== '''[[Grille Ciphers]]''' == ==='''The Cardan Grille and its Variations'''=== Grille ciphers are written with cardboard sheets that have holes cut in them at regular or irregular intervals. The original [[Cardan grille]], proposed in 1550 by [[Girolamo Cardano]], was a rectangular stencil which allowed single letters, syllables and words to be written and read through its various apertures. A hidden text was disguised to appear as an innocent message by filling in gaps between its fragments with anodyne words. Such a method of disguise is considered to be an aspect of [[Steganography]]. Although [[Francis Bacon]] used the words "''steganography''" and "''cryptography''" interchangeably, he recognised the modern sense in his three cipher principles which can be paraphrased as:- 1. a cipher method should not be difficult to use 2. it should not be possible for others to read the cipher 3. in some cases, messages should not be suspicious It is difficult to fulfil all three conditions. Condition 3 applies to steganography (which is given as an obsolete word in older Oxford Dictionaries). Bacon meant that a cipher message should, in some cases, not appear to be a cipher at all; and the original Cardan Grille was intended to meet that aim. Variations on Cardano, however, felt no need to take account of condition 3 and generally failed to meet condition 2: yet, so few if any ciphers have ever achieved this second condition that the point is a quibble and a cryptanalyst’s delight. The attraction of a grille cipher lies in its fulfillment of condition 1: ''that it be not laborious to operate''. In short, it’s dead easy to do. ==='''Single-Letter Grilles'''=== Consider an instance of an isolated grille. Not all ciphers are meant to be communicated to others: records and reminders may be kept in cipher for use of the author alone. A grille is suited to short information such as a key word or a key number. [[Image:Tangiers2.png|frame|
A cardboard grille with eight single-letter apertures
]] In the following example, a grille has eight random holes – equal to the length of a key word TANGIERS. The grille is placed on a grid and the letters written in from top to bottom. [[Image:Tangiers1.png|frame|
A grid filled with random letters and numbers surrounding a key word entered from a grille
]] Removing the grille, the grid is filled out with random letters and numbers. Then, only the possessor of the grille can read back the hidden letters or numbers – which could, for example, be the key to a polyalphabetic cipher such as proposed by [[Giambattista della Porta]]. The grille and the grid are kept separately. If there is only one copy of the grille and one of the grid, the loss of either results in the loss of both. Clearly, in the case of communication by grille cipher, both sender and recipient must possess an identical copy of the grille. The loss of a grille leads to the loss of all secret correspondence with that grille – in the sense that either the messages cannot be read back or that someone else may be reading them. A further use for such a grille has been suggested: that it is a method of generating pseudo-random nonsense from a pre-existing text. This view has been proposed in connection with the [[Voynich manuscript]]. It is an area of cryptography that '''David Kahn''' termed '''''enigmatology''''' and touches on the works of [[Dr John Dee]] and [[Shakespeare authorship]] which [[William F. Friedman]] examined with amusement. ==='''The Trellis'''=== The Elizabethan spymaster [[Sir Francis Walsingham]] (1530-1590) is reported to have used a "''trellis''" to alternate the letters of a text in communication with his ''intelligencers'' or ''newsgatherers'' (spies); however, he generally preferred the code-cipher method of his day known as a [[nomenclator]]. The trellis was described as a device with spaces that was reversible. It appears to have been a transposition device that produced something like the [[Rail fence]] cipher and resembled a chess board. Cardano may not have been responsible for this variation but he was a chess player who wrote a book on gaming, so the pattern would have been familiar to him. Whereas the ordinary Cardan grille has arbitrary perforations, if his method of cutting holes is applied to the white squares of a chess board then a regular pattern is obtained. The encipherer begins with the board in the wrong position for chess. Each letter of the message is written in a single square. If the message is written vertically, it is taken off horizontally – and vice versa. [[Image:ChessBoardCipher.png|frame|
A trellis or chessboard cipher
]] After filling in 32 letters, the board is turned through 90 degrees and another 32 letters are written; (though flipping the board either horizontally or vertically is the same). Shorter messages are filled out with null letters. Messages longer than 64 letters require another turn of the board and another sheet of paper. Each square must be filled up entirely with nulls. J M T H H D L I S I Y P S L U I A O W A E T I E E N W A P D E N E N E L G O O N N A I T E E F N K E R L O O N D D N T T E N R X This transposition method produces an invariant pattern and is not satisfactory for anything other than cursory notes. 33, 5, 41, 13, 49, 21, 57, 29, 1, 37, 9, 45, 17, 53, 25, 61, 34, 6, 42, 14, 50, 22, 58, 30, 2, 38, 10, 46, 18, 54, 26, 62, 35, 7, 43, 15, 51, 23, 59, 31, 3, 39, 11, 47, 19, 55, 27, 63, 36, 8, 44, 16, 52, 24, 60, 32, 4, 40, 12, 48, 20, 56, 28, 64 A second transposition is needed to obscure the letters. Following the chess analogy, the route taken might be the knight’s move or some other path can be agreed upon, such as the reverse spiral, together with a number of nulls to pad the start and end of a message. ==='''Turning Grilles'''=== Rectangular Cardan grilles can be placed in four positions. The trellis or chessboard has only two positions, but it gave rise to a more sophisticated turning grille with four positions that can be rotated in two directions. [[Image:Fleissner.png|frame|
