Codes and ciphers. Still unsolved ciphers and mysterious codes
When the complex cipher is finally solved, it may contain the secrets of world leaders, secret societies and ancient civilizations. Before you - a dozen of the most mysterious ciphers in the history of mankind, which have not yet been solved.
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Notes by Ricky McCormick
In June 1999, 72 hours after one person was reported missing, a body was found in a Missouri cornfield. Strangely, the corpse decomposed more than it should have in such a time. At the time of his death, 41-year-old Ricky McCormick had two encrypted notes in his pockets. He was unemployed with incomplete schooling, living on welfare, and he didn't have a car. McCormick also served time in prison for the rape of a minor. He was last seen alive five days before his body was found, when he came for a routine checkup at Forest Park Hospital in St. Louis.
Neither the FBI's cryptanalysis unit nor the American Cryptoanalytic Association was able to decipher the notes and made them public 12 years after the assassination. Investigators believe the mysterious notes were written about three days before the murder. McCormick's relatives claim that the victim has been using this technique of coding messages since childhood, but, unfortunately, none of them knows the key to this cipher.
Cryptos
This is a sculpture by American artist Jim Sanborn, which is installed in front of the entrance to the headquarters of the CIA in Langley, Virginia. It contains four complex encrypted messages, three of which have been decrypted. Until now, 97 characters of the last part, known as K4, remain undeciphered.
In the 1990s, CIA deputy head Bill Studman tasked the NSA with deciphering the inscriptions. A dedicated team was formed that was able to decipher three of the four messages in 1992, but did not make them public until 2000. Also three parts were solved in the 1990s by CIA analyst David Stein, who used paper and pencil, and computer scientist Jim Gillogly, who used a computer.
The decoded messages are reminiscent of CIA correspondence, and the sculpture is shaped like paper coming out of a printer during printing.
Voynich manuscript
The Voynich manuscript, created in the 15th century, is one of the most famous mysteries of the Renaissance. The book bears the name of the antiquary Wilfried Voynich, who bought it in 1912. It contains 240 pages and some pages are missing. The manuscript is full of biological, astronomical, cosmological and pharmaceutical illustrations. There is even a mysterious folding astronomical table. In total, the manuscript contains more than 170 thousand characters that do not comply with any rules. There is no punctuation or breaks in the writing of cipher characters, which is not typical for handwritten cipher text. Who created this manuscript? Researcher? Herbalist? Alchemist? The book once allegedly belonged to the Holy Roman Emperor Rudolf II, who was fond of astrology and alchemy.
Leon Battista Alberti, an Italian writer, artist, architect, poet, priest, linguist and philosopher, could not choose any one occupation. Today he is known as the father of Western cryptography, and he lived during the same years that the manuscript was created. He created the first polyalphabetic cipher and the first mechanical cipher machine. Maybe the Voynich manuscript is one of the first experiments in cryptography? If the code for the Voynich manuscript is deciphered, it could change our knowledge of the history of science and astronomy.
Shagborough lettering
Shepherd's Monument is located in picturesque Staffordshire in England. It was erected in the 18th century and is a sculptural interpretation of Nicolas Poussin's painting The Arcadian Shepherds, but some details have been changed. Below the picture is a text of 10 letters: the sequence O U O S V A V V between the letters D and M. Above the picture there are two stone heads: a smiling bald man and a man with goat horns and pointed ears. According to one version, the man who paid for the monument, George Anson, wrote an abbreviation of the Latin saying "Optimae Uxoris Optimae Sororis Viduus Amantissimus Vovit Virtutibus", which means "To the best of wives, best of sisters, devoted widower dedicates this to your virtues."
Former CIA linguist Keith Massey linked these letters to John 14:6. Other researchers believe that the cipher is associated with Freemasonry. Former Bletchley Park analyst Oliver Lawn has suggested that the code may be a reference to Jesus' family tree, which is unlikely. Richard Kemp, head of the Shugborough estate, initiated an advertising campaign in 2004 that linked the inscription to the location of the Holy Grail.
Linear A
Linear A is a variation of the Cretan script containing hundreds of characters and has not yet been deciphered. It was used by several ancient Greek civilizations between 1850 and 1400 BC. After the Achaean invasion of Crete, it was replaced by Linear B, which was deciphered in the 1950s and turned out to be one of the earliest forms of the Greek language. Linear A has never been deciphered, and the codes for Linear B are not suitable for it. The reading of most of the signs is known, but the language remains incomprehensible. Mostly its traces were found in Crete, but there were written monuments in this language in mainland Greece, Israel, Turkey, and even in Bulgaria.
Linear A, which is said to be the forerunner of the Cretan-Minoan script, is believed to be exactly what can be seen on the Phaistos Disc, one of the most famous archaeological mysteries. It is a baked clay disk approximately 16 cm in diameter, dating from the second millennium BC. and found in the Phaistos Palace in Crete. It is covered in symbols of unknown origin and meaning.
1000 years after Crete-Minoan, Eteocretan appeared, which is not classified and may be somehow related to Linear A. It is written in the Greek alphabet, but it is definitely not Greek.
Dorabella cipher
The English composer Edward Elgar was also very interested in cryptology. In memory of him, the first cipher machines of the early 20th century were named after his work Enigma Variations. Enigma machines were able to encrypt and decrypt messages. Elgar sent his girlfriend Dora Penny "a note to Dorabella" - that's what he called a girlfriend who was twenty years his junior. He was already happily married to another woman. Maybe he had an affair with Penny? She never deciphered the code he sent her, and no one else has ever been able to.
Bale cryptograms
The Virginia man who creates ciphers for the secrets of hidden treasures is Dan Brown's stuff, not the real world. In 1865, a pamphlet was published describing a huge treasure that would be worth over $60 million today. It has allegedly been buried in Bedford County for 50 years. Perhaps the person who did this, Thomas J. Bale, never existed. But the pamphlet indicated that Bale gave the box of three encrypted messages to the hotel owner, who did nothing with them for decades. Bale was never heard from again.
Bale's only report that has been deciphered states that the author left a huge amount of gold, silver, and jewels in a stone cellar six feet deep. It also says that another cipher describes the exact location of the cellar, so there should be no difficulty in finding it. Some skeptics believe that Bale's treasure is a duck that was successfully used to sell pamphlets at 50 cents, which would be $13 in today's money.
Zodiac Killer Mysteries
A notorious California serial killer known as the Zodiac taunted the San Francisco police with several ciphers, claiming that some of them would reveal the location of bombs planted throughout the city. He signed letters with a circle and a cross - a symbol denoting the Zodiac, the celestial belt of thirteen constellations.
The Zodiac also sent three letters to three different newspapers, each containing a third of the 408-character cipher. A schoolteacher from Salinas saw the symbols in the local newspaper and deciphered the cipher. The message said, "I like killing people because it's so much fun. It's more fun than killing wild animals in the forest because man is the most dangerous animal of all. Killing gives me the most thrill. It's even better than sex. The best is waiting for me to die. I will be born again in paradise, and all those I have killed will become my slaves. I won't tell you my name because you'll want to slow down or stop the recruitment of slaves for my afterlife."
The zodiac claimed responsibility for killing 37 people and was never found. He has imitators all over the world.
Taman Shud
In December 1948, a man's body was found on Somerton Beach in Australia. The identity of the deceased could not be established, and the case is shrouded in mystery to this day. The man may have been killed with a non-marking poison, but even the cause of death is unknown. The Somerton man was dressed in a white shirt, tie, brown knit pullover, and tan jacket. The clothes tags had been cut off and the wallet was missing. The teeth did not match any available dental records.
In the pocket of an unknown person, they found a piece of paper with the words "tamam shud", or "finished" in Persian. Later, when publishing material on this topic in one of the newspapers, a typo was made: instead of “Tamam”, the word “Taman” was printed, as a result of which the erroneous name entered the story. It was a fragment of a page from a rare edition of the Rubaiyat collection by the 12th-century Persian poet Omar Khayyam. The book was found and the inside cover was inscribed with a local phone number and an encrypted message. In addition, a suitcase with belongings was found in the storage room of a nearby railway station, but this did not help to identify the victim. Was the Somerton man a deep-cover Cold War spy? Amateur cryptographer? Years pass, but the researchers have not come close to unraveling.
Blitz ciphers
This riddle is the newest of all listed, as it was only made public in 2011. Blitz ciphers are a few pages discovered during World War II. They lay for years in wooden boxes in one of the basements of London, which was opened as a result of German bombing. One soldier took these papers with him, and it turned out that they were full of strange drawings and encrypted words. The documents contain over 50 unique calligraphic-like characters. It is not possible to date the documents, however, according to the popular version, blitz ciphers are the work of occultists or Freemasons of the 18th century.
define invariant parts. Looking ahead, we can cite as an example the Enigma cipher machine (see Chapter 9), which contained several wheels; there were wires inside these wheels; the wiring inside the wheels did not change, but the order of the wheels inside the car itself changed daily. Thus, the wiring was an unchanging part, and the order of the wheels was a variable. Hacking the system is the most time-consuming part of the job; it may last for several weeks or even months and require the application of mathematical methods, the search for and use of operator errors and even information obtained by spies.
Once all the immutable parts of the system have been determined, it is necessary to determine all the variable parts (such as the initial positions of the wheels in the Enigma cipher machine, which changed for each message). This is the task opening message keys. After solving it, the messages will be decrypted.
So, cracking refers to the encryption system as a whole, and opening the keys is associated with the decryption of individual messages.
Codes and ciphers
Although the words code and cipher are often used loosely, we will make a distinction between these concepts. In code, frequently occurring text elements (which may consist of one or more letters, numbers, or words) are usually replaced by four or five letters or numbers, which are called code groups and are taken from the codebook. For especially frequently used expressions or characters, the code book may offer several code groups. This is done so that the cryptographer can vary them in order to make it difficult to identify them. So, for example, in a four-digit numeric code for the word "Monday" there can be three alternative code groups - for example, 1538, or 2951, or 7392. We will consider the codes in Chapter 6.
Codes are a special case encryption systems, but not all encryption systems are codes. We will use the word cipher in relation to encryption methods that use non-codebooks, and the ciphertext is obtained from the original plaintext according to a certain rule. Nowadays, instead of the word "rule" they prefer to use the word "algorithm", especially when it comes to a computer program. The distinction between the concepts of code and cipher is sometimes not entirely clear, especially for simple systems. Perhaps we can assume that the Julius Caesar cipher uses a one-page code book, where each letter of the alphabet is associated with a letter that is three positions further in the alphabet. However, for most of the systems we'll be looking at, this distinction will be fairly clear-cut. So, for example, "Enigma", which is often
erroneously called the "Enigma code", is certainly not a code at all, but
cipher machine.
Historically, until relatively recently, cryptography has been dominated by two main ideas, and many encryption systems (including almost all of those described in the first eleven chapters of this book) were based on one or both of them. The first idea was to shuffle the letters of the alphabet (as a deck of cards is usually shuffled) in order to get something that can be considered a random order, a permutation, or an anagram of the letters. The second idea is to convert the letters of the message into numbers (for example, by setting A=0, B=1, ..., Z=25), and then add to them (number by number) other numbers, called gamma, which , in turn, can be letters converted to numbers. If the result of addition is a number greater than 25, subtract 26 from it (this method is called modulo addition 26). The result is then converted back
in letters. If the numbers added to the text are obtained by a rather difficult to predict process, then the message encrypted in this way is very difficult, or even impossible, to decipher without knowing the gamma.
It is curious to note that Julius Caesar's cipher, however simple, can be considered an example of both. In the first case, our "deck shuffle" is equivalent to simply moving the last three cards to the beginning of the deck, so that all letters are moved down three positions, and X, Y, and Z are at the beginning. In the second case, the gamma is the number 3, repeated an infinite number of times. It is impossible to imagine anything "weaker" than such a scale.
Translation of a message into another language, perhaps, could also be considered a certain type of encryption using a code book (that is, a dictionary), but this is still too free use of the word code. However, this way of translating into another language, when every word is climbed
in Dictionary as in a code book should definitely not be recommended. This is known to anyone who has tried to learn a foreign language.*) On the other hand, sometimes it is quite reasonable to use a little-known language to convey messages, the relevance of which is limited in time. It is said, for example, that during World War II, American troops in the Pacific sometimes used soldiers from the Navajo Indian tribe as telephone operators to transmit
*) I remember how a certain schoolboy wrote an essay in French about how in the Middle Ages a traveler arrives at a hotel at night and knocks on the door. In response, he hears "What Ho! Without." ("What the hell! Get out!" - Approx. Transl.). The student translated this expression into French word for word, substituting the French words: "Que Ho! Sans." (it turned out "What a ho! Without." - approx. transl.). The French teacher, having read this, was speechless for a moment, and then noticed; "You probably found these words in the dictionary, which is given away for free with bags of sugar."
messages in their own language, quite reasonably assuming that even if telephone conversations were intercepted, the enemy would hardly find in his ranks a person who speaks this language and is able to understand the content of the message.
Another way to hide the content of information is to use some kind of personal shorthand. Even in the Middle Ages, this method was used by the authors of personal diaries - for example, Samuel Pepys (Samuel Pepys). Such codes are not difficult to open if there are enough entries in the diary. Regular repetitions of certain characters (for example, signs indicating the days of the week) are a good help for reading certain words and expressions. An example of a more thorough work is the decipherment of ancient Mycenaean writing, known as "Linear B", where the signs corresponded to the syllables of the ancient Greek language; the credit for deciphering this type of writing belongs to Michael Ventris *) (see).
The widespread use of computers and the possibility of practical construction of complex electronic circuits on silicon crystals revolutionized both cryptography and cryptanalysis. As a result, some modern encryption systems are based on advanced mathematical concepts and require a solid computing and electronic base. Therefore, in the pre-computer era, it was almost impossible to use them. Some of them are described in chapters 12 and 13.
Evaluation of the strength of the encryption system
When a new encryption system is proposed, it is very important to evaluate its resistance to all known attack methods in conditions where the cryptanalyst knows the type of encryption system used, but not in all details. You can evaluate the strength of an encryption system for three different situations:
(1) the cryptanalyst knows only ciphertexts;
(2) the cryptanalyst knows the ciphertexts and their underlying plaintexts;
(3) the cryptanalyst knows both the ciphertexts and the plaintexts that he himself has picked up.
