A cipher device used by king Henry II

Kommentare (2)

1. #1 Thomas

   17. Juli 2018

   The mode of operation is described here (in French): https://docplayer.fr/24810084-La-boite-a-chiffrer-d-henri-ii.html

2. #2 Thomas

   17. Juli 2018

   Translated by Google translate:

   1 The Encryption Box of Henri II Hervé Lehning The operation of the box to quantify and decipher Henry II, exposed to the Renaissance Museum at the castle Ecouen, has long been forgotten and seems to have never been rediscovered. In view of an exhibition on state secrets in the national archives, the curator asked ARSI if any of its members could study the issue. and article is the result of our study in view of the object, as well as the history of cryptography. The object dubbed “box to quantify and decipher” of the museum Ecouen was acquired in 1843 by the museum of luny as an astrological instrument. It was donated to the Ecouen Renaissance Museum when it was created in 1977, but as a box to quantify. It looks like a book consisting of four pages. Pages 3 and 4 of the Encryption Box ARSI Newsletter n

   2 page 2 of the figure box, page 3 is similar Detail of two dials on page 1 90 ARSI Newsletter n

   3 Detail of two dials on page 4 The first page of the book consists of 24 dials divided into four columns of six. Each dial is a small wheel with four spokes, forming a cross, rotatable around its hub and whose rim is divided differently according to the columns. In columns 1 and 3, it is divided into 24 angles of 15, each bearing a symbol. Clockwise: ABDEFGHIKLMNOPQRSTVXYZ. The letters A to Z are silvered and inscribed in the direction of the circumference. The absences of the letters J, U and W are classic in cryptography, the letters I and J on the one hand and U, V and W on the other hand being often confused. The addition of a walleye and turned 90 is more original. The presence of these alphabetic dials confirms the current assumption that this box was used to quantify. The relation to astrology seems more doubtful. Even if the number 12 evokes the 12 signs of the zodiac, it is not clear what the alphabetic dials would then correspond to. The aim of a letter was to be horizontal to the right, position where it is easy to read. In the following figure, it is therefore the letter A. We have also found that no mechanism connects the dials between them. They are therefore independent of each other. alphabetical adran of page 1 ARSI Newsletter n

   In columns 2 and 4, the wheels are divided into 12 angles of 30 each bearing a number between I and XII. The inscriptions are arranged as on a clock, but in the opposite direction. The aim of a digit was to be vertical above because it was then facilitated by its orientation and the grid of the page. In the following figure, it is therefore the number III. The number 12 being half of 24, these digital dials can be compared with the alphabetical dials, a number corresponding to two letters. digital adran of page 1 The second page consists of a larger digital dial, subdivided into 18 angles of 20 each numbered from I to XVIII as on a clock. It has three spokes in the shape of croissants whose arrangement suggests that the natural way to turn it is the opposite direction of the needles of a watch. Large digital dial on pages 2 and 3 92 ARSI Newsletter n

   The third page is identical to the second. The fact that this number 18 is neither a multiple nor a divisor of 12 and 24 excludes a direct comparison of these large dials with the small ones. The fourth page is similar to the first. the wheels of columns 1 and 3 have only two spokes and those of columns 2 and 4 have radii in the form of croissants. On the other hand, the digital dials are now in columns 1 and 3, the numbers are oriented in the circumference direction and the alphabetic dials in columns 2 and 4. The digits of the digital dials are now fully readable when they are on horizontal, left. it may mean that it was used upside down but it is not certain. The two types of alphabetical dials on page 4 are equivalent. The numerical dials on page 4 the differences in shapes and positions do not seem relevant. Pages 1 and 4, like 2 and 3, should work the same way.We will consider them as identical despite the few material differences. ARSI Newsletter n

