Roberto Baggio

This article summarizes the history of cryptography of the Antiquité to today. Cryptography is the science of the coding of the messages using secret codes or of key . The coding of the messages aims at ensuring of it the Confidentialité, the authenticity and the integrity.

In Antiquity

First methods of coding

The oldest quantified document

The first known quantified “document” goes back to the Antiquité. It is about a clay shelf, found in Iraq, and dating from potter had engraved its secret receipt there by removing consonants and by modifying the orthography of the words.

Greek technique

Between the {{Xe}} and seventh century BC, the Greeks use with fine soldiers a technique of coding per transposition, i.e. resting on the change of position of the letters in the message. They make use of a Scytale, also called stick of Plutarque , around of which they roll up in jointed whorls a leather band and register the message there. Once unrolled, the message is sent to the recipient who has an identical stick necessary to the deciphering.

Only a person having a stick of diameter identical to that having been used to write the message, can decipher it.

The principal weakness of this system lies in the fact that a stick of a roughly equal diameter is enough to decipher the text. Safety thus resides on the secrecy around the process of coding.

Technique of the Hebrews

From, one of the first techniques of coding is used in the religious texts by the Hebrew which know several processes.

Most known called Atbash is a method of reversed substitution alphabetical. Its name is formed by initial first and last Hebrew letters of the alphabet has leph, T with, B eth, HS in.

It consists in replacing each letter of the plaintext by another letter of the alphabet chosen in the following way: Has becomes Z, B becomes Y, etc

Nabuchodonosor

In the neighborhoods of -600, Nabuchodonosor, king of Babylon, employed an original method: he wrote on shaven cranium of his slaves, waited until their hair pushed back, and he sent them to his generals. It was then enough to again shave the messenger to read the text. It is however about steganography strictly speaking and not of cryptography: information is hidden and not coded.

One notices in this process a certain reliability: indeed the interception of the message by a third is immediately noticed.

First “truths” systems of cryptography

It is necessary to await -200 to see appearing first “truths” systems of cryptography. They are primarily codings by substitution.

There exist 4 types of substitutions:

  • mono-alphabetical : replace each letter of the message by another poly-alphabetical letter of the alphabet

  • : use a succession of mono-alphabetical figures (the key) re-used periodically
  • homophonic : fact of corresponding to each letter of the message in light a possible whole of other characters
  • polygrammes : substitute a group of characters in the message by another group of characters

The code of César

See also: Figure of César

The code of César is the cryptographic method, by the mono-alphabetical substitution, oldest ().

This method is used in the Roman army and although it is much less robust than the technique Atbash, the weak elimination of illiteracy of the population makes it sufficiently effective.

Method of coding

Its system is simple, it consists in shifting the letters of the alphabet of a number N . For example, if one replaces has by D (n=3), one replaces B by E, C by F…

The text which we wish to code being the following: “to shift the letters of the alphabet”

The coded text is then: “ghfdohu ohv ohwwuhv gh o' doskdehw”

Limits of this process

Unfortunately, it will be understood that this system is far from sure, since there are only 26 letters in the alphabet thus only 26 ways of quantifying a message with the code of César. However its simplicity led the officers Southerners to employ again it during the American Civil War. The Russian army made some in the same way in 1915.

A known system and yet…

It should be noted that the code of César was used on forums Internet under the name of ROT13 (rotation of 13 letters or has-->N…). The purpose of the ROT13 is not to make text confidential, but rather to prevent the involuntary reading (of an answer to a riddle, or intrigue of a film, etc). Its use is simple: it is enough Re-to quantify a text, coded in ROT13, second once to obtain the plaintext.

The Square of Polybe

The Greek historian Polybe is at the origin of the first process of coding by homophonic substitution.

Method of coding

It is a system of transmission based on a square of 25 boxes (one can increase this square with 36 boxes, in order to be able to add the figures or to quantify alphabets comprising more letters, like the Cyrillic alphabet).

In French, one removes the W , which will be replaced by V . There exists an alternative where they are I and J which divides the same box. Each letter can be thus represented by a group of two digits: that of its line and that of its column. Thus E = (1; 5), U = (5; 1), N = (3; 4)…

An original transmission resource

Polybe proposed to transmit these numbers by means of torches. A torch on the right and five to transmit the letter E on the left for example. This process thus made it possible to transmit messages on long distances.

