Codes and cryptograms: From yesterday to today. Part 2o

To first part of the dedication to cryptography (encryption) we mentioned the way Julius Caesar used to communicate with his generals, called the "Caesar's transposable cryptogram" and in the table of Polybius.

crypto encryption encryption encryption encryption
In this section we will analyze several ways encryption, the Middle Ages this time, which will slowly lead us to understand the new digital ways that flood our time and everyday life!

First, learn your language!

Frequency analysis is the most basic tool a decryptor needs. Although the exact frequency with which each letter of the alphabet appears differs from one text to another, there are some regular patterns that are very useful in analyzing and scrambling an encrypted message.

In Greek the letter α occurs very often, you average an average of 12% in the total of the letters of any text. The following letters with the most frequent appearance are: ο, τ, ε, ν, ι and π. The less common are: β, ξ, ζ and ψ.

Relative frequencies of the letters in a Greek text.


Taking advantage of this knowledge, you can measure the frequencies of the letters or symbols in an encrypted text and compare them to the usual frequencies in a regular text.

There is no guarantee that whatever text corresponds to the above frequencies, a scientific work will obviously contain a different choice of words than an erotic letter.

Yet, using these critical pieces of knowledge, crypto-analyzers can make correlations between the encrypted and the actual text and draw a plot of the possible corresponding letters according to their appearance.

Let's look at an example. One could find his encrypted message competition of iGuru using frequency analysis?

This is the encrypted phrase given to all the code breakers:


If we count the most frequent letters of the above phrase we will have the following result:

The letter Η we will find it 10 times in the total of 72 letters of the phrase, ie at a rate of about 13,89% and it is the letter with the highest frequency in the phrase. If we combine it with the data of the above table, according to which the letter Α about 12% in a Greek text, we can well assume that H = A.

If we continue with the above hypothesis (why is it a case and we will explain below why) how the letter Η of the encrypted text corresponds to the letter Α of the decrypted, we will have the following observation, that the alphabet was shifted by 7 positions, that is, where H = A, where Th = B coke. Continuing the case should result in the following:


If the above is put in a table A = [8,9] as was said in solution of the enigma, we will have the answer!

Obviously this was a simple example in which frequency analysis worked on the letter A. If someone measured them for example Ψ, would notice that it is 7 out of 72 and the second most frequent letter of the sentence at 9,72% and logically according to the frequency table should be the letter Ο which is the second most frequent letter in Greek text. Close to the rate at which they meet Ψ, are also the letters N, T, E of the frequency table. With whichever of the four if we combined it, we would not find the solution, because the letter Ψ of the encrypted message corresponds to the letter Ρ of the decrypted one that according to the frequency table you meet at a rate of only 5,009% and not 9% that we would like. This proves to us how much time a cryptographer has to devote and how many combinations he has to make to find the solution!

But the answer to the question, if the frequency analysis could give us the solution to the iGuru puzzle, is rather positive!

Uniform cryptograms.

Already at the beginning of 15th It was clear that crypto-analyzers were working in all royal courts in Europe. In a cryptogram made for the Duchy of Mantova, for each vow of the normal text, several different ones were given respectively. This type of cryptography is known as unanimous substitution. Decryption is more difficult for the cryptanalyst as it requires more ingenuity than simple mono-alphabetic cryptograms and as always irritating persistence. The presence of the cryptography is a clear indication that the cryptographic secretary of Mantua knew the principles of frequency analysis. Unicorn cryptograms need more cryptographic correspondences than alphabet letters.

In the example below, numerals are used to substitute the letters (in other cases capitalized, lower or upside down).

Uniform cryptogram table.


Using my homonymous cryptogram my name for example could be written as: 55135730552208 ή 55475730556342 etc .;

Breaking an unanimous cryptogram.

Although unifen cryptograms successfully hide the frequencies of individual letters, frequencies of the two or three letter combinations are not covered so well, especially when it comes to large encrypted text. A basic method for breaking unanimous encryption is to look at repetitions. For example the two sequels

55135730552208 and 55475730556342 

responding both, a cryptanalyst will wonder if they do 13 & 47, 22 & 63, 08 & 42 correspond to the same letters as all the rest remain the same and in the same position.

Also, in a large text, someone who knows how the most common two-letter combinations between words are for example: "The", "the", "will", "yes" etc. Slowly and after a lot of trouble you can understand how 12 corresponds to "T" and the 36 on "I". So by continuing the process the secrets to be revealed.

The table, or the square of Trimetho.

John Tritemios was an avenger of German origin who wrote the first printed book on cryptography. He was a controversial personality with an interest in the occultism that cherished the people around him and was exaggerating those who did not know him.

His giant contribution to the art of cryptography was materialized in his work on codes and cryptograms titled, Polygraphia, which was published in six volumes after 1516's death. His work sets out what is now a standard method for writing polylinetic cryptographic systems, the table.

encryption encryption encryption
Table of Trimethyos in the Greek alphabet.

Code analysis.

The idea was to draw a table A = [24,24]. Each row contains the known alphabet, but in each successive line the alphabet is shifted one position.

To write an encrypted message, Tritemius suggested using the first line to encrypt the first letter, the second line for the second letter and so on.

The technique of Trithimios offered considerable advantages over it Alberti, to make a message unaffected by frequency analysis. In particular, it concealed the repetition of letters in a word that could be an important element for decoding.

Let's say we want to encrypt the message "All good”By the Tritheumatic Method. The first letter will be encrypted in the first letter, namely "Ο" it will remain "Ο“. The second letter, namely “λ" It will be done "μ”And so on.

In a nutshell, we spell the sentence in the first line, and for each letter go down.

Encrypted message "All right".

The message "All good"Consists of letters"ο ”, twice the letter“ λ ”, three times the letter“ α ” and "K". So first the letter "ο" remains "ο", Because it is the first letter of the proposal"Όall right“. The second letter of the proposal “ΌλOh sure","λ" It will be done "μ"That is, the second letter is encrypted in the second letter, the third letter"α"Will become the letter"γ"Of the third coke paste as shown in the table. The end result will be “omg neep".

With the analysis of Trithemios in the second part Codes and cryptograms, we have pretty much analyzed the most important ways of encrypting the Middle Ages that we can say to have influenced modern cryptography. In the next section we will begin to analyze more modern forms of encryption.


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