The daily synchronicity apparatus of world trading. US5915209A - Bond trading system - Google Patents

Cryptography

USA - Bond trading system - Google Patents

Terminology[ edit ] Alphabet shift ciphers are believed to have been used by Julius Caesar over 2, years ago. In other words, the letters in the alphabet are shifted three in one direction to encrypt and three in the other direction to decrypt.

The first use of the term cryptograph as opposed to cryptogram dates back to the 19th century—originating from The Gold-Buga story by Edgar Allan Poe. A cipher or cypher is a pair of algorithms that carry out the encryption and the reversing decryption. The detailed operation of a cipher is controlled both by the algorithm and, in each instance, by a " key ".

Cryptography

The key is a secret ideally known only to the communicantsusually a string of characters ideally short so it can be remembered by the userwhich is needed to decrypt the ciphertext. In formal mathematical terms, a " cryptosystem " is the ordered list of elements of finite possible plaintexts, finite possible cyphertexts, finite possible keys, and the encryption and decryption algorithms which correspond to each key.

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Keys are important both formally and in actual practice, as ciphers without variable keys can be trivially broken with only the knowledge of the cipher used and are therefore useless or even counter-productive for most purposes.

Historically, ciphers were often used directly for encryption or decryption without additional procedures such as authentication or integrity checks. There are, generally, two kinds of cryptosystems: symmetric and asymmetric.

In symmetric systems, the only ones known until the s, the same key the secret key is used to encrypt and decrypt a message. Data manipulation in symmetric systems is faster than asymmetric systems in part because the generally use shorter key lengths. Asymmetric systems use a "public key" to encrypt a message and a related "private key" to decrypt it.

Use of asymmetric systems enhances the security of communication, largely because the relation between the two keys is very hard to discover. In colloquial use, the term " code " is often used to mean any method of encryption or concealment of meaning.

However, in cryptography, code has a more specific meaning: the replacement of a unit of plaintext i.

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A cypher, in contrast, is a scheme for changing or substituting an element below such a level a letter, or a syllable or a pair of letters or Cryptanalysis is the term used for the study of methods for obtaining the meaning of encrypted information without access to the key normally required to do so; i.

Some use the terms cryptography and cryptology interchangeably in English, while others including US military practice generally use cryptography to refer specifically to the use and practice of cryptographic techniques and cryptology to refer to the combined study of cryptography and cryptanalysis. History of cryptography and cryptanalysis[ edit ] Main article: History of cryptography Before the modern era, cryptography focused on message confidentiality i.

Encryption attempted to ensure secrecy in communicationssuch as those of spiesmilitary leaders, and diplomats. Reconstructed ancient Greek scytalean early cipher device The main classical cipher types are transposition cipherswhich rearrange the order of letters in a message e.

Simple versions of either have never offered much confidentiality from enterprising opponents. An early substitution cipher was the Caesar cipherin which each letter in the plaintext was replaced by a letter some fixed number of positions further down the alphabet. Suetonius reports that Julius Caesar used it with a shift of three to communicate with his generals. Atbash is an example of an early Hebrew cipher. The earliest known use of cryptography is some carved ciphertext on stone in Egypt ca BCEbut this may have been done for the amusement of literate observers rather than as a way of concealing information.

The Greeks of Classical times are said to have known of ciphers e. An early example, from Herodotuswas a message tattooed on a slave's shaved head and concealed under the regrown hair. In the Kautiliyam, the cipher letter substitutions are based on phonetic relations, such as vowels becoming consonants.

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In the Mulavediya, the cipher alphabet consists of pairing letters and using the reciprocal ones. After the discovery of frequency analysisby the Arab mathematician and polymath Al-Kindi also known as Alkindus in the 9th century, [22] [23] [24] nearly all such ciphers could be broken by an informed attacker. Such classical ciphers still enjoy popularity today, though mostly as puzzles.

Al-Kindi wrote a book on cryptography entitled Risalah fi Istikhraj al-Mu'amma Manuscript for the Deciphering Cryptographic Messageswhich described the first known use of frequency analysis and cryptanalysis techniques.

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For those ciphers, language letter group or n-gram frequencies may provide an attack. Essentially all ciphers remained vulnerable to cryptanalysis using the frequency analysis technique until the development of the polyalphabetic cipher. While it was known to Al-Kindi to some extent, [25] [26] it was first clearly described in the work of Al-Qalqashandi —based on the earlier work of Ibn al-Durayhim —describing a polyalphabetic cipher in which each plaintext letter is assigned more than one substitute.

He also invented what was probably the first automatic cipher devicea wheel which implemented a partial realization of his invention. Breaking a message without using frequency analysis essentially required knowledge of the cipher used and perhaps of the key involved, thus making espionage, bribery, burglary, defection, etc.

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It was finally explicitly recognized in the 19th century that secrecy of a cipher's algorithm is not a sensible nor practical safeguard of message security; in fact, it was further realized that any adequate cryptographic scheme including ciphers should remain secure even if the adversary fully understands the cipher algorithm itself.

Security of the key used should alone be sufficient for a good cipher to maintain confidentiality under an attack. This fundamental principle was first explicitly stated in by Auguste Kerckhoffs and is generally called Kerckhoffs's Principle ; alternatively and more bluntly, it was restated by Claude Shannonthe inventor of information theory and the fundamentals of theoretical cryptography, as Shannon's Maxim—'the enemy knows the system'.

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Different physical devices and aids have been used to assist with ciphers. One of the earliest may have been the scytale of ancient Greecea rod supposedly used by the Spartans as an aid for a transposition cipher. In medieval times, other aids were invented such as the cipher grillewhich was also used for a kind of steganography. With the invention of polyalphabetic ciphers came more sophisticated aids such as Alberti's own cipher diskJohannes Trithemius ' tabula recta scheme, and Thomas Jefferson 's wheel cypher not publicly known, and reinvented independently by Bazeries around Since then the emphasis has shifted, and cryptography now makes extensive use of mathematics, including aspects of options copier theorycomputational complexitystatisticscombinatoricsabstract algebranumber theoryand finite mathematics generally.

Cryptography is also a branch of engineeringbut an unusual one since the daily synchronicity apparatus of world trading deals with active, intelligent, and malevolent opposition; other kinds of engineering e. There is also active research examining the relationship between cryptographic problems and quantum physics.

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Just as the development of digital computers and electronics helped in cryptanalysis, it made possible much more complex ciphers. Furthermore, computers allowed for the encryption of any kind of data representable in any binary format, unlike classical ciphers which only encrypted written language texts; this was new and significant. Computer use has thus supplanted linguistic cryptography, both for cipher design and cryptanalysis.

Many computer ciphers can be characterized by their operation on binary bit sequences sometimes in groups the daily synchronicity apparatus of world trading blocksunlike classical and mechanical schemes, which generally manipulate traditional characters i.

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However, computers have also assisted cryptanalysis, which has compensated to some extent for increased cipher complexity. Nonetheless, good modern ciphers have the daily synchronicity apparatus of world trading ahead of cryptanalysis; it is typically the case that use of a quality cipher is very efficient i.

Advent of modern cryptography[ edit ] Cryptanalysis of the new mechanical devices proved to be both difficult and laborious. In the United Kingdom, cryptanalytic efforts at Bletchley Park during WWII spurred the development of more efficient means for carrying out repetitious tasks. Extensive open academic research into cryptography is relatively recent; it began only in the mids. In recent times, IBM personnel designed the algorithm that became the Federal i. Following their work init became popular to consider cryptography systems based on mathematical problems that are easy to state but have been found difficult to solve.

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Some modern cryptographic techniques can only keep their keys secret if certain mathematical problems are intractablesuch as the integer factorization or the discrete logarithm problems, so there are deep connections with abstract mathematics.

There are very few cryptosystems that are proven to be unconditionally secure. The one-time pad is one, and was proven to be so by Claude Shannon. There are a few important algorithms that have been proven secure under certain assumptions. For example, the infeasibility of factoring extremely large integers is the basis for believing that RSA is secure, and some other systems, but even so proof of unbreakability is unavailable since the underlying mathematical problem remains open.

In practice, these are widely used, and are believed unbreakable in practice by most competent observers. The discrete logarithm problem is the basis for believing some other cryptosystems are secure, and again, there are related, less practical systems that are provably secure relative to the solvability or insolvability discrete log problem. For instance, continuous improvements in computer processing power have increased the scope of brute-force attacksso when specifying key lengthsthe required key lengths are similarly advancing.

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See also