Its originality

The modern cryptologists saw in the “square of 25” several extremely interesting characteristics:

  • the conversion of letters into figures,
  • the reduction of numbers, symbols,
  • the representation of each letter by two separate elements.

This system of coding can be complicated with a password. For example, if the password is DIFFICULT , one will start to fill the square with the letters of this word, after having removed the identical letters, then one will supplement the table with the unutilised letters.

Antiquity with the war

1379: Gabriele de Lavinde, secretary of the pope, writes a collection of codes and keys called nomenclator . This dictionary allows crypter words or syllables currents and will be used during several centuries by the European and American diplomats.

15th century

  • 1412 : Knowledge of Arab civilization in the field of cryptology is exposed in Subh went sha , an encyclopedia of 14 volumes written by the Egyptian Al-Qalqashandi.

  • 1467 : The Italian scientist Leone Battista Alberti exposes for the first time coding by polyalphabetic substitution which it applies using a disc to chiffrer.
    Ce proceeded consists in replacing each letter of the plaintext by a letter of another alphabet and changing several times of alphabet of substitution during coding, returning the cryptanalyse by analysis of frequency inefficace.
    Le principle of the disc to quantify will be taken again and improved by the colonel Wadsworth in 1817, then by Charles Wheatstone in 1867.
    Alberti also presents for the first time the surchiffrement codique one, i.e. the coding of the text already quantified first once, technique which will be really used only several centuries later.

16th century

  • 1518 : The monk Benedictine Jean Trithème written Polygraphiæ , the first printed book dealing with cryptology, in which it exposes a process steganographic consisting in replacing each letter of the plaintext by a word group, the encrypted text resembling a poème.
    Trithème then exposes also a technique of coding by polyalphabetic substitution at the origin of the technique known under the name of Chiffre of Vigenère.

  • 1553 : Giovan Batista Belaso publishes the book Cifra , a collection of literal keys used in codings by polyalphabetic substitution, easy to retain and use, that it calls passwords .

  • 1563 : The Italian Giambattista della Porta exposes in his book De Furtivis Literarum Notis, vulgo of ziferis knowledge in cryptology known until this époque.
    Il exposes a technique of diagrammatic substitution consisting in replacing each couple of letters of the plaintext by a symbol and presents a process of coding by polyalphabetic substitution using 11 different alphabets which will remain effective during 3 centuries.

the figure of Vigenère

In 1586, the French diplomat Blaise de Vigenère present in its book Traicté of the figures or secret manners of escrire (http://gallica.bnf.fr/notice?N=FRBNF31575919) a technique of coding by polyalphabetic substitution inspired by that of Trithème. The coding of Vigenère will be deciphered only in 1854.

Method of coding

Coding uses a literal key or password, whose each letter indicates the alphabetical shift to apply to the plaintext.

One defers the letters of the alphabet on a grid of 26 X 26 boxes; the first line containing has , B ,…, the following columns each one are shifted of a position compared to the preceding one. The quantified text is obtained by taking the intersection, of the line which starts with the letter to code, with the column which starts with the first letter of the password, and so on. As soon as the end of the password is reached, one starts again with the first letter. To decode, it is enough to make the same thing in the other direction.

Strong points of this method

This algorithm of cryptography comprises many strong points. It is very easy to use, and the deciphering is quite as easy if the key is known. The great characteristic of the figure of Vigenère is that it is impossible by an statistical analysis simple to find where are certain letters. Another advantage lies in the fact that one can produce an infinity of keys. It was necessary to wait nearly four centuries so that it is cryptanalysé in the middle of the 19th century. See Cryptanalyse of the figure of Vigenère.

17th century

  • 1623 : In its book Of dignitate and augmentis scientiarum , Francis Bacon exposes a steganographic technique which consists in representing each letter of the plaintext by a group of 5 letters has or B . The resulting encrypted text thus consists of a succession from these two lettres.
    Ce proceeded is equivalent to a binary coding of the letters of the alphabet on 5 bits, preceding the numerical coding of the letters on 8 bits used currently in data processing (code ASCII).

