We already know that a cryptographic system consists of four basic elements of expressive sources, ciphertext, key and encryption operations. Here we will further give their mathematical models. 1. It is intuitive, and the mutant sources are a mutant alphabet or a plain text. For example, all English letters, all Chinese characters are typical expressive alphabets. Accurate, the expressive sources should also include the probability distribution of the original letters. If you use x to indicate a mutant alphabet, its element x∈x is a plaintext letter. In the mutant alphabet, the frequencies of different plain letters are often different, such as in 26 English letters, generally the maximum frequency "E" frequency is the highest; and in Chinese characters, it may be "the highest" word frequency. . Therefore, a plain text source is s = [x, p (x)], where x is the mutant alphabet, p (x) is the probability of displaying the letter x∈x, and P (x) satisfies the following conditions: Any x∈x, p (x) ≥ 0, and σp (x) = 1. 2, cipherology code consists of ciphertext alphabet Y and Cixin letters y∈y, the secretory alphabet generally refers to the collection of all letters that may be used by ciphertext, and y∈y is its element. The ciphertent alphabet can be the same as the mutant alphabet, or it can be different. 3, the key and encrypted operation key is used to select a encryption operation (or an encrypted step) from a set of encryption operations from the cryptographic system, and the key allows you to change encryption, such as every day, or each copy according to the previously established rules. After the newspaper, or after each character. Typically, the organization and proofability of the key must be made to generate separate add-in steps through simple rules. The combined complexity of the encryption method depends on the number of keys under this method. If you use K to indicate the key space, that is, the selection set of the encrypted step is selected, and k∈k is called a key. The plus step is a mapping of the mutant alphabet x to the secret literacy alphabet y: E: x → y, for each x∈XX. Since adding step is not single, it is a family operation, so we can remember EK = Ek (x), where x∈x, k∈k. Except for special coding methods, such as multi-code or multi-speaking, for each k∈k, EK (X) is a 1-1 mapping of X to Y. Usually requiring the user's choice of keys to random, and the selection of the key is independent of the clear text. The probability of use of such a key is P (K), and the probability of k∈k and its plaintext is independent of each other. 4, the cryptographic system After the mathematical model of several components of the cryptographic system, we can give a mathematical model of a cryptographic system. We define s = {x, y, k, p (x, k), ek (x), x∈x, k∈} as a cryptographic system. In fact, from the perspective of the operation, the cryptographic system includes two parts: encryption system and decryption system. If a cryptographic system is designed, the corresponding plaintext, ciphertext, key relationship is determined, and the probability method is represented as: for any x∈x, k∈k, y∈e (x), p (x, y, k) = p (x, k) = p (x) p (k). The application of password technology has been accompanied by the development of human culture, and its ancient or even original methods have laid the foundation of modern cryptography. The goal of using a password is to make a message or record a non-authorized person is not understandable. Some people may think that this is easy, but you must consider whether the original recipient can interpret the message. If the recipient is not experienced, he may not read it for a long time. Therefore, it is not necessarily required to encrypt and decrypt how to be particularly complex, and it must adapt to the intelligence, knowledge and environment of the person who uses its personnel. Let's introduce the process of developing evolution of classical secret system. 1. The classical encryption method is the classical encryption method that is familiar with the most, is it. It usually hides secret messages in other messages, making real secrets send out through a non-harmful message. Involtage is divided into two types, language intact, and technology.
