Unit 23 Mathematics for Software Development

Unit 23 Mathematics for Software Development




Message encrypting and decrypting has been around for over a thousand years. New techniques are created to ensure the privacy and security of communication networks. This technique utilizes synchronized emitters and receivers to encode and decode data. The generated chaotic carrier from the emitter hides the information that can only be accessed using the right type of receiver, meaning the information from point A is not accessible until it reaches point B. There are different encryption techniques like the chaos shift keying where the message is encoded by switching the transmitter current between 1 and 0, the chaos modulation where the carrier is modulated by the message and finally the chaos masking where the message is not encoded on the carrier signal but just added to it. Chaos shift keying is the most popular method because of the robustness and simplicity of its receiver. Using these techniques changed the way we communicate with each other. It has its advantages and disadvantages depending on how we use it. (J. Liu, H. Chen, S. Tang, R. Vicente, T. Perez and C. R. Mirasso 2002)

In an effort to further enhance the security of optical communications researchers find new ways to enhance the encrypting and decrypting of the message. They discovered that self-pulsating vertical-cavity surface emitting lasers or VCSEL with the active region surrounded by a saturable absorber can display vectorial chaos or chaos in both intensity and polarization. VCSEL or Vertical-cavity surface emitting lasers are semiconductor lasers characterized by light emission orthogonal to the active layer, and showing substantial practical advantages in comparison to the more conventional edge-emitting lasers (EELs), for example, their compactness, superior beam quality, low threshold currents, and high efficiencies. From the nonlinear dynamics and laser physics point of view. From this they proposed a new scheme which can replace the chaos shift keying. In this new scheme the total intensity of the two VCSELs remains synchronized while the intensities in the polarization modes synchronize following the phase modulation. The message is then recovered by detecting the two linearly polarized components of the outcoming field. Chaos shift keying systems were limited by the relaxation oscillation frequency, while this technique allows, in principles, to transfer 100Gbit/Sec of secured data. With this new scheme communication is faster and yet safer. (C. R. hlirasso, P. Colet and P. Garcia-Fernandez 1996; V. Annovazzi-Lodi, S. Donati and A. Scirk 1997; G. Van Wiggeren and R. Roy 2002)

Transmission systems using chaos dynamics created a new way of securing their data using opto-electronic oscillators. Opto-electronic oscillator or OEO is an optoelectronic device that produces repetitive electronic sine waves and is used as a modulator together with a fiber-optic delay line to convert light energy into stable, spectrally pure RF/microwave reference signals. The signal is then delayed in time, and filtered by the speed limiting element of the oscillation loop, before being fed back to the linear source. (J.-P. Goedgebuer, P. Levy, L. Larger, C.-C. Chen and W.T. Rhodes 2002)

Proposal of a replacement sequence cipher manufacturing methodology that relies on the Particle Dynamics. Considering PDEA relies on the law of entropy increasing, the principle of energy minimum of particle systems and therefore the transport operate abstracted type the method of particles, it create the comparatively equal chance of all the particles to participate within the operation of crossover and mutation, that brings the deserves that uniformity and variety of particles within the system and then on. The algorithmic program this paper provides relies on these deserves. (Congress on Evolutionary Computation 2008)

Digital watermark formula has 2 kinds: time and area watermark formula and remodel watermark formula. Recently, an oversized of remodel digital watermark algorithms square measure place out, these algorithms in the main aim at grey scale image, and few analysis color image. However compared with grey watermark, color watermark includes additional info. Therefore the paper introduces a color image knowledge watermark technique supported the chaos encrypting. consistent with characteristic of Human Vision System, human eyes is most insensitive to blue, therefore it's potential to implant info by modifying blue component pels of RGB area, and a pseudo-random sequence is created by mistreatment chaos formula as embedding positions of watermark info. This formula is straightforward to realization, and embedding watermark satisfies invisibleness and hardiness within the same time. (Ye Fei, Jing qing Luo, Shilong Wu 2004)

In order to fulfill the requirements of period transmission and access of video data the coding and secret writing algorithms cannot bring abundant delay to the transmission and access. H.264 is that the latest video compression customary, its compression potency is additionally the best and doubly the maximum amount as H.263 and MPEG4 within the similar image quality. H.264 will greatly enhance compression potency and improve transmission of image knowledge within the network. This paper discusses issues concerning video security supported H.264 video compression secret writing customary, puts forward a style theme of coding concerning video meeting. The video coding system combines with AES formula, H.264 and also the chaos coding. During this theme, AES is employed to cypher video knowledge. Chaos coding technology is employed to come up with the video conference keys to make sure the unpredictability of the key. Public key coding is employed in key distribution. Experiments show that the system are able to do speedy video coding computing and swish video conferencing .It can also shield video knowledge well and meet the necessities of period video. (Hua-Zhen YAO and Ya-Tao JING 2002)

Characterization the separate Lyapunov exponent in terms of the utmost DP of a given map F . That is, we tend to derive a bound and an bound on the separate Lyapunov exponent of the map F given the dimensions of the domain and therefore the most DP of the map. we are able to use these bounds to spot an area wherever the separate Lyapunov exponent of AN coding transformation with a given domain size and smart most DP (close to 2/M) ought to belong. Both, the utmost DP and therefore the Lyapunov exponent area unit outlined by the distribution of the output distinction of a given map. whereas the separate Lyapunov exponent is outlined by the distribution of the output distinction once the input distinction is one, the maximum DP may be a lot of general characteristic of the map, and it's outlined by the distribution of the output distinction for each nonzero input distinction. we tend to use this observation to produce the subsequent bounds on the separate Lyapunov exponent given the parameter M and therefore the most DP.( G. Jakimoski and K. P. Subbalakshmi 2007 )

Synchronization of chaos in lasers has attracted nice interest as a result of 01 its potential applications for optical secure telecommunications. Some optical secret writing systems victimization chaos are proposed; like chaotic masking. Chaos shift keying, And chaotic modulation. Recently, a chaotic masking methodology victimization lasers has been through an experiment incontestable, wherever messages embedded in an exceedingly chaotic signal were recovered from domestically generated chaotic wave that exactly synchronize with the initial chaotic elements. A key a part of the chaotic masking methodology is replica of only the initial chaos from the transmitted signal with the messages.(M. Shinozuka. A. Uchidar. T. Ogawa. Y. Shiniainura, K. Otani. S. Yoshimorii, and E Kanriari 2000)

With the event of net and therefore the more and more outstanding of the data security, as a result of its high speed, block cryptography technology is that the 1st selection in a very sizable amount of data cryptography algorithms to boost the data security throughout the method of storage, transferring, reading and authorization management. Currently, DES, AES and Loch Ness monster, utilized in large-scale data cryptography, area unit all administered supported block cryptography. Aiming at low-scale data cryptography wide utilized in those instrumentation that possess restricted computing capability, small-size storage, and solely exchange a low-scale data once, like mobile phones, intelligent appliances, a variable-length block cryptography algorithmic program supported chaos particle swarm is advises that utilizes chaos characters to vary the length of block chaos, and carries out scrambling and cryptography victimization chaotic iteration supported bit-XOR therefore on accomplish high security, low machine complexness, high cryptography speed and low storage needs the initial chaos from the transmitted signal with the messages.( Zhu Shun-le, Wang Ya-xiang, Li Xin 2010)

A common attribute to any or all chaos-based block secret writing algorithms is that their security isn't analyzed in terms of the techniques developed in sepulchral analysis. As an example, the secret writing formula planned in is sepulchral analyzed in , showing that the formula will be broken mistreatment glorious plain text attack. we tend to recently analyzed the performance and security of chaos based mostly secret writing schemes planned. The analysis shows that the secret writing rates these algorithms supply are not competitive to the secret writing rates of the quality crypt graphic algorithms, and, what is more, the algorithms will be simply broken mistreatment glorious plain text attacks.( Goce Jakimoski and Ljupˇ co Kocarev 2001)

Digital watermarking in riffle remodel is one amongst study intensive activities. it's robust strength and sensible physical property. The most discussing within the paper is that the digital watermarking made by supply or Chebyshev chaos model is created “and or” operation to vital binary image watermarking through Arnold remodel scrambling to create secret watermarking, that then is embedded into carrier image in riffle remodel domain. A lot of, the retrieving algorithm of watermarking and strength checking against standard process furthermore as hostile attack square measure given. The experimental results show that the theme includes a sensible at visual physical property and strength against attack for concealment secret image information. (Zhu Xi’an, Wang Yongsheng 2010)

A new feedback chaotic cryptography theme is usually recommended during this Letter for secure and quick image cryptography. we have a tendency to projected a new feedback image cryptography algorithmic program supported new compound chaotic operate using 2 one-dimensional chaotic functions combined with cipher pixels substitution and permutation image cryptography. Meanwhile, to confuse the relationship between cipher-image and plain-image, a quick confusion method among pixels is performed mistreatment compound chaotic operating. Finally the protection of recent compound chaos cipher is given by theoretical and sensible experiment proof and it passes all types of randomness normal check. (Xiaojun Tong and Minggen Cui 2008)

Digital speech secure communication supported chaos includes the subsequent steps: A/D transformation and committal to writing, sequence generation, chaos secret writing, cipher text transmission, cipher text receiving, chaotic secret writing sequence generation, chaotic secret writing transformation and D/A transformation and secret writing. the prevailing speech secret writing strategies supported chaos usually use a comparatively straightforward sequence and transport knowledge by victimization transmission control protocol, that solely applies to the higher scenario on the network. usually speaking, these algorithms have the subsequent shortcomings: (1) it's easier to be decrypted due to the secret writing by the chaotic sequence generating from one chaotic system, single parameter and initial condition; (2) once an oversized quantity of information is encrypted, the sequences in periodical scale back the safety of cipher text due to the restricted preciseness of computers; (3) once transport the cipher text on the network, knowledge errors or loss in transmission won't be ready to be decrypted correctly; (4) it's troublesome to attain auto-synchronization in period secret writing and secret writing. Once the information square measure loss, the following-up isn't ready to be decrypted accurately. (Jing Liu, Fei Gao, Haiyan Ma 2001)

A secure communication system supported the idea of generalized synchronization (GS) and its combination with CS was originally advised by Murali and Lakshmanan. Since they used one line, the signal itself created a synchronization error that reduced the communication quality. a distinct approach consisted of 2 identical combines of chaotic systems (master and slave); one combine within the transmitter and therefore the alternative pair within the receiver. A bi-nary message was encrypted within the coupling strength between master and slave within the transmitter and was recovered by analyzing the error dynamics within the receiver; if truth be told, this technique was a modification of a chaos shift keying with a crucial innovation, it used 2 channels: one to supply cesium between the transmitter and therefore the receiver master systems, and therefore the alternative channel to match the 2 slave trajectories. However, within the chaos shift keying schemes a binary bit message inherently produces a synchronization error, thence limiting the communication rate with the synchronization time as a result of the transmitter and therefore the receiver don't seem to be endlessly synchronous. ((Murali and Lakshmanan, 1998; Terry and Van-Wiggeren, 2001)

Recently, quantum cryptography has been planned as another to computer code encoding. Despite its potential, its pertinence continues to be terribly off from being well-tried. the target of “Quantum Cryptography”—also termed “Quantum Key Distribution” (QKD)—is to use the properties of quantum optics so as to on the QT share a random bit sequence between 2 users. Once the key has been changed, the 2 parties will communicate, by standard suggests that, a message over a public channel by encrypting with the key a message of equal length. This theme belongs to the category of hardware-key cryptography and might be used solely to exchange a secret key. it's not appropriate for an entire message. In QKD schemes, security is secured by the basic laws of quantum physics, and so is very high. The secret's sent over a quantum channel. If AN auditor faucets the road, transmission errors occur owing to the quantum-mechanical nature of photons. To discover these errors, the legitimate users verify statistically a group of shared bits. If errors are detected within the verification method, the users conclude that the road is attacked. another and easy thanks to improve the protection of AN encrypted message will be completed by to boot encryption at the physical layer victimization chaotic carriers generated by elements operational within the nonlinear regime. Semiconductor lasers are ideal candidates for the conclusion of those nonlinear electrode and receiver systems. They’re already inherently nonlinear devices that, below numerous operational conditions, exhibit nonlinear high-octane behavior related to, e.g., quick irregular pulsations of the optical power or wavelength hopping. (Silvano Donati and Claudio R. Mirasso 2002)

