Then the keys are calculated from those prime numbers in a series of steps based on a two-century-old theorem of Euler. The public-key scheme is secure unless those two prime numbers can be recovered by factoring one of the public key numbers; the rsa system uses numbers of 129 digits because their prime factors are so difficult to find. Indeed, rivest, Shamir, and Adleman believed their scheme to be so secure that in 1977 they challenged the world to decode a message that had been encoded into 128 digits. At that time, they estimated that factoring would take 23,000 years! Yet in 1994, an informal group of 600 volunteers in more than two dozen countries, communicating through the Internet, collected idle cpu cycles on all sorts of computers - even fax machines - to put to work carl Pomerance's 1981 quadratic sieve algorithm, a descendant. After eight months of work, the 64 and 65 digit factors were discovered. The rsa 128 digit challenge number was cracked using the Internet, albeit not very quickly.
Ielts, essay : Internet and communication
The second is the problem of biography digital signatures: how can an Internet merchant be sure that the signature on an electronic check is genuine? The solutions to both problems rest squarely on the shoulders of number theory, a deceptively deep branch of mathematics. Conventional encryption schemes like the data Encryption Standard (DES) function like a locked mailbox to which the sender and hotel recipient each have the only two keys. The problems here are securely transmitting keys to new pairs of correspondents and managing the large collection of keys a busy correspondent needs. Public-key or rsa systems (named for. Adleman, who published the first workable scheme in 1978, based on ideas. Hellman) have been likened to open mailboxes that can be slammed shut by any sender who wishes to deposit a message but opened only by the owner of the mailbox, the recipient. That is, anyone can code a message for a given recipient but only the recipient can decode. Coding a public-key message requires knowledge of two (large) numbers, the so-called public key; decoding it requires a third number, the private key known only to the recipient. The coding and decoding steps use modular arithmetic, a kind of clock face arithmetic (for example, dividing a journey time of many, many hours by 24 to find the remainder that determines the time of day of arrival). When new members join a public-key encryption scheme, the first step in establishing their keys is their (random) choice of two large prime numbers.
The rapidly growing Internet marketplace, for example, depends heavily on secret codes that combine centuries-old number theory with discoveries of the past two decades. Moreover, efforts to break such codes use the Internet to distribute the computing burden over a wide array of machines. That distributed computing in turn depends in a crucial way on modern extensions of an old idea of Fermat for methodically searching for prime factors of large numbers. Internet security can be seen in two complementary parts. One is the problem of sending a message that only the recipient can read, insuring both confidentiality of the message and its fidelity. The other is verifying general the identity of the sender of a message. The first amounts to finding a code which is hard to crack while still permitting rapid transmission and decoding.
Wavelets are a mathematical tool that has been developed in the last decade. Grossman, Stephen Mallet, Ingrid daubechies and others to circumvent the limitations of classic fourier analysis, which is restricted to analyzing fundamental frequencies. The fourier approach can easily reproduce a long continuous tone by knowing just the amplitudes of its key harmonics. But short, bursty signals - the kind heard in real music or seen in an image like a fingerprint - require a tool that can work across different frequency scales and time windows. Although fourier analysis can be bent to this task, wavelets are much better suited to many signal-processing applications because they are built by reproducing a particular scaled view of a fundamental signal component. They naturally accommodate compact storage of an image like a fingerprint, for example, even though its pattern of ridges extends for only a finite distance across the page. Security on the Internet Security on the Internet is as important as the security of a bank vault. Security concerns encompass privacy of messages, integrity of computers connected to the Internet, and trust in financial transactions, among many other issues.
Ielts, essay, topic: The, internet and communicationSome say that the
The sender can attach the remainder from that division to the message without adding much to its length, but the extra information enables the receiver to verify the message by repeating the division. Getting the wrong remainder means the message was corrupted. The relevant coding ideas were first introduced in the early 1950s;. Huffman did some of the earliest work. The mathematical ideas of algebraic coding theory, which emerged in the 1960s and built on the older discipline of finite fields, enabled persuasive error detection and correction to blossom to its current effective state.
For example, the reed-Solomon error-correcting codes, which were introduced in the 1960s by Irving reed and Gustave solomon as an application of ideas in finite fields, provide error detection and correction so effective that they are used in devices ranging from satellites to compact disks. Like error correcting codes, data compression derived ideas are also shared across a wide range of technologies, including the forthcoming digital television. (One second of high definition, uncompressed video would require more than seven hours to arrive over a conventional home modem!) The challenge of data compression is to reduce by many orders of magnitude the volume of data, and hence the transmission time, while preserving all. Good data compression schemes help World Wide web graphics appear quickly and attractively on a computer screen. The same tools bring sound files that please the ear, even though selected parts have been removed or reconstructed. Some of the latest data compression ideas use wavelets, a kind of multiscale analysis tool.