The technique of technology is easier to imagine: For example, the ink, onion and milk law are also proven to be universal and effective methods (as long as the back is heated or ultraviolet irradiation). Language hidden writing and password coding relationship is closely related, it mainly provides two types of methods: symbol code and public code. The symbol code is a visible way, such as handwritten body or graphics, hidden secret writing. The selected letters selected, such as point or dashed, such as point or dashed, which are marked on the book or newspaper, which is easier to be suspected, unless the ink is used, but this method is easy to implement. A deformation application is to reduce the letter of interest, so that the horizontal position is slightly lower than other letters, but this reduction is almost impossible. A secret letter or camouflage message should be transmitted through the public channel, and the two sides need to agree, that is, a public code is needed. This may be the most ancient form of confidential technology, and it can often be seen in the public literature. The businessmen and gamblers in the East and the Far East are unique in this regard, they are very skilled in the application of gestures and expressions. The more popular ways in the US card liar are: Hand take a smoke or flex it with hand, indicating that the card held is good; one hand is put on the chest and the thumbs up, meaning "I will win this Bureau, is there anyone is willing to follow me? "The right hand palm is put on the table, indicating" Yes ", and holds a fist to express" no ". The language often used in a particular industry or society is often referred to as a jar. Some languages used by 乞丐, tramps, and gentle rogue are also known as black words, they are amulets of these social groups. In fact, it also uses camouflage, and the secrets of camouflage are therefore also known as specialized covers. The language of the black society criminal gang is particularly hidden, and there are many examples in French in French. Some of them have become popular usage. For example, Rossignol indicates "universal key", starting at 1460; mouche, said "Dosal", and so on. The second type of public code is to use virtual code and hidden. The rules of hidden messages are relatively common: "the first few characters after a particular character", such as the next letter after space ("family code ", In World War II was widely circulated, but it has caused great dissatisfaction of the review authority); more better, there is a third letter after space, or the third letter after punctuation. The leak method can be traced back to Cardano (1550) era, which is a way to master, but the deficiency is that the two sides need the same leaks, especially the soldiers on the battlefield, not very convenient . 2. Instead of the password instead of the password is to replace each character in the mutual alphabet to the characters in the ciphertent alphabet. Here, the corresponding ciphertext may be one or more. The recipient is reversely replaced by the ciphertext. There are five ways to replace the password:
Single meter instead of the password or a single letter instead, one character in the mutant alphabet corresponds to a character in the ciphertent alphabet. This is the simplest method in all encryption. Multi-code replacement is to map characters in the mutual alphabet to multiple characters in the ciphertent alphabet. Multiple code is simply used in 1401 by Duchymantua. In English, the vowel letter has the highest frequency, and a method of reducing the frequency of corresponding ciphertext letters is to use multiple codes, such as e-ciphertext 5, 13 or 25. Multi-speaking replacement is to replace multiple bright characters as a ciphertext character. For example, the alphabet "I" and "J" are "K", "V" and "W" instead "L" the oldest multi-letter encryption "L" in 1563 by the wave of "Write evaluation" ( DE FURTIOIS LITERARUM NOTIS) a book. Multi-table instead of consisting of multiple simple replacements, that is, two or more instead of tables. For example, use 5 simple instead of the table, the first alphabet of the plaintext is used in the first replacement table, the second letter with the second table, the third letter with the third table, with this type, cycle Use these five instead of table. Multi-table instead of the password by Leon. Batista in 1568, the famous Virginian password and Boffite password are multi-table instead of the password. The transfer is different from the instead of the table, which may be composed of a large number of representative words, phrases, syllables and letters. Such as 1563- BAGGAGE, 1673-BOMB, 2675-Catch, 2784-Custom, 3645-Decide to, 4728-from Then ON, etc. In a sense, the midbook is a huge replacement table, and its basic plaintext unit is word and chicony, letters and syllables are mainly used to spell all words in the middle. In actual use, the difference between the secret and replacement table is also more obvious, instead of the table is operated in accordance with the expressing length of the rules, while the mids are operated in accordance with the explicit length of variable length. The earliest appearance of the mids of 1400 is more than 400 years old, and most applied to the business sector. Merchant ships in the Second World War II, the GRAY secret use of the US diplomatic system is a typical example. 