The first case reflects a "typical" situation: if under these conditions the encryption system can be broken in a short time, then it should not be used. The second situation arises, for example, if the same messages are encrypted both according to the new system and according to the old one, which
*) Linear B is one of the most ancient systems of Greek writing. Found on clay tablets at Knossos (Crete) and Pylos. Transcribed by Michael Ventris (1922-1956), English architect and linguist.
a cryptanalyst can read. Such situations related to cases of serious violation of data protection rules occur quite often. The third situation arises mainly when a cryptographer, wishing to assess the security of the system he has created, invites his colleagues, playing the role of an adversary, to break his cipher and allows them to dictate to him the texts to be encrypted. This is one of the standard procedures for testing new systems. A very interesting task for a cryptanalyst is to compose texts in such a way that, after encryption, they obtain maximum information about the details of the system. The structure of these messages depends on how the encryption is performed. The second and third situations can also arise if the cryptanalyst has a spy in the cryptographer's organization: this is exactly what happened in the 1930s, when Polish cryptanalysts received clear and cipher texts of messages encrypted on the German Enigma cipher machine. An encryption system that cannot be broken even in this situation (3) is a really strong cipher. This is exactly what the cryptographer strives for and what the cryptanalyst fears.
Codes that detect and correct errors
Another class of codes is designed to provide error-free transmission information, not to hide its content. Such codes are called detecting and correcting errors, they are the subject of extensive mathematical research. These codes have been used since the earliest days of computers to protect against errors in memory and data stored on magnetic tape. The earliest versions of these codes, such as the Hamming codes, are able to detect and correct a single error in a six-bit character. A more recent example is the code used on the Mariner spacecraft to transmit data from Mars. Designed to take into account the possible significant distortion of the signal on its long journey to Earth, this code was able to correct up to seven errors in each 32-bit "word". A simple code example of another level, revealing, but not correcting errors, is the ISBN code (International Standard Book Number - International Standard Book Number). It consists of ten characters (ten digits or nine digits with an X at the end, which means the number 10), and allows you to check for errors in the ISBN. The check is performed as follows: calculate the sum
(first digit) 1+(second digit) 2+(third digit) 3+...+(tenth digit) 10.
Since there are a huge number of ciphers in the world, it is impossible to consider all ciphers not only within the framework of this article, but also the whole site. Therefore, we will consider the most primitive encryption systems, their application, as well as decryption algorithms. The purpose of my article is to explain the principles of encryption / decryption to a wide range of users as clearly as possible, as well as to teach primitive ciphers.
Even at school, I used a primitive cipher, which my older comrades told me about. Let's consider a primitive cipher "A cipher with the replacement of letters by numbers and vice versa."
Let's draw a table, which is shown in Figure 1. We arrange the numbers in order, starting with one, ending with zero horizontally. Below, under the numbers, we substitute arbitrary letters or symbols.
Rice. 1 The key to the cipher with the replacement of letters and vice versa.
Now let's turn to table 2, where the alphabet is numbered. 
Rice. 2 Correspondence table of letters and numbers of alphabets.
Now let's encrypt the word K O S T E R:
1) 1. Convert letters to numbers: K = 12, O = 16, C = 19, T = 20, Yo = 7, P = 18
2) 2. Let's translate the numbers into symbols according to table 1.
KP KT KD PSHCH L KL
3) 3. Done.
This example shows a primitive cipher. Let's consider fonts similar in complexity.
1. 1. The simplest cipher is the CIPHER WITH THE REPLACEMENT OF LETTERS WITH NUMBERS. Each letter corresponds to a number in alphabetical order. A-1, B-2, C-3, etc.
For example, the word " TOWN" can be written as "20 15 23 14", but this will not cause much secrecy and difficulty in deciphering.
2. You can also encrypt messages using the NUMERIC TABLE. Its parameters can be anything, the main thing is that the recipient and the sender are aware of it. An example of a digital table. 
Rice. 3 Numerical table. The first digit in the cipher is a column, the second is a row, or vice versa. So the word "MIND" can be encrypted as "33 24 34 14".
3. 3. BOOK CIPHER
In such a cipher, the key is a certain book that both the sender and the recipient have. The cipher denotes the page of the book and the line, the first word of which is the clue. Decryption is not possible if the sender and the correspondent have books of different years of publication and release. Books must be identical.
4. 4. CAESAR CIPHER(shift cipher, Caesar shift)
Known cipher. The essence of this cipher is the replacement of one letter by another, located at a certain constant number of positions to the left or to the right of it in the alphabet. Gaius Julius Caesar used this method of encryption in correspondence with his generals to protect military communications. This cipher is quite easy to break, so it is rarely used. Shift by 4. A = E, B= F, C=G, D=H, etc.
An example of a Caesar cipher: let's encrypt the word " DEDUCTION ".
We get: GHGXFWLRQ . (shift by 3)
Another example:
Encryption using the key K=3. The letter "C" "shifts" three letters forward and becomes the letter "F". A solid sign moved three letters forward becomes the letter "E", and so on:
Source alphabet: A B C D E F G I J K L M N O P R S T U V W Y Z
Encrypted: D E F G H I J K L M N O P R S T U V W Y Z A B C
Original text:
Eat some more of those soft French buns and have some tea.
The cipher text is obtained by replacing each letter of the original text with the corresponding letter of the cipher alphabet:
Fezyya iz zyi akhlsh pvenlsh chugrschtskfnlsh dtsosn, zhg eyutzm gb.
5. CIPHER WITH A CODE WORD
Another simple way in both encryption and decryption. A code word is used (any word without repeating letters). This word is inserted in front of the alphabet and the remaining letters are added in order, excluding those that are already in the code word. Example: the code word is NOTEPAD.
Source: A B C D E F G H I J K L M N O P Q R S T U V W X Y Z
Replacement: N O T E P A D B C F G H I J K L M Q R S U V W X Y Z
6. 6. ATBASH CODE
One of the easiest encryption methods. The first letter of the alphabet is replaced by the last, the second by the penultimate, and so on.
Example: "SCIENCE" = HXRVMXV
7. 7. FRANCIS BACON CIPHER
One of the simplest encryption methods. For encryption, the Bacon cipher alphabet is used: each letter of the word is replaced by a group of five letters "A" or "B" (binary code).
a AAAAA g AABBA m ABABB s BAAAB y BABBA
b AAAAB h AABBB n ABBAA t BAABA z BABBB
c AAABA i ABAAA o ABBAB u BAABB
d AAABB j BBBAA p ABBBA v BBBAB
e AABAA k ABAAB q ABBBB w BABAA
f AABAB l ABABA r BAAAA x BABAB
The complexity of decryption lies in determining the cipher. Once it is defined, the message is easily alphabetized.
There are several ways to encode.
It is also possible to encrypt a sentence using a binary code. Parameters are defined (for example, "A" - from A to L, "B" - from L to Z). So BAABAAAAABAAAABABABB means TheScience of Deduction ! This method is more complicated and tedious, but much more reliable than the alphabetical version.
8. 8. THE BLUE VIGENERE CIPHER.
This cipher was used by the Confederates during the Civil War. The cipher consists of 26 Caesar ciphers with different shift values (26 letters of the Latin alphabet). Tabula recta (Vigenère's square) can be used for encryption. Initially, the key word and the source text are selected. The key word is written cyclically until it fills the entire length of the original text. Further along the table, the letters of the key and the plaintext intersect in the table and form the ciphertext.
Rice. 4 Blaise Vigenère cipher
9. 9. LESTER HILL CIPHER
Based on linear algebra. Was invented in 1929.
In such a cipher, each letter corresponds to a number (A = 0, B =1, etc.). A block of n-letters is treated as an n-dimensional vector and multiplied by an (n x n) matrix mod 26. The matrix is the cipher key. To be able to decrypt, it must be reversible in Z26n.
In order to decrypt the message, it is necessary to convert the ciphertext back into a vector and multiply by the inverse of the key matrix. For more information - Wikipedia to the rescue.
10. 10. TRITEMIUS CIPHER
An improved Caesar cipher. When decrypting, it is easiest to use the formula:
L= (m+k) modN , L is the number of the encrypted letter in the alphabet, m is the serial number of the letter of the encrypted text in the alphabet, k is the shift number, N is the number of letters in the alphabet.
It is a special case of an affine cipher.
11. 11. MASONIC CYFER
12. 12. GRONSFELD CYFER
The content of this cipher includes the Caesar cipher and the Vigenère cipher, but the Gronsfeld cipher uses a numerical key. We encrypt the word “THALAMUS” using the number 4123 as a key. We enter the numbers of the numerical key in order under each letter of the word. The number under the letter will indicate the number of positions to which the letters need to be shifted. For example, instead of T, you get X, and so on.
T H A L A M U S
4 1 2 3 4 1 2 3
T U V W X Y Z
0 1 2 3 4
Result: THALAMUS = XICOENWV
13. 13. PIG LATIN
More often used as children's fun, it does not cause any particular difficulty in deciphering. The use of English is mandatory, Latin has nothing to do with it.
In words that begin with consonants, these consonants are moved back and the “suffix” ay is added. Example: question = estionquay. If the word begins with a vowel, then ay, way, yay or hay is simply added to the end (example: a dog = aay ogday).
In Russian, this method is also used. They call it differently: “blue tongue”, “salty tongue”, “white tongue”, “purple tongue”. Thus, in the Blue language, after a syllable containing a vowel, a syllable with the same vowel is added, but with the addition of the consonant “s” (because the language is blue). Example: Information enters the nuclei of the thalamus = Insiforsomasacisia possotusupasesa in the nucleus rasa tasalasamusususas.
Pretty interesting option.
14. 14. POLYBIUS SQUARE
Like a digital table. There are several methods for using the Polybius square. An example of a Polybius square: we make a 5x5 table (6x6 depending on the number of letters in the alphabet).
1 METHOD. Instead of each letter in the word, the corresponding letter from below is used (A = F, B = G, etc.). Example: CIPHER - HOUNIW.
2 METHOD. The numbers corresponding to each letter from the table are indicated. The first number is written horizontally, the second - vertically. (A=11, B=21…). Example: CIPHER = 31 42 53 32 51 24
3 METHOD. Based on the previous method, let's write the resulting code together. 314253325124. We make a shift to the left by one position. 142533251243. Again we divide the code in pairs. 14 25 33 25 12 43. As a result, we get a cipher. Pairs of numbers correspond to a letter in the table: QWNWFO.
