祭奠亲人的诗句
On The Limits of Steganography Abbas Alfaraj, MS.c. Information Security, UCL, April 18, 2006
Abstract—The is a summery of Andeson & Fabien paper titled “On The Limits of Steganography” published in May 1998 for the IEEE Journal of Selected Area in Communications . I will introduce the definition and the history of Steganography as will as the us and the application. In the paper I prent the conventional steganography and the new method using power of the parity. I will briefly explore the theoretical limits of the steganography. Finally, I will discus public-key Steganography. Index Terms—steganography, traffic curity, watermarking
一时兴起的反义词
I.I NTRODUCTION
低压验电器T his paper, we will define steganography and it will
introduces some of applications can be expected. Steganography is an art and science of hidding information within other information. The word itlf comes from Greek and means “hidden writing”. First book covering steganography was written by Johannes Trithemius in 1499. The book Steganographia itlf was published later in 1606 and immediately placed on the Index Librorum Prohibitorum.
油泼干豆腐
In recent years cryptography become very popular science. As steganography has very clo to cryptography and its applications, cryptography is about concealing the content of the message. Steganography goes a step further and makes the ciphertext invisible to unauthorized urs. Hereby we can define steganography as cryptography with the additional property that its output looks unobtrusively.
A famous example of steganography is Simmons 'Prisoners' problem. Bob and Alice are in a jail and wish to escape. Their cells are far apart from each other and the only allowed communication is nding messages via prison warden. If warden detects any sign of conspiracy, they will cure their cells even more. Bob and Alice are well aware of the facts. Before they got arrested, they have agreed a Stegosystem. Stegosystem describes the way the cret message is embedded into a covertext (emingly innocent message). According to the standard terminology of information hidding a covertext with hidden information is called stegotext. Examples of historical Stegosystems can be cret inks, wax tablets or microdots ud during WWII. In modern era the methods can invoke smile on face, but image their power, when they were not widely known.
Nowadays methods still hold the same simplicity; just exploit advantages of digital media and communications. We can distinguish between Stegosystem with passive warder and active warder.
Passive warder just monitors the communication channel. He can pass the covertext through veral statistical tests, but do not modify them. It is the same situation as when the network packets go through Intrusion Detect System. Applications from this field are often referred to as traffic curity. On the other side, active warden manipulates covertext in order to preclude the possibility of hidden communication. Bob and Alice have to u very sophisticated embedding algorithm. Hidden information must withstand various recoding of covering medium, the u of error correction codes is recommended. Typical real-life application is watermarking and fingerprinting. Watermark is a small piece of embedded information which can proof copyrighted material. Fingerprint is very similar, but is intended to track the concrete copy of copyrighted data.
II.E MBEDDING PROCESS
吃鸡头Least Significant Byte (LSB) substitution is well known and widely ud method. Take for example a True-Color BMP image file format. A color of pixel is coded in 3 byte array of indices to RGB palete. If you change only LSB bit in each color element, then the picture will em still the same, but is not. It carries hidden information. A picture with size 120x100 pixels can hold approximately up to 4500B of hidden data, if this method is ud.
To cure out our Stegosystem algorithm at least a bit more, we can with advantage u some conventional pudo-random number generator. Supplied password or key will rve as initial ed. Generated numbers will specify which pixel to u for encoding next bits of embedded data. The adversary, even with the complete knowledge of Stegosystem, cannot extract the hidden message without the key. This system is cure in a n of Keckhoffs' assumption, that everything is known except the key.
Similar procedures can be successfully applied to wide variety of multimedia formats. Only instead of the color indices we slightly modify the Discrete Cosine Transformation (DCT) or Fourier Transformation (FT) coefficients. The changes have usually projection to specific statistical properties of common multimedia data. For few formats the properties have been already discovered, for many not yet. The main problem is that the tests are still quite fragile. They tend to fail, if only a small amount of hidden information is embedded or algorithm is modified.
III. T HEORETICAL LIMITS
麻成语Possibilities how to add hidden information to existing data are almost endless. Even in a very cure operating system, programs can still communicate by measuring CPU load or memory usage,
考报名时间
and so on. Information theoretic scientists try to ek for the limits of steganography. Currently we know
two mathematical frameworks. The first one is informatics-theoretic model and the cond is complex-theoretic view. Data which hold effective information often has some redundancy. End urs usually tend to think that redundancy is evil which cost extra money, as more disk space or network bandwidth is needed. Well, they are partially right, but optimal compression hardly ever exists. Moreover common compress ratio is mostly question of efficiency. Anderson on his paper pointed out one interesting
conclusion in ca we have optimal compression. Image an
algorithm A, which can optimally compress files. Algorithm B then does the decompression. Here, steganography is either impossible or trivial. We cannot add anything to the compresd file, otherwi the decompression will fail. On the other hand, we can take our cret information and algorithm B will trivially convert it to some fine familiar sound or video.
The entropy of the stegotext S is equal to the sum of the covertext C entropy and the embedded material E entropy:
H(S) = H(C) + H(E)
For cure embedding we need to increa H(C) or keep the H(E) much less uncertain than H(C). However, this will not help in all ca as we don’t know how competent is the opponent in measuring the entropy?
The correct lection channel is another limit for steganography. Anderson and Fabien, suggest sharing one-time pad as the lection to decide which bit to tweak it on the
covertext with the next ciphertext bit. Another lection
channel is the u of shared book between the nder and the receiver. It is just looks like the book cipher. This is cure provided that the opponent doesn’t know which book is being
ud. The limitation of the shared book channel is the repetition of the book after a while of using that book.
If the covertext has unusual statistics then the Stego capacity well be lower and the lection channel will be limited. Which will make the ciphertext doesn’t look like random enough.
Newly developed Stegosystem introduced new embedding process. , using the parity. Instead of embedding bad on the lected bit of the covertext they lect a t of bits or pixels k and embed the ciphertext as their parity. The grater the k the more we can hide in the covertext. However, we still have limitation, the maximum covert capacity will be H(E) –
H(M); where H(M) is the entropy of the allowed t of the
covert texts, and H(E) is the measure of the allowed encodings. In other words, this will give only the upper bound of how much we can embed but the safety bound where we can embed without attack or noi.
Equivalence class of messages are tied up with the compression. If covertext C1 has a meaning or effect that is
equivalent to that of cover text C2, then a compression algorithm need only lect one reprentative from this equivalence class. If C1≠C2, then this choice throws away information and the compression is lost. IV. PUBLIC -KEY STEGANOGRAPHY The u of the direct embedding process of the power of parity requires a key to lect the channel or the candidate bit. This technique assumed that both Alice and Bob share a key. What if they are not? In this ca Alice can
u Bob public-key to encrypt the message then embedded as the parity of each successive block of the covertext. Public-key stenography means parties can communicate confidentially in
双曲线的几何性质
the abnces of pre shared key. The encrypted values using public-key are a ssion key plus padding, and ssion key to
drive conventional steganography scheme. V. C ONCLUSION This paper was a short summary of Andrson and Petitcolas which introduces the world of steganography in short. We have shown how the simplest methods work and how they can
be explored. The main two propos of the paper is to prent the theoretical limits of the theory of steganography and the public-key steganography. The paper was prented for IEEE Journal of Selected Areas in Communications , May 1998.
Many development and progress has be done in this field.
Therefore, some of the theoretical limits are not any more
limits.
R EFERENCES [1] R. J. Anderson, F. A. P. Petitcolas, “On The Limits Of the
Steganography”, IEEE Journal of Selected Areas in Communications, 16(4):474-481, May 1998.