   6 ontext of the history of cryptography To continue our analysis, we must place this object in the context of the history of cryptography. The figures used in the Renaissance succeeded the figures of Antiquity and the Middle Ages, which were generally simple alphabetic substitutions, one alphabet being replaced by another as in the figure of the Knights Templar. Alphabetical substitution used by the Templars The use of the frequency method to decrypt the encrypted messages is attested as early as the 9th century, when Abu Yusuf Al-Kindi () explains very clearly in his manuscript on the decipherment of cryptographic messages (archives d Istanbul). The numbers by alphabetic substitutions n thus ensured more efficiently the secrecy of the correspondences for a long time when the box to be encrypted was created. To circumvent the frequency method, the cryptologists of the Renaissance found two parades. The most commonly used was that of homogeneous alphabetic substitutions, where the same letter could be encrypted in several different ways, to which we added some nulls (that is to say, letters meaning nothing, simply intended to distort the frequencies a little more ) and a nomenclator to encrypt commonly used words such as “the pope”, “his highness” or “war”. There are several figures of this type used in the time of Henry II, as evidenced by the papers of the Baron de Fourquevaux () reported by Jean Brunon and Jean Barruol in The French in Italy under Henry II (Marseille, 1952). Here for example, following page, the one used by Philibert Babou de la Bourdaisiere, cardinal and ambassador of Henry II in Rome. It is typical of the numbers of the time. Raised at the court of Henry II, Mary Stuart naturally used a comparable figure, which cost her life. Indeed, if the homophone figures are not vulnerable to the frequency method, they remain that to the probable word and, above all, any decrypted symbol remains forever. The secret of the figure falls thus little by little and irreparably. 94 ARSI Newsletter n

   The second parade was invented several times, it is numbers by polyalphabetic substitutions. The first known description of this idea can be found as early as 1466 in De omponendis ifris by Leone Battista Alberti (). he last describes an object with two concentric discs, of different sizes, which can turn around their common center. The largest is marked with letters of the alphabet (except H, J, K, U, W, Y) plus numbers from 1 to 4. The smaller one is marked with a 24-letter alphabet. The Alberti dial matches the letters from A to Z (except H, J, K, U, W, Y) plus the numbers from 1 to 4 to symbols in the disorder. ARSI Newsletter n

   8 A priori, this system allows an alphabetic substitution which becomes polyalphabetic if one is allowed to turn the inner wheel periodically, according to an agreed rule. To use it to encrypt, the correspondents had to agree on an initial position (for example: A and x corresponding to the preceding figure), which served as a key, and a rule (for example: turning the small dial of a clockwise after encrypting 4 letters). The numbers from 1 to 4 allowed to use a nomenclator, each combination of these four numbers having a meaning as “pope”, “sire” or “besieging”. However, the best known inventor of polyalphabetic substitution ciphers is Blaise de Vigenère (). His system is perfectly described in his Traicté des chiffres, or Secret Ways of Writing dated 1586 (BNF). The substitution varies with each letter according to a key exchanged between the correspondents. In spite of these inventions, the figures essentially remained homogeneous alphabetical substitutions until the arrival of the family of Rossignols who created the Great Huff of Louis XIV, which was a ciphered dictionary, and was therefore of another nature. On the other hand, before that time, the habit had remained to keep the division of words, even if it strongly weakens the figures. To finish this historical study, we can notice that this box has no direct descendants, perhaps because of its complexity and its difficulty of use. The same is true of polyalphabetic substitution ciphers, which were hardly used before the nineteenth century, no doubt because of the difficulty of using them without an adequate instrument.Marie-Antoinette’s exception, which used only one letter out of two, which made her very vulnerable to probable word attack, confirms this impression. Substitution by pair of dials If we exclude the two large digital dials, the box is composed of pairs of alphabetic and numerical dials. In a natural way, by positioning the alphabetic dial on a letter (D in the figure) and the numerical dial on a digit which will play the role of key (V in the figure), one can encrypt the letter according to the key. The tests of effective use show that it was not easy because the dials are small (3.2 cm in diameter) and the indications are even more and are sometimes half erased, but this may be due to the wear of time. To continue our study, we will admit that the encryption performed well in this way, by operating a digital dial on an alphabetic dial. It’s about finding the rule to do this! Of course, this rule was part of the instructions for use of the box. as it is lost, we can only imagine the most logical rules and not too difficult to apply. In all cases, they must take into account the positions of the two dials. A natural rule is to perform on the alphabetical dial the rotation that leads from V to I on the digital dial (see figure on the next page). If you use a compass, or any other instrument to postpone distances, this is to bring the distance from V to I in D, which gives M. In the current state of the dials, this seems the only safe way to operate but we can admit that a person in the safe hand can perform this operation without the help of any instrument. 96 ARSI Newsletter n