There are a lot of ciphers, and you can also come up with your own cipher, but it is very difficult to invent a strong cipher, since the science of decryption has stepped far forward with the advent of computers and any amateur cipher will be broken by experts in a very short time.
Methods for opening monoalphabetic systems (decoding)
With their simplicity in implementation, single-alphabetic encryption systems are easily vulnerable.
Let us determine the number of different systems in an affine system. Each key is fully defined by a pair of integers a and b that define the mapping ax+b. There are j(n) possible values for a, where j(n) is the Euler function returning the number of coprime numbers with n, and n values for b that can be used regardless of a, except for the identity mapping (a=1 b =0), which we will not consider.
Thus, there are j(n)*n-1 possible values, which is not so much: with n=33, there can be 20 values for a (1, 2, 4, 5, 7, 8, 10, 13, 14 , 16, 17, 19, 20, 23, 25, 26, 28, 29, 31, 32), then the total number of keys is 20*33-1=659. Enumeration of such a number of keys is not difficult when using a computer.
But there are methods that simplify this search and which can be used in the analysis of more complex ciphers.
frequency analysis
One such method is frequency analysis. The distribution of letters in the cryptotext is compared with the distribution of letters in the alphabet of the original message. The letters with the highest frequency in the cryptotext are replaced by the letter with the highest frequency from the alphabet. The probability of a successful opening increases with the length of the cryptotext.
There are many different tables on the distribution of letters in a given language, but none of them contains definitive information - even the order of the letters may differ in different tables. The distribution of letters depends very much on the type of test: prose, spoken language, technical language, etc. The guidelines for the laboratory work give frequency characteristics for various languages, from which it is clear that the letters of the letter I, N, S, E, A (I, N, C, E, A) appear in the high-frequency class of each language.
The simplest protection against attacks based on frequency counting is provided by the system of homophones (HOMOPHONES), monosounding substitution ciphers in which one plaintext character is mapped to several ciphertext characters, their number is proportional to the frequency of the letter. Encrypting the letter of the original message, we randomly choose one of its replacements. Therefore, a simple calculation of frequencies does not give anything to the cryptanalyst. However, information is available on the distribution of pairs and triplets of letters in various natural languages.
Use an old and little known recording system. Even Roman numerals are not always easy to read, especially at a glance and without a reference book. Few people will be able to determine “on the fly” that the number 3489 is hidden in the long line MMMCDLXXXIX.
Many people are familiar with the Roman numeral system, so it cannot be called reliable for encryption. It is much better to resort, for example, to the Greek system, where the numbers are also indicated by letters, but there are much more letters used. In the inscription OMG, which can be easily mistaken for an expression of emotions common on the Internet, the number 443 written in Greek can be hidden. The letter “O micron” corresponds to the number 400, the letter “Mu” denotes 40, and “Gamma” replaces the three.
The disadvantage of such letter systems is that they often require exotic letters and signs. This is not difficult if your cipher is written in pen and paper, but becomes a problem if you want to send it, say, by e-mail. Computer fonts include Greek characters, but they can be difficult to type. And if you chose something even more unusual, like an old Cyrillic notation or Egyptian numbers, then the computer simply cannot transmit them.
For such cases, we can recommend a simple method that in Russia in the old days was used by all the same itinerant merchants - peddlers and ofen. For successful trading, it was vital for them to coordinate prices among themselves, but in such a way that no outsider would know about it. Therefore, pedlars have developed many ingenious encryption methods.
They dealt with numbers in the following way. First you need to take a word that has ten different letters, for example, "justice." The letters are then numbered from one to zero. "P" becomes the sign for one, "v" for four, and so on. After that, any number can be written in letters instead of numbers in the usual decimal system. For example, the year 2011 is written in the ofene system as "repp". Try it yourself, hidden in the line "a, pvpoirs".
"Justice" is not the only Russian word suitable for this method. "Industriousness" is no worse: it also contains ten non-repeating letters. You may well look for other possible bases on your own.
No wonder the history of Egypt is considered one of the most mysterious, and the culture of one of the most highly developed. The ancient Egyptians, unlike many peoples, not only knew how to build pyramids and mummify bodies, but were literate, kept score, calculated heavenly bodies, fixing their coordinates.
Decimal system of Egypt
The modern decimal appeared a little over 2,000 years ago, but the Egyptians owned its counterpart as far back as the time of the pharaohs. Instead of cumbersome individual alphanumeric designations of the number, they used unified signs - graphic images, numbers. They divided the numbers into units, tens, hundreds, etc., designating each category with a special hieroglyph.
As such, there was no rule of numbers, that is, they could be in any order, for example, from right to left, from left to right. Sometimes they were even made up in a vertical line, while the direction of reading the digital series was set by the type of the first digit - elongated (for vertical reading) or flattened (for horizontal).