19th century

  • 1854 : A pioneer of the telegraph, Charles Wheatstone, contributes his share to cryptology by inventing the coding of Playfair, of the name of that which did it technical connaître.
    Cette is based on a method of diagrammatic substitution consisting in replacing a couple of adjacent letters by another couple chosen in a grid which constitutes the key.

  • 1883 : Dutch Auguste Kerckhoffs publishes a book on cryptology military cryptography .
    Il exposes to it in particular some rules to be respected to currently conceive a good cryptographic system, always valid, whose principal one is the following one: the safety of a system should not rest on the secrecy of the method of encoding.

The Figure of Delastelle

The inventor of this system is French named Felix-Marie Delastelle. He uses a grid of coding/deciphering similar to that of the figure of Polybe.

Method of coding

First of all, it is necessary to gather the letters of the clear message 5 by 5 (if need be, one adds the null ones to arrive at a multiple of five).

To decipher, one carries out the operation in the opposite direction.

A simple adaptation

The figure of Delastelle differs little from that of Polybe. It is presented here however to show the diversity of the methods of coding, but also that the majority of these methods are simple adaptations of already existing methods.

Large figure of the king Louis XIV

The historians have some documents which were quantified to what one names the Grand Figure of the king Louis XIV, and which was used in theory only for communications of extreme importance. It is to say the interest for the historians to know the contents of these documents, or even simply the prone about which they spoke. Alas, even statistical fault of information on the nature of the texts, and of knowledge would be this only of some words of their contents, they had to await a long time the solution of this mystery. Towards 1893, Etienne Bazeries delivered some finally after three centuries of perplexity.

At the time of the Second world war

The machine Enigma

Invented for the civilians

The history of the machine Enigma starts in 1919, when a Dutch engineer, Hugo Alexander, deposit a patent of machine to be quantified electromechanical. Its ideas are taken up by Dr. Arthur Scherbius, which creates with Berlin a company intended to manufacture and market a machine to be quantified civil: Enigma. This company makes a fiasco, but the Enigma machine drew the attention of the soldiers.

The operation of Enigma

The coding carried out by the machine Enigma is at the same time simple and astute. Each letter is replaced by another, the easy way is that substitution changes from one letter to another. The machine is supplied by a battery. When one presses on a key of the keyboard, an electrical circuit is closed, and a lamp ignites which indicates which coded letter one substitutes. Concretely, the electrical circuit consists of several elements in chain:

  • the plugboard: it makes it possible to exchange pairs of the alphabet, two to two, by means of cards. There are 6 cards which thus make it possible to exchange 12 letters. A plugboard is thus a very particular permutation where one exchanged with more the 6 pairs. For example, in the following table (with simply 6 letters), one exchanged has and C , D and F , while B and E remains invariants.

  • rotors: a rotor is also a permutation, but this unspecified time. To each letter in entry another letter corresponds.

One can compose the rotors, i.e. to put them the ones following the others. The Enigma machine will lay out, with the liking of its successive evolutions, 3 to 6 rotors. Among these rotors, only 3 are used for coding, and there are the choice to place them in the order which one wishes (what will constitute part of the key). Especially, the rotors are cylindrical, and they can turn around their axis. Thus, with each time one typed a letter, the first rotor turns of a notch, and the permutation which it generates is changed. Let us observe this change on the following figure: the rotor initially transforms D into B . When it turns of a notch, this electric connection D ---> B is found gone up in C ---> has .

Each rotor thus has 26 positions. With each time a letter is typed, the first rotor turns of a notch. After 26 letters, it returned to its initial position, and the second rotor turns then of a notch. One starts again to turn the first rotor, and so on… When the second rotor found its initial position, it is the third rotor which turns of a notch.

  • reflectors: At the end of the 3 rotors a last permutation is which makes it possible to retrogress. One permutes last once letters 2 by 2, and one makes them recross the rotors, and the plugboard.