3, the transposition password is in the transposition password, the expressive character set remains unchanged, just the order of letters being disrupted. For example, a simple longitudinal chamber is written on a table paper according to the fixed width, and then read the ciphertext in the vertical direction. This encryption method can also be explained in the following manner: It is divided into a block that is divided into M element, and each piece is arranged in accordance with N. This means a multi-table encryption process of a single letter having a repetition and a width of m, that is, the sliding position is a transposition of the overall unit. Simple transpositions can be easily achieved, and less chances are more chances than sluggish. Although it runs through the entire plaintext, it is not more password security than the overall unit. In the second big world, the Germans once used a double longitudinal changing password called BCHI, and as an emergency password of the Army and the Navy, but only the key is transformed daily, and in the following units . At this point, the British has long been able to interpret the news, and the use of two different keywords or even three longitudinal lines do not help. 4, the wheel password With the use of electric typewriters, the electric cryptography starts in the confidential communication. In the Second World War, the use of the rotary cryptography is quite common. It mainly uses mechanical movements and simple electronic lines, with a keyboard and several runners, in fact it is an implementation of the Virginian password. Each wheel consists of an insulating circular film, and there is a metal bump on the edge of the rubber plate in front of the edge line, and each metal bump is labeled a letter, the position of the letter is aligned with each other. The alphabet of the film is connected to the metal connection to form a replacement operation. Different runners are fixed on a concentric shaft, which can be rotated independently, and each runner can select a certain rotational speed. For example, a runner may be connected to a wire to replace A, with U instead of B, replace C, etc.
In order to prevent cryptographic analysis, some rotary cryptography also set different position numbers on each wheel, so that the position of the wheel, the number of rotters, the gear on the wheel, increase the cycle of the machine. The most famous runner cipher is a German Sherbius designed a Hargelin cryptographue machine (US military called M-209). The Germans used the Ennigma machine with a total of 5 runners, and 3 can be selected. A piece of tablet and a reflect wheel designed in the rotor can operate twice a mutant letter. Another feature is that the rotary is controlled to form an irregular carry. Poland's password researchers built the German Nicma and provided the method to the British. M-209 is the main encryption device of the US military in the Second World War, which is a gear device having a variable number of teeth. There are six key wheels, a print wheel. In a particular encryption job, how many teeth are available instead of the table, and use this instead of table encryption. The various components of the apparatus functions to generate a long periodless key key. 1, the Caesar system Caesar system is a single-meter-additive cryptographic system, which is the same alphabet, secretory alphabet, and key alphabet, such as English alphabet. The plus step can be represented by a simple bonus: Y = X K, where x∈x, y∈y, k∈k. The simplest is that the first mutant is replaced by the third letter from the right side, replaced by D, B is replaced by E, ..., y, by B instead, Z is replaced by C. The generalized Caesar system introduces two key parameters, encrypted steps to Y = K1X K2, where x∈x, y∈y, K1, K2∈K. 2, double word PLAYFAIR system in 1854, Charles Wheatstone invented a special double bull double code instead of password, his friend Leon, Pleifel recommended it to High-level people in the government and the military community. The first use of this institution is during the Crimea War, which is officially reported in the Boer War, and its name is named in Playfair. The army value is a little bit of it is that this method does not require the table and does not require an instrument, which is easy as a war code. The British army is almost a century, and it is guaranteed that it has always been confidential. However, in 1915 in the World War, the Germans deciphered. PlayFAIR encryption is performed as follows: Starting by a password, a z25 is placed (Z26 Z26 in Z26) is arranged 5 × 5 square array. P a L m E R S t O N B C D f G H i K q u V W x Y Z or T O m R S D f G B C K q u H i x y z v w M E P A add-in step does not define a double letter is the same letter, and there is a case where the last letter is incompatible. The results of the above two examples are the same. If the two letters of a double letter are in the same row (or a column), they replace them with their right (correspondingly, under bottom) letters, such as AM → Le, DL → KT. Another situation is that the two letters are not in the same row or the same column, then the first letter is replaced by the letter in the same line and in the second letter; the second letter is from the same line, and is Instead of the letter where the first letter is located, for example: AG → EC, HO → QR. 3. The Virginia system Virginia system is one of the oldest and most famous multi-table password systems, which is named in the French censorser Blaise de Vigenere (1523--1596).
