifications.

--------The lower embedding efficiency is related to undetectability in the

worst case. It implies steganographic security in the worst case. Thus,

the lower embedding efficiency is also an important security factor for a

steganographic system.

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2nd class

---------Before embedding and extraction, a location finding method determines a

sequence of locations that point to elements in the cover object.

-----------The embedding algorithm modifies the elements in these locations to hide

the message

------------the extraction algorithm can recover the message by inspecting the same

sequence of locations.

---------The TBPC (tree based parity check )method is a least significant bit (LSB)steganographic method.

------Only the LSBs of the elements pointed by the determined locations

are used for embedding and extraction.

-----The TBPC method constructs a complete N-ary tree, called the

master tree, to represent the LSBs of the cover object.

-----Then it fills the nodes of the master tree with the LSBs of the cover

object level by level, from top to bottom and left to right. Every node of

the tree corresponds to an LSB in the cover object. Denote the number

of leaves of the master tree by L.

------The TBPC embedding algorithm derives an L-bit binary string,

called the master string, by performing parity check on the master tree

from the root to the leaves (e.g. see Figure 1.).

------The embedding algorithm hides the message by modifying the bit values of

some nodes in the master tree.

-----Assume that the length of the message is also L. Performing the bitwise

exclusive-or operation between the message and the master string, we obtain a

toggle string (e.g. see Figure 1).

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----------Then the embedding algorithm constructs a new complete N-ary tree,

called the toggle tree in the bottom-up order and fills the leaves with the bit values

of the toggle string and the other nodes with 0.

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---------Then level by level, from the bottom to the root, each non-leaf node

together with its child nodes are flipped if all its child nodes have bits 1 (e.g. see

Figure 2).

-------The embedding algorithm obtains the stego tree by performing exclusive-or

between the master tree and the toggle tree (e.g. see Figure 3).

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------The TBPC extraction algorithm is simple. We can extract the message by

performing parity check on each root-leaf path of the stego tree from left to right.

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N-ary Trees

In the preceding section we considered trees in which the nodes can have arbitrary

degrees. In particular, the general case allows each of the nodes of a tree to have a

different degree. In this section we consider a variation in which all of the nodes ofthe tree are required to have exactly the same degree.

Unfortunately, simply adding to Definition the additional requirement that all of the

nodes of the tree have the same degree does not work. It is not possible to construct a

tree which has a finite number of nodes all of which have the same degreeNin anycase except the trivial case ofN=0. In order to make it work, we need to introduce the

notion of an empty tree as follows:

Definition (N-ary Tree) AnN-ary tree Tis a finite set ofnodes with the following

properties:

1. Either the set is empty, ; or

2. The set consists of a root,R, and exactlyNdistinctN-ary trees.

That is, the remaining nodes are partitioned into subsets, ,

, ..., , each of which is anN-ary tree such that

.

According to Definition , anN-ary tree is either the empty tree, , or it is a non-empty set of nodes which consists of a root and exactlyNsubtrees. Clearly, the emptyset contains neither a root, nor any subtrees. Therefore, the degree of each node of

anN-ary tree is either zero orN.

There is subtle, yet extremely important consequence of Definition that often goes

unrecognized. The empty tree, , is a tree. That is, it is an object of the same type

as a non-empty tree. Therefore, from the perspective of object-oriented program

design, an empty tree must be an instance of some object class. It is inappropriate to

use the null reference to represent an empty tree, since the null reference refers to

nothing at all!

The empty trees are called external nodes because they have no subtrees and

therefore appear at the extremities of the tree. Conversely, the non-empty trees are

called internal nodes .

Figure shows the following tertiary (N=3) trees:

http://www.brpreiss.com/books/opus5/html/page257.html#figtree3http://www.brpreiss.com/books/opus5/html/page257.html#defnnarytreehttp://www.brpreiss.com/books/opus5/html/page257.html#defnnarytreehttp://www.brpreiss.com/books/opus5/html/page253.html#defntree

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In the figure, square boxes denote the empty trees and circles denote non-empty

nodes. Except for the empty trees, the tertiary trees shown in the figure contain the

same sets of nodes as the corresponding trees shown in Figure .

Figure: Examples ofN-ary trees.

http://www.brpreiss.com/books/opus5/html/page253.html#figtree1

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3rd class

MAJORITY VOTE STRATEGY

Two critical issues for a steganographic method are: (1) reducing distortion on cover objects, and

(2) better efficiency for embedding and extraction. We give a majority vote strategy on building

the toggle tree. It uses the least number of 1s under the tree based parity check model. Since the

number of 1s in the toggle tree is the number of modifications on the master tree (i.e., the cover

object), the majority vote strategy can produce a stego tree with least distortion on the master

tree.