In the history of cryptography, a grille cipher was a technique for encrypting a plaintext by writing it onto a sheet of paper through a pierced sheet (of paper or cardboard or similar). The earliest known description is due to Jacopo Silvestri in 1526.[1] His proposal was for a rectangular stencil allowing single letters, syllables, or words to be written, then later read, through its various apertures. The written fragments of the plaintext could be further disguised by filling the gaps between the fragments with anodyne words or letters. This variant is also an example of steganography, as are many of the grille ciphers.
The Cardan grille was invented as a method of secret writing. The word cryptography became the more familiar term for secret communications from the middle of the 17th century. Earlier, the word steganography was common.[citation needed] The other general term for secret writing was cypher - also spelt cipher. There is a modern distinction between cryptography and steganography
Sir Francis Bacon gave three fundamental conditions for ciphers. Paraphrased, these are:
a cipher method should not be difficult to use
it should not be possible for others to recover the plaintext (called 'reading the cipher')
in some cases, the presence of messages should not be suspected
It is difficult to fulfil all three conditions simultaneously. Condition 3 applies to steganography. Bacon meant that a cipher message should, in some cