# Watermarking And Cryptography Algorithm Computer Science Essay

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Cryptography Algorithm: One of the first audio watermarking algorithms that we developed (Paper I) is a time domain spread spectrum algorithm. It embeds a spread-spectrum-based watermark into an uncompressed, raw audio by slightly modifying the values of samples of the host audio in time domain. The main motivation was the development of an algorithm with a low computational complexity and with an embedding and extraction of watermarks in time domain. One of the most robust methods already developed for audio watermarking was a time domain algorithm. Therefore, we tried not to use transforms, like DFT, or cepstrum transform that shift the host audio to transform domains and back to

temporal domain consequently. It would definitely be hard to prove mathematically that watermarking in time domain gives smaller computational complexity in comparison with other, non-temporal algorithms because it is hard to compare complexity with each developed

watermarking scheme. However, time domain algorithms have at least a lower implementation complexity and a smaller number of blocks in embedding and extraction algorithms. In order to describe the link between watermarking and standard data communications,

the traditional model of a data communications system is often used to model watermarking systems. One of the most important parts of the communications models of the watermarking systems is the communications channel, because a number of classes of the communications channels have been used as a model for distortions

imposed by watermarking attacks. The other important issue is

the security of the embedded watermark bits, because the design of a watermark system has to take into account access that an adversary can have to that channel The main elements of the traditional data communications model are depicted in the diagram. The main objective is to transmit a message m across a communications channel.

The channel encoder usually encodes this message in order to prepare it for transmission over the channel. The channel encoder is a function that maps each possible message into a code word drawn from a set of signal that can be transmitted over the communications channel. The code word mapped by the channel encoder is denoted as x. It is common,

as we deal with digital data and signals, that the encoder consists of a source coder and a modulator. The source coder removes the redundancy from the input message and maps a message into a sequence of symbols drawn from some alphabet. The duty of the modulator is to convert a sequence of symbols from the source coder into a signal suitable for transmission through a physical communications channel. It can use different modulation techniques such as amplitude, phase or frequency modulation. The definite form of the channel encoder&acirc;€™s output depends on the type of the transmission channel used in a particular model, but it is usually described as a sequence of real

values, quantized to some arbitrary precision. In addition, we assume that the range of values of the channel encoder is limited in some way, usually by a power or amplitude constraint. The signal x is subsequently sent over the communications channel, which is assumed to be noisy. The consequence of the presence of noise is that the received signal, conventionally denoted as y, is generally different from x. The extent of the change depends of the level of the noise present in the channel and is modeled here as additive noise. In other words, the transmission channel is modeled as adding a random noise n to the encoder&acirc;€™s output x. At the receiver part of the system, the received signal, y, is forwarded, as the

input signal, to the channel decoder which inverts the encoding process and attempts to correct for errors caused by the presence of noise. This is a function that maps transmitted signals into messages mr. The decoding process is typically a many-to-one function, so that correct decoding is possible even using noisy coded words. If the channel

code is well matched to a given channel model, the probability that the decoded message contains an error is negligibly small.

## Secure data communications

An important issue in watermarking is the security of the embedded watermark bits because the design of a watermark system has to take into account access that an adversary can have to the communications channel. In particular, we are interested in applications that demand security against passive and active adversaries. In the case of passive attacks, an adversary monitors the transmission channel and attempts to illegally read the message.

In the active attack case, the adversary actively tries either to disable communication or transmit unauthorized messages. There are two main methods of defence against attacks. cryptography is used to encrypt a message using a secret key and after that the encrypted

message is transmitted. On the receiver side, the encrypted message is received and then decrypted using the same or a related key to reveal the message. Cryptography introduces two advantages in a data communications

system. The first is to prevent passive attacks in the form of an unauthorized reading of the message and the second is to prevent active attacks in the form of illicit writing. However, cryptography does not necessary prevent the adversary from knowing that a message is

being transmitted. In addition, cryptography is helpless if an adversary intents to distort or remove a message before it is delivered to receiver.

Signal jamming (the deliberate effort by an adversary to inhibit communication between transmitter and receiver) was a great problem for military communications and has led to the development of the spread spectrum communication. In those systems, the

modulation is performed according to a secret code that spreads the signal across a wider bandwidth than is regularly required. The code can be modeled as a form of the key used in the channel coder and decoder, as depicted in Figure 4.3. One of the examples of the spread spectrum communications is the frequency hopping method, one of the earliest

and simplest spread spectrum techniques. In a frequency-hopping system, the transmitter broadcasts a message by first transmitting a part of the message bit stream on one frequency, the next fraction of the bit stream on the another frequency, and so on. A secret key that is known at the receiver as well as on the transmitter side controls the order of

frequencies used for frequency hopping. Without a key, an adversary could monitor the transmission. The disruption of the transmission is also very difficult, because it could be done only by introducing noise at all possible frequencies, which would require too much power.

The cryptography and SS communications are complementary. The SS guarantees the delivery of signals, while the cryptography guarantees the secrecy of messages. Thus, it is common that these two technologies are combined in watermarking applications.