Ancient papyri with numbers found during excavations testify that the Egyptians already at that time considered various arithmetic, carried out calculations and fixed the result with the help of numbers, used digital designations in the field of geometry. This means that digital recording was widespread and generally accepted.
The figures were often endowed with magical and symbolic meaning, as evidenced by their image not only on papyri, but also on sarcophagi, walls of tombs.
Number type
Digital hieroglyphs were geometric and consisted only of straight lines. The hieroglyphs looked quite simple, for example, the number "1" among the Egyptians was indicated by one vertical strip, "2" - by two, "3" - by three. But some numbers written defy modern logic, an example is the number "4", which was depicted as one horizontal strip, and the number "8" in the form of two horizontal stripes. The numbers nine and six were considered the most difficult to write, they consisted of characteristic features at different angles.
For many years, Egyptologists could not decipher these hieroglyphs, believing that they were letters or words.
One of the last to decipher and translate hieroglyphs denoting mass, totality. The complexity was objective, because some numbers were depicted symbolically, for example, on papyri, a person depicted with raised ones meant a million. The hieroglyph with the image of a toad meant a thousand, and the larvae -. However, the whole system of writing numbers was systematized, it is obvious - Egyptologists say - that the hieroglyphs were simplified. Probably, even ordinary people were taught how to write and designate them, because the numerous trading letters of small shopkeepers that were discovered were compiled correctly.
History is full of mysteries and unsolved mysteries, among which are encrypted messages that attract attention. Most of them have already been read. But there are mysterious ciphers in the history of mankind that have not yet been solved. Here are ten of them.
The Voynich Manuscript is a book that bears the name of the antiquary Wilfried Voynich, who bought it in 1912. The manuscript contains 240 pages, is written from left to right using a strange, non-existent alphabet, and consists of six sections that have been given conventional names: "Botanical", "Astronomical", "Biological", "Cosmological", "Pharmaceutical", "Prescription".
The text is written with a quill pen and ink based on gallic acid ferrous compounds. They also made illustrations depicting non-existent plants, mysterious diagrams and events. The illustrations are crudely painted with colored paints, possibly after the book was written.
There are many versions of the origin of this book, the most popular of which say that the book may have been written in the dead language of the Aztecs. There is an assumption that the manuscript tells about the secret Italian medieval technologies and contains alchemical knowledge.
The Rohonci Codex is less well-known than the Voynich manuscript, but no less mysterious. This book is a "pocket format" - 12 by 10 cm, contains 448 pages, dotted with some letters-symbols, written, perhaps, from right to left. The number of unique characters used in the Code is about ten times greater than in any known alphabet. Somewhere on the pages there are illustrations depicting religious and everyday scenes.
Examination of the paper of the Codex Rohonzi showed that it was most likely made in Venice at the beginning of the 16th century. In what language the manuscript was written, the scientists could not establish, since the letters do not belong to any of the known writing systems. Opinions were expressed that the Code was written in the language of the Dacians, Sumerians or other ancient peoples, but they did not receive support in the scientific community.
So far, no one has been able to decipher the Code, which is probably why most scholars share the opinion of Karol Szabo (expressed in 1866) that the Rohontsi Code is a fake, the work of the Transylvanian antiquarian Literati Samuil Nemesh, who lived at the beginning of the 19th century.
The disk was found by the Italian archaeologist Luigi Pernier on the evening of July 3, 1908, during excavations of the ancient city of Phaistos, located near Agia Triada on the south coast of Crete, and is still one of the most famous mysteries in archeology. The disk is made of terracotta without the help of a potter's wheel. Its diameter ranges from 158-165 mm, thickness is 16-21 mm. On both sides, grooves are applied in the form of a spiral, unfolding from the center and containing 4-5 turns. Inside the strips of spirals there are drawings-hieroglyphs, divided by transverse lines into groups (fields). Each such field contains from 2 to 7 characters.
The writing of the disc is fundamentally different from the Cretan writing that existed on the island at that historical period. The uniqueness of the artifact lies in the fact that it is probably the earliest fairly long connected text typed using a prefabricated set of "seals", each of which could be used repeatedly. It is believed that it was made presumably in the II millennium BC.
For more than a hundred years, researchers from many countries have been trying to unravel the mystery of the Cretan pictograms, but their efforts have not yet been crowned with success. The longer the disk is studied, the more various conjectures arise around it. There is a hypothesis that this pictogram is the only material evidence of the existence of Atlantis.
Kohau rongo-rongo
Kohau rongo-rongo - wooden tablets with mysterious writings made of toromiro wood. They were found in the caves of the island, and later found in many of the houses of its inhabitants. The language in which they are written is called rongo-rongo by the locals. In total, at present, according to I.K. Fedorova, 11 complete texts of kohau rongo-rongo and 7 extremely corrupted ones are known. These inscriptions contain 14,083 characters in 314 lines.
More than a dozen scientists tried to decipher rongo-rongo, among them - the Hungarian Hevesy, the American Fisher, the German Bartel, the Frenchman Metro, the Russians Butinov, Knorozov, father and son Pozdnyakov, Fedorova and others. They looked for similarities between rongo-rongo and the already unraveled languages of the Sumerians, Egyptians, ancient Chinese, the writing of the Indus Valley, and even with the Semitic languages. However, each of them adheres to their own version of the decoding of the mysterious letters, and in the scientific world there has not been a single point of view. In fact, rongo-rongo still remains a completely unsolved language.
The shepherd's monument of the middle of the 18th century, located in Shagborough (Staffordshire, England), was erected on the territory of an old estate that once belonged to the Earl of Lichfield, and is a sculptural interpretation of the 2nd version of Poussin's painting "The Arcadian Shepherds" in a mirror image and with the classic inscription " ET IN ARCADIA EGO. The letters O·U·O·S·V·A·V·V are carved under the bas-relief, framed by the letters D and M, located one line below. DM may mean Diis Manibus - "the hand of God", while the central abbreviation remains unclear.
According to one version, this inscription is an abbreviation of the Latin phrase "Optimae Uxoris Optimae Sororis Viduus Amantissimus Vovit Virtutibus", which means: "To the best of wives, the best of sisters, a devoted widower dedicates this to your virtues."
Former CIA linguist Keith Massey linked these letters to John 14:6. Other researchers believe that the cipher is associated with Freemasonry and may be a clue left by the Knights Templar as to the location of the Holy Grail.
Bale cryptograms
Bale's cryptograms are three encrypted messages that supposedly carry information about the location of a treasure of gold, silver and precious stones, allegedly buried in Virginia near Lynchburg by gold prospectors led by Thomas Jefferson Bale. The price of the treasure, not found until now, in terms of modern money should be about 30 million dollars. The riddle of cryptograms has not been solved so far, in particular, the question of the real existence of the treasure remains controversial.
It is assumed that Bale encrypted his messages using a polyalphabetic system, that is, several numbers corresponded to the same letter. Cryptogram #1 described the exact location of the cache, while cryptogram #2 was a listing of its contents. The list of names and addresses of potential heirs was the content of cryptogram number 3. Of the three ciphergrams, only the second was decoded and the key was the US Declaration of Independence.
In 1933, the Shanghai General Wang received a package - seven unusual gold bars that looked like banknotes. But only all the inscriptions on the ingots were coded. The cipher, according to a number of cryptologists, includes Chinese characters and cryptograms in Latin. There is a version that this is a description of a deal for more than 30 million dollars.
Neither the sender, nor the reason for such an "impressive" message, nor its contents are known to this day.
The Georgia Guidestones are a large granite monument from 1980 in Elbert County, Georgia, USA. It contains a long inscription in eight modern languages, and at the top there is a shorter inscription in 4 ancient languages: Akkadian, Classical Greek, Sanskrit and Ancient Egyptian.
The height of the monument is almost 6.1 meters, and it consists of six granite slabs with a total weight of about 100 tons. One plate is located in the center, four - around it. The last slab is located on top of these five slabs. The stones are carved with ten brief commandments proclaiming the importance of controlling the earth's population and other rules of human behavior on Earth. For example, the first commandment says: "Keep the number of mankind below 500 million in eternal balance with wildlife."
Some "conspiracy theorists" believe that the structure was created by representatives of the "global shadow hierarchy", trying to control the peoples and governments of the world. The messages call for a new world order. More than a quarter of a century has passed since the opening of this monument, and the names of the sponsors have remained unknown.
Kryptos is a cipher text sculpture created by artist Jim Sanborn and located in front of the Central Intelligence Agency headquarters in Langley, Virginia, USA. Since the discovery of the sculpture, on November 3, 1990, there have been constant discussions around it about unraveling the encrypted message.
Despite the fact that more than 25 years have passed since the installation, the text of the message is still far from being deciphered. The global community of cryptanalysts, along with employees of the CIA and the FBI, have been able to decipher only the first three sections during all this time.
Until now, 97 characters of the last part, known as K4, remain undeciphered. Regarding the solution of the cipher, Sanborn says that he took all necessary measures to ensure that even after his death there will not be a single person who knows the complete solution to the riddle.
Notes by Ricky McCormick
Notes with incomprehensible text were found in the pockets of 41-year-old Ricky McCormick, who was discovered in the summer of 1997 in a cornfield in St. Charles County, Missouri. The body was found several miles from the home where the unemployed disabled man lived with his mother. No evidence of a crime or any indication of the cause of death was found. The case was sent to the archive along with mysterious messages.
Twelve years later, the authorities changed their mind, believing that it was a murder and perhaps the notes found could lead to the trail of the killer or killers. During the investigation, it was possible to establish that McCormick used a similar way of expressing his own thoughts from early childhood, but none of the relatives knows the key to his cipher. Attempts to decipher the chaotic combinations of numbers and letters were unsuccessful, despite the fact that the authorities posted the encryption on the Internet with a call for help. Currently, the entire public is trying to help the FBI decipher them.
Elena Krumbo, especially for the World of Secrets website