The Internet also supports distributed computing such as the recent cooperative effort which linked computers across dozens of countries to crack a code once thought secure for 20 millennia. The 1997 Mathematics Awareness week theme poster uses visualizations developed by, bell. Laboratories that depict world-wide Internet traffic over a two-hour period. The color and thickness of arcs between countries show inter-country traffic, with higher and redder arcs indicating larger traffic flows. Note: as additional web links are proposed and verified they will be incorporated as hypertext in this essay. Managing data on the Internet, as most people know, Internet messages - email, graphics, sound, the results of database searches - are transmitted as strings of 0's and 1's.
Mathematics is central to two parts of this digital translation and transmission: accurately transmitting a text message, say, that has been translated into binary numbers requires codes for detecting and correcting errors (not to be confused with secret codes and reducing the volume of data. When massive strings of 0's and 1's are forced over computer networks, some errors are inevitable, and even small losses of data can be catastrophic. Error detecting codes introduce mathematical tools to detect many of those losses, much like counting the number of pages in a long letter as a way of determining if anything was lost in the mail. A standard tool for detecting errors in Internet transmission are cyclic codes; a common choice is crc-16, a cyclic redundancy code that can detect errors in as many as 16 consecutive bits in a message. Crc-16 can also catch about 99 of errors longer than 16 bits. When an error is detected, the receiving computer simply fails to acknowledge its arrival, and the sender knows to retransmit. These codes perform a special kind of division on the numerical representation of the message.
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Computers were born in the language of mathematics. Binary numbers let computers represent words, music, images and more so that machines can now communicate across the Internet with an alphabet of 0's and 1's. The impartial rules of mathematical logic govern computer operations, Internet addressing, and even Web search engines. Within the Internet, mathematics is at the heart of security for messages and financial transactions. It is the basic tool of data compression, coding, list and error correction for transmitting large files. It is the foundation of databases for managing email addresses and for searching the world Wide web, and it is the agent for routing messages and managing networks. The Internet is also helping advance mathematical research and education. Groups of educators and researchers communicate through email, newsgroups, and special World Wide web sites.presentation
This will cause less communication skill. In some cases they even get a fraud by get rob their online banking account, one more thing that can ruin your life if you believe in the online fake mail that tell you to send out your personal information this may lead to the crime. In conclusion, the Internet has help people improve a quality of life by the mean time there are some people has diminished. As a smart internet user people have to know how to well manage their good amount of time to spend on internet and it is necessary to set an internet security system to the good enough level or buy the anti-virus and spam to protect. Table of Contents, introduction, managing data on the Internet, security on the Internet. Databases and searching, routing and network configuration, mathematics on the web. Mathematics and the Internet, introduction he relationship between mathematics and the Internet is like that between language and the works of Shakespeare: his work could not have been conceived without language, while his poems and plays have enriched language as it evolved.
of people life in some cases. The Internet has improve our quality of life a lot by make our life more convenience and economically cheaper. For examples: If someone wants to send mail to a friend he or she can send it by email. It is much faster plus does not has to pay for a mail fee, paying bills online. It is not only save your time to go to the place it also save petro or public transportation fare. Studying online is the one choice of educations students who has study over the Internet have such a huge library to searching for knowledge which is really help to save money to buy many books. However, the Internet could diminished quality of many people life as much as they do not realize what can happen by using the Internet. For examples: some people prefer to spend a lot of time on the Internet either surfing the websites, listening to the music or watching the movie alone at home rather to hang out with family and friends.
Internet has diminished our quality of life. Less communication.Spend to much time on the professional Internet. Listen to music or watch a movie alone at home. Cause some crimes. Spam mail, modern life cannot live without the technology. One of the popular new technology is the Internet. Most of offices, schools and houses in Canada have internet at their places.
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Internet is very popular by comparing with other new technology. It has made the global get smaller by just press the computer keyboard or on new model cell phone for searching whatever you my opinion the Internet help improve and diminished the quality of people life in some cases. The internet has improved our quality of life. Make life easier and faster. Pay bills online. Blouse the websites,. Save thesis bus fare or petrol. Save mail fee. Save money to buy a book.