Encryption may be a technique or a method for shielding info from undesirable attacks by changing it into a kind non-recognizable by its attackers. Adding security to quality of service (QoS) architectures are mentioned in. we have a tendency to assign unequal secret writing mechanisms in numerous multimedia system signals. On the opposite hand, chaos primarily based secret writing formula may be a new and attention-grabbing analysis topics for real time secret writing, like audio and video signal. The performance of chaos primarily based visual secret writing mechanism that apply in JPEG2000 X-ray and graphical record (ECG) medical signals, has been conscientiously studied in our earlier work. How to understand the secret writing mechanism is to scramble the bit streams of the input EKG signal by scrambling 1D chaotic sequence to randomize EKG signal bit streams, so a chaotic address scanning order secret writing is applied to the randomize reference bit streams. In distinction, a little stream mapping of 1D chaotic scrambler are granted to messages that may tolerate low level secret writing however meet high speed secret writing. it's a possible secret writing theme that will apply in real time audio and video signal. Simulation results show once correct deciphering parameters ar place in, the signal are utterly recovered. As long as there's associate input parameter error, as an example, with 0.00000001% initial purpose error, it might build chaotic array, and also the medical signals won't be recovered back. (Chin-Feng Lin, Cheng-Hsing Chung, Zhi-Lu Chen, Chang-Jin Song, and Zhi-Xiang Wang 2003 – 2005)

The advantage of the chaotic coding over alternative encrypting suggests that is that it prices less. These days most data on the web is transmitted in an exceedingly sort of stream. Data forms onedimension knowledge stream within the sequence of plain message from the initial crunodes and is transmitted to alternative crunodes. A client and a snatcher have virtually an equivalent likelihood to amass a region or maybe all of the knowledge flow. (Jinhong Luo , Haiyi Shi 2004)

Database management systems were created up of a heap of modules closing information inquiring and information and document regulation through identification, connected access and information represent lists. These management systems applied all types of languages: a knowledge definition language sustained the logical definition of the knowledgebase; developers use a data manipulation language; associate degreed an inquire language was applied by recreational end-users. information management systems had a heap of the similar security demands as operative systems, however there were necessary discrepancies as a result of the former were particularly accessible to the menace of inappropriate disclosure; amend of data and conjointly resignation of service. lots of the most meaning security demands for information management systems were: (1) Multi-Level Access management. (2) Confidentiality. (3) Responsibility. (4) Totality. (5) Improvement. (Zhang Deng-Hong 2010)

The potency and security necessities of data transmission cause a considerable quantity of analysis add data compression and cryptography. So as to enhance the performance and also the flexibility of transmission applications, it's worthy to perform compression and cryptography in an exceedingly single method. In general, there are 2 distinct analysis directions during this space. One among them embeds key-controlled confusion and diffusion in source-coding schemes, whereas another incorporates compression in cryptologic algorithms. Some tries of introducing key-controlled operations in entropy secret writing may be found in. The approach supported multiple Huffman tables at the same time performs cryptography and compression by a key-controlled swapping of the left and right branches of the Huffman tree. Some approaches like irregular arithmetic secret writing and key-based interval rending were planned to en graft cryptologic options in arithmetic secret writing. The compression capability of those algorithms is near that of ancient entropy secret writing. However, security and potency issues were found, and additional modifications are needed. (Jianyong Chen, Junwei Zhou, and Kwok-Wo Wong 2011)

Chaos-based cryptography has many sensible properties, like sensitivity to initial conditions, namely, the supposed outcome. However, chaotic maps enforced by computers with finite preciseness can result in dynamic degradation. The dynamic degradation can cause the sensible behavior of a chaotic system immensely completely different from the theoretical one. As an example, issues like cycle length, non-ideal distribution and correlation. These issues scale back the cryptosystem security strength greatly and therefore the generated sequence might not be used because the key stream. To beat these issues, many ways are projected, like the utilization of upper finite preciseness, perturbed-based formula, clock-controlled and therefore the use of multiple chaotic systems. During this paper a rattled couple chaotic pseudo-random bit generator with sensible cycle length and applied math property is employed to construct a stream cipher for JPEG 2000 image encoding. (Shun-Cheng Hong, Chun-Te Li, Hsi-Kuan Chen and Chin-Hsing Chen 1991)

Fridrich projected a cruciform block secret writing technique adapts invertible two-dimensional chaotic maps to shuffle the positions of image pixels. The 2nd chaotic map used is baker map. it's been shown that generalized map have blessings to inherits all necessary properties like the sensitivity to initial conditions and parameters, and also the compounding properties. In chaotic primarily based secret writing theme, the sensitivity property may be used for key generation as adopted in our projected procedure. Meanwhile, compounding properties will create correlate data become scattered everywhere the space. Pareek et al projected a picture secret writing supported 2 chaotic provision maps. In projected theme to create the cipher safer against any attack, eight differing kinds of operations area unit wont to write the pixels and also the secret is changed when every secret writing of the image. (Rashidah Kadir, Rosdiana Shahril, Mohd Aizaini Maarof 2006)