Let us summarize on the following simplified machine (6 letters, 2 rotors) how letter a: is coded

  • one crosses the plugboard: one obtains C

  • one crosses the 2 rotors: one obtains successively has and F
  • one crosses the reflectors where one obtains E , then one returns in the rotors to obtain F , has and finally C after the plugboard.

Let us notice that if C had been typed, the current would have circulated in the other direction and one would have obtained has .

Many possible keys

There are three elements to know to be able to code a message with the Enigma machine:

  1. the position of the 6 cards of the plugboard: initially, it is necessary to choose 12 letters among 26. It is thus the number of combinations of 12 among 26, that is to say 26! /(12! 14!) =: 9657700. Now, it is necessary to choose 6 pairs of letters among 12, that is to say 12! /6! , and like the pair ( has , D ) same connection gives as the pair ( B , has ), it is still necessary to divide by 26. One finds finally: 100391791500.
  2. the order of the rotors: there are as many orders as in ways of ordering 3 elements: 3! =6.
  3. the initial position of the rotors: each rotor having 26 elements, there is 26*26*26=: 17576 choices.

All that is multiplied, and one obtains more 1016 possibilities, which is enormous for the time!

It is important to notice that the permutations employed in the rotors and the reflectors cannot be regarded as belonging to the secrecy. Indeed, all the machines use the same ones, and it thus suffices to have some for provision. The British, for example, recovered some during the war in a cast submarine. This is an illustration of a general principle in cryptography, known as principle of Kerckhoffs , which wants that all the secrecy must lie in the secret key of coding and deciphering, and not in any confidentiality of the algorithm (here of the machine) which cannot be reasonably guaranteed.

Strong points and weaknesses

We already described the strong points of the machine Enigma . Essentially, it is the enormous number of keys, and the reversibility: if, with the same initial secret key, one types the clear message, one obtains the coded message, and with the coded message, one obtains the clear message.

One of the faults of the machine Enigma is that never the letter has will not be coded by an A. That eliminates a certain number of cases to be inspected. One of the other weakness depends rather on the protocol used by the Germans: certain operators - for example, those which informed of the weather - took few precautions and always began their messages with the same words (typically “My general… ”). The British thus knew for part of the message at the same time the clear text and the coded text, which helps to find the key. And as it is the same key which is useful for all the machines Enigma of the German army for a day given, an error of protocol in a message can compromise the safety of all the others!

Deciphering of the Enigma messages

The Polish intelligence service seems was the first with really working “to break” the German code in the years 1930. They worked then in collaboration with the cryptographic service of the 2nd French office, directed by the colonel Gustave Bertrand, helped in this task by information provided by the French mole Hans Thilo Schmidt (“Asche” for the French services). Finally, a collaboration is established with the British services, which gathered their specialists cryptographes with Bletchley Park. It is there that Alan Turing conceived what was the first computer, Colossus, which made it possible to increase the speed of deciphering of the Enigma messages. The Kriegsmarine having developed Enigma modified, it is only towards 1942, after the capture of a machine modified on a U-boot that the allies could know the content of the coded messages of the German navy.

Enigma and UNIX

A student had fun one day to program in Langage C the simulation of the operation of a Enigma machine. This program was included in the distributions UNIX under the name of crypt (usable like an UNIX order). Until the declassification of work of the group of Bletchley Park, the research departments of engineering believed this very sure coding and used it to exchange their confidential informations. For the greatest joy, let us not doubt it, of the National Security Agency, which saw of it its work considerably facilitated!

The Lorenz code

The code of the German top-ranking executives

If the Énigma machine is most known, the Lorenz code led to repercussions even more important today. This code was used by the high German hierarchy to make safe the communications of the leaders.

To reverse the code

Strictly, the coding of Énigma “was not cracké”. German used it badly, sometimes very badly, sufficiently so that the research of the single key among all the keys becomes possible. This attack, the rough force, will overcome all codings. A coding “is cracké” only when there exists better than the rough force to reverse it.

On the contrary, the Lorenz code “was indeed cracké”. Thus, without finding the key of coding, the clear text was recomputed since the quantified text.

Analysis of the Lorenz code

The Lorenz code practiced coding by flood (stream cipher). This type of coding has a weakness mortal: it becomes commonplace to reverse when two messages are quantified with the same key.

By considering that has is the clear text, B is the key, the coded message A' = has + B If two messages are quantified with the same key, A' = has + B and It = C + B, it is enough to make the addition of the two texts quantified to eliminate the key!

A' + It = (has + B)+ (C + B) = (has + C) + (B + B) = has + C since B + B = 0.

Since all the effects of the key are now withdrawn, it does not remain that to make an statistical analysis “to separate” the two texts has and C and to thus find each one of them. The key becomes also commonplace to calculate (it is equal to A' + A).

It is this only and single weakness which destroyed all the code.

An operator transmitted a long message to receive in answer a NACK (message not received). Rather than to comply with the rules and to produce a new key, it took again the same key and returned its message. If it had returned EXACTLY the same text letter by letter, the attack would not have been possible. On the other hand, by using a diminutive here and a synonym there, it technically sent this second coded message with the same key.

From there all déboulé…

After having found the two messages and the single key, this one revealed its secrecies. The technique used coded the letters on five bits where each bit crossed a channel of different coding. The key showed certain repetitions. Those was deduced all the principle from the generation of the key and that of the Lorenz machine. Another distinction between Énigma and Lorenz is that the allies had been in possession of a Énigma machine before the war and others had obtained some during. On the contrary, the allies transfer an authentic Lorenz machine only after the end of the war.

The weakness of the Lorenz code

If the mechanism of generation of key of Lorenz were now known, it was not enough to reverse the other coded messages. Moreover, the statistical analysis of the key showed that this one would remain random on each channel even if it were controlled by nonrandom parameters like the preponderance of certain letters in a language.

A weakness in the Lorenz code in spite of was very found. Two identical consecutive letters produced a constant result on each of the 5 channels in the quantified text. An example is the doubled bloom “S”, in addition to those imposed by the language.

The consequence of the Lorenz code

If a weakness were found, to exploit it was other thing. Indeed, the statistical analysis necessary to find these doubled blooms required a non-existent power for the time. It is at this time that the ultimate weapon for coding was developed, the computer. Colossus, the first computer, was thus built.

Several can discuss on the identity of the first computer. If one defines a computer as being an electronic circuit able to carry out programs, Colossus was indeed the first computer.

It is thus with Colossus that the Lorenz code could be reversed. The details of its algorithms overflow however the objectives of this section.

In addition to bequeathing the computer, the attack of the Lorenz code, just like that of Énigma, made an enormous difference in the war. To say that it shortened war the one year old or even made the difference between victory and defeat is only speculation. The best formulation was made by German after he learned the existence from the programme of deciphering of the allies. Its reaction was to affirm that the difference brought by the deciphering will have been that the nuclear bomb will have exploded in Japan rather than in Germany.

Indeed, with a weapon like the nuclear bomb, the allies would not have needed to wait one year before destroying Germany Nazi. They would not have either escaped the victory. Thanks to the decoding of Énigma and Lorenz code, they did not need the nuclear bomb in Germany and such is probably the best estimate of the concrete difference played by the allied deciphering.

The Navajo S

Although the electromechanical means of codings, such as the machine Enigma , proved their effectiveness in term of safety, they do not remain less cumbersome and slow about it because requiring a double seizure of the messages. These two major disadvantages making this process almost not exploitable in environment hostile, they pushed the American to seek a means of coding ensuring an effective communication on the ground at the time of the war which opposed them to the Japan board.

This process was imagined by American engineer Philip Johnston. This last having grown in the reserves navajos, it had the idea to use their language like cryptographic process. The quasi total ignorance of this language like its very particular grammatical construction, making it impenetrable the abroads, decided on his use.

However an main issue remained: the usual words employed by the armed did not exist in the language navajo. It was thus decided to find a correspondence between words navajos and the military dialect. This table of correspondence was drawn up by association of ideas in order to make it more easily memorable. The term “bomber” for example was translated by “tube” whereas the “bombs” released by these machines became “eggs” in the language navajo.

Here are how the Speaker-of-code ( Windtalkers ) navajos took share with the countryside of the Pacific. Their bravery with the combat was recognized in an official way by the US government when it dedicated to them, in 1982, the day of August 14th.

See too

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