A Fleissner grille of dimensions 8x8 before the apertures are cut
]] Baron '''Edouard Fleissner von Wostrowitz''' (1825-1888), a retired Austrian cavalry colonel, described a variation on the chess board cipher in 1880 and his grilles were adopted by the German army in the First World War. One form of the Fleissner (or Fleißner) grille makes 16 perforations in an 8x8 grid – 4 holes in each quadrant. If the squares in each quadrant are numbered 1 to 16, all 16 numbers must be used once only. This allows many variations in the placing of apertures. The grille has four positions – North, East, South, West. Each position exposes 16 of the 64 squares. The encipherer places the grille on a sheet and writes the first 16 letters of the message. Then, turning the grille through 90 degrees, the second 16 are written, and so on until the grid is filled. It is possible to construct grilles of different dimensions; however, if the number of squares in one quadrant is odd, (despite the total being an even number) one quadrant or section must contain an extra perforation. Illustrations of the Fleissner grille often take a 6x6 example for ease of space: the number of apertures in one quadrant is 9, so three quadrants contain 2 apertures and one quadrant must have 3. There is no standard pattern of apertures: they are created by the user, in accordance with the above description, with the intention of producing a good mix. The method gained wider recognition when [[Jules Verne]] used a turning grille as a plot device in his novel ''Mathias Sandorf'', published in 1885. Verne had come across the idea in Fleissner’s short ''Handbuch die Kryptographie'' which appeared in 1881. [[Image:ExampleTurningGrille.png|frame|
One of the many variations on a Fleissner grille which can be rotated clockwise or anticlockwise
]] Fleissner Grilles were constructed in various sizes during the First World War and were used by the German army at the end of 1916. Each grille had a different code name:- 5x5 ANNA; 6X6 BERTA; 7X7 CLARA; 8X8 DORA; 9X9 EMIL; 10X10 FRANZ. Their security was weak and they were withdrawn after four months. Another method of indicating the size of the grille in use was to insert a key code at the start of the cipher text: E = 5; F = 6 and so on. The grille can also be rotated in either direction and the starting position does not need to be NORTH. Clearly the working method is by arrangement between sender and receiver and may be operated in accordance with a schedule. The following two cipher texts contain the same message. They are constructed from the example grille, beginning in the NORTH position; but one is formed by rotating the grille clockwise and the other anticlockwise. The cipher is then taken off the grid in horizontal lines - but it could equally be taken off vertically. CLOCKWISE ITIT ILOH GEHE TCDF LENS IIST FANB FSET EPES HENN URRE NEEN TRCG PR&I ODCT SLOE ANTICLOCKWISE LEIT CIAH GTHE TIDF LENB IIET FONS FSST URES NEDN EPRE HEEN TRTG PROI ONEC SL&C In 1925 '''Luigi Sacco''' of the Italian Signals Corps began a preliminary book on ciphers which included reflections on the codes of the Great War – ''Nozzioni di crittografia''. He observed that Fleissner’s method could be applied to a fractionating cipher, such as a [[Delastelle]] [[Bifid]] or [[Four-Square]], with considerable increase in security. The grille is also a useful device for transposing Chinese characters. After the First World War, machine encryption began to make simple cipher devices obsolete and grilles were largely relegated to history; yet, grilles provided seed ideas for transposition ciphers that are reflected in modern cryptography. == Cryptanalysis == The original Cardano Grille was a literary device for gentlemen’s private correspondence. A suspicion of its use can lead to discoveries of hidden messages where no such hidden messages exist at all. And, as in the case of letters/numbers in a random grid, obtaining the grille itself is the key. The later variants of Cardano present problems which are common to all transposition ciphers. Frequency analysis shows a normal distribution of letters and hints at the language in which the cipher is written; then the problem, easily stated and less easily done, is to identify the pattern and put the text back into an order that makes sense. Possession of several messages written in the same way is an aid. '''Gaines''', in her standard work on cryptanalysis, gave a lengthy account of transposition ciphers and devoted a chapter to the turning grille, which cannot easily be summarised. == Books == * David Kahn, ''The Codebreakers — The Comprehensive History of Secret Communication from Ancient Times to the Internet'', 1996, ISBN 0684831309. * Helen Fouché Gaines, ''Cryptanalysis – a study of ciphers and their solutions'', 1939; reprinted Dover Publications, New York, 1956 * Richard Deacon, A'' History of the British Secret Service'', Frederick Mũller, London, 1969 * Luigi Sacco, ''Nozzioni di crittografia'', privately printed, Rome, 1930; revised and reprinted twice as ''Manuale di crittografia'' == External links == http://www.turning-grille.com/ http://www.quadibloc.com/crypto/pp0102.htm http://www.crystalinks.com/voynich.html