The development of optical telecommunications systems has return associate interest in secure optical transmissions and in optoelectronics techniques for signal secret writing. Many optoelectronics systems are projected that exploit quick chaotic dynamics as a potential various to classical secret writing techniques supported numerical algorithms. The primary schemes projected relied on signal masking: atiny low amplitude data signal is hidden by a large-amplitude noise-like chaotic signal. Optical systems are reported on paper and through an experiment from Nd: YAG lasers, erbium-doped fiber lasers, and semiconductor lasers. With such schemes, signal secret writing is performed through the continual modulation of a renascent variable of a chaotic oscillator; decryption is achieved by synchronizing a chaotic receiver to the chaotic transmitter. A additional refined technique uses chaos shift-keying (CSK), e.g., with a Chua electronic circuit, as represented by Dedieu, Parlitz, and Pinkney, or with a Lorenz-based electronic circuit, as represented by Cuomo. Alternative optoelectronic-based schemes are reported by Celka, by Anno-vazzi–Lodi and by Nilotic. The CSK technique operates with digital data. The method once more consists of modulating one among the generator parameters, thereby causing a amendment within the chaotic dynamics of the generator, however the modulation is currently binary. associate eaves-dropper detects a pseudo-random or chaotic signal, regardless of the price of the parameter, whereas a fitly synchronic chaos decoder will differentiate between a chaotic signal secret writing a “1” bit and a chaotic signal secret writing a “0” bit. (J.-B. Cuenot, L. Larger, J.-P. Goedgebuer, and William T. Rhodes 2001)

Oscillators were wide studied within the development of the speculation of driving systems. The oscillators examined in these studies will typically be realized as electrical circuits; and in reality circuits were typically employed in such studies to research the systems. Early studies of the van der politician and Duffing oscillators, exhibited behavior what would nowadays be known as chaos? Revisiting this earlier work has typically been fruitful in developing Associate in Nursing understanding method of chaotic synchronization which may be used because the secret writing process for signals that are chaotically encrypted. An alternate to the Pecora Dodgson synchronization theme was developed by Murali and Lakshmanan through revisiting van der Pol-Duffing and Duffing oscillators. (Stephen R. Addison and John E. Gray 2006)

Video secret writing algorithms should with efficiency cater to the characteristics of video bitstream that area unit totally different from traditional digital knowledge stream: Video content is larger in size and structured ways that to modify different applications and network communications. Moreover, multimedia system internet services over heterogeneous architectures like mobile phones and laptops want scalable media transmission schemes that have low coding and re-encryption value overhead, shorter delays and QoS needs. Future video search engines should be ready to hunt for a specific person or object from secure video libraries. The increased trend towards embedded devices needs such algorithms to possess low machine overhead. It’s troublesome to cater the multiple needs of low machine overhead, high security levels and different desires of compressed multimedia system bitstreams by the standard compress-then-encrypt paradigm. Generic secret writing algorithms area unit so inopportune for multimedia system security. Selective secret writing schemes are developed however most of them have tested to be weak against cryptology. JVCE schemes return to the rescue by providing secret writing at low overheads and while not dynamical the structure of multimedia system content. During this paper, a JVCE theme supported Arithmetic committal to writing is conferred and security enhancements area unit planned to create this theme secure against cryptology. Arithmetic committal to writing involves associating a sequence of symbols with an edge within the vary, and is sometimes enforced recursively. It generally permits terribly high committal to writing potency as multiple symbols area unit coded collectively. It’s been adopted to be used in compression standards, as well as JPEG2000 and H.264 to produce loss less entropy committal to writing. due to giant volumes of multimedia system knowledge and helpful properties of compressed bitstream like rate-adaptive trans-mission, quantifiable, DC-image extraction for content looking out etc. generic secret writing algorithms like AES, DES etc. have disadvantages for multimedia system security. Several multimedia-specific algorithms are planned in analysis literature. Recently some efforts are created towards joint style of secret writing and compression modules to produce a a lot of versatile secret writing of knowledge. These techniques permit secret writing at little/ no machine overhead and preserve the format compatibility of compressed bitstream. (Amit Pande, Joseph Zambreno, and Prasant Mohapatra 2010) 

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