   9 An alphabet dial and a digital dial positioned on D and V A way to operate a number of the dial (V here) on a letter (D here) that gives the numerical letter (M here) It is easy to to do the same on page 4, the rule we propose does not take into account the shapes of the dials’ spokes.The additional symbol can be used to refer to a nomenclator of 23 words, followed by a letter from A to Z. For example, A can mean “church”, B, “king of Spain”, and so on. If we imagine a nomenclator like that of Babou de la Bourdaisière, we obtain a table of the type: ABDEFGL church Le Roy d Espaigne Monseigneur Kingdom His Holiness Pope Make Faict A possible nomenclator We can increase the size of the nomenclator by following up two letters but that was certainly not the case because the nomenclators of the time were rather short. The symbol may also represent a space or a null, but these hypotheses seem to us less probable because they are not very consistent with the figures of the time. ARSI Newsletter n

   10 Adjusting the digital dials By admitting this action of the digital dials on the alphabetical dials that adjoin them, we have to see how to adjust them. The presence of the two large digital dials opposite the two pages of small dials suggests that they are the key to the system. In this hypothesis, it seems logical to think that the position of each large dial allows to define the positions of the 12 small digital dials of the corresponding page. Mathematically, this means producing a sequence of twelve numbers between 1 and 12. Two constraints seem natural. The first is that the suite is obtained in a simple way by manipulating the large dial, the second is that the suite is as dispersed as possible. To understand the possible choices, it is necessary to examine the mathematics of the time, which is just prior to François Viète (), the great French mathematician and cryptologist of the sixteenth century. For example, Pierre Forcadel, who holds a chair in mathematics at the College of France from 1560, wrote an arithmetic book in 1556, called L arithméticque (BNF), in which he describes in particular the arithmetic progressions, which were therefore commonly used by a mathematician of the time of Henri II. On the other hand, mechanical clocks as we know them had been invented for two centuries. The numbered dials and their properties were therefore well known. A natural idea for a mathematician with the knowledge of Pierre Forcadel in his book is to consider a starting number on which we position the large dial and an increment. Both can be the key unless, for the sake of simplicity, the increment is always the same. The method does not directly explain the fact that large dials have 18 positions and small ones only 12. However, these two numbers have a common mathematical property, that of having the same prime factors, 2 and 3. Specifically, 12 = 2 2 x 3 and 18 = 2 x 3 2. An increment of 2 or 3 will give very regular results. For example, if we start from position 1 on the big dial and use increment 2, that is to say turn the wheel 2 notches twelve times in a row, we get 1, then 3 = 1 + 2, and same: 5, 7, 9, 11, 13, 15, 17. At this level, we go back through 18 and then get again 1 and then 3 and 5. By putting this on the small dials, as they have only 12 positions , the numbers are reduced to their remains in the division by 12, ie: 1, 3, 5, 7, 9, 11, 1, 3, 5, 1, 3, 5. The same settings (1, 3 and 5) find themselves several times. The creator of the box may have wanted to avoid that. To ensure the best possible dispersion, it is best to avoid 2 and 3 as increments and therefore to use a number such as 4 or 5. To avoid heavy handling, it is unlikely, although possible, that the increment was higher. The key would then be limited to the first position of the large dial plus an increment, probably less than 5. In this case, if the key is 2 for the initial position and 5 for the increment, using the large dial, we obtain by a series of rotations of this dial, without any calculation: 2, 7, 12, 17, 4, 9, 14, 1, 6, 11, 16, 3. Reducing to 12, we obtain: 2, 7, 12 , 5, 4, 9, 2, 1, 6, 11, 4, 3 which allows to adjust the small digital dials of the page 1. The use of 5, prime number with 12, has the advantage of avoiding to obtain a continuation periodic and better disperse the sequence of numbers, which the mathematicians of the time knew. The same is true for page 4. Of course, many other solutions are possible for setting small dials from a key, but the device can be used for the purpose.

   11 work like this, and the other methods are similar. The only thing surprising is that the large dials have 18 divisions and not 12. In fact, this can be considered as a voluntary complication of small dial settings to make the sequence of offsets less predictable. The choice of 18 s probably explains why this number has the same prime factors as 12. Examples of encryption To illustrate our point, let us quote the message “association of reservists of numbers and security of information” with the keys II, V and X, V according to the method exposed. We start by setting the 24 digital dials on pages 1 and 4 using the large digital dials on pages 2 and 3 that are set to II for the first and X for the second. Following the rule explained above, that is to say by turning them 12 times each of 5 clockwise, we get for page 1: II, VII, XII, V, IIII, IX , II, I, VI, XI, IIII, III and for page 4: X, III, II, VII, XII, V, IIII, IX, II, I, VI, XI. The settings will remain the same until the end of the encryption process, even if one could imagine a more complex rule. We then set the 24 alphabetical dials in order from top to bottom and from left to right, even if we can once again imagine that we do it from left to right and from top to bottom, which would be preferable for Cryptographic reasons as we see it later, but unnatural given the object. We then have the digital dials act on the alphabetical dials and note the results. For the first, A + II =, for the second S + VII = F, etc.Everything happens in fact as in the method of Vigenère, each number causing a double shift therefore. It gives an offset of 2 in the alphabet, VII, of 12. We obtain: fqyiacttkt hzy trqnzmlseav qs loahfca lz yi nn qnimtiea fr i rtycryxanhr. By way of example, the reader will be able to decrypt the message: Kleyb sybk cvpc trsbwa c dpzzfizge an sxvsllg pfrmyte lqll ee dbgcl r ehtkheca kx keznp rc. The strength of the proposed encryption algorithm encryption is strong if the secret of the underlying algorithm is kept. whatever it is if it remains of the type described above. If the secret of the algorithm is not kept, because of indiscretion or espionage, but the key remains secret, it may seem solid for the time. Indeed, it uses two keys, which decompose each between a position (from 1 to 18) and an increment (theoretically from 1 to 18 but probably small: from 1 to 5), which gives a priori, 18 x 5 = 90 possibilities for each key so 90 2 = 8100 possibilities in all. however, if the operations are performed as described above, the number of attempts to decrypt a message is reduced to twice 90. Indeed, just try the 90 possible keys of the first dial on the first 12 letters. If they form a pronounceable suite, it is likely that we have found the right key. For example, in the previous message, we isolate the first 12 letters: Kleyb sybk cvp. By setting the first dial to I and V, we get the following settings: 1, 6, 11, 4, 3, 8, 1, 6, 5, 10, 3, 2 and therefore the first letters Kaiqy that are not suitable. not. We continue like this. By setting the first dial to V and V, we get the following settings: 5, 10, 3, 2, 7, 12, 5, 4, 9, 2.1, 6 and the first letters: Bravo you have. The first ARSI Bulletin n

   12 key is obviously good. We have to find the second by the same process and the message. Used in this form, the encryption is less solid than it seems a priori if the secret of the encryption algorithm is not kept. However, it is possible to resist this method of decryption by writing the messages on pages 1 and 4 together from left to right and from bottom to top. In this case, tests are necessary and make it improbable to decipher with the means of the time. Type of Encryption Of course, unless very improbable discovery of a user manual, or encrypted messages using it, we can never ensure with certainty the exact operation of the box to quantify Henri II. however, the arrangement of dials in pairs, an alphabetic and a numerical, makes it very likely that the number of the digital dial should act on the letter of the alphabetic dial to encrypt it. The simplest way to do this is to shift the letter according to the number, the only uncertainty is to know in what sense it was operating. This idea assumes that the alphabetic dials were set from the text to be encrypted, 24 letters by 24 with the possibility of a nomenclator corresponding to the symbol (the turn of 90, as we see a few lines later). The digital dials were to be adjusted according to the corresponding large digital dial. The use of a key indicating the initial position of the latter and a rather small increment is likely but one can imagine more complex methods. In this short article, we have shown why the studied object seems to us to have been used to quantify and decipher and was not, as it was advanced, an astrological instrument. We have also shown a method, compatible with the knowledge of the time, to use this box to encrypt, and therefore also to decipher since these two operations remained symmetrical in all the numbers until the configuration of the alphabetic dials accompanied by digital dials makes almost certain that each pair was designed to generate an alphabetic substitution. The presence of a supernumerary symbol (here) reminds us of the use of a nomenclator, which was part of the shared secret between correspondents. The two points are corroborated by the fact that all the figures of the time are based on this principle. The multiplicity of these pairs of wheels militates for a polyalphabetic substitution figure. The central position of the large digital dials makes them think that they control the positions of the small digital dials, and thus constitute the key of the number. We showed how it could be done, but there are many possibilities. In any case, the complexity of the implementation of this box to cipher probably explains that she had no descendants. References The historical references cited on the BNF website, the referenced books are available on Gallica and the important passages in my book The universe of secret codes of antiquity on the Internet published by Ixelles in the Bulletin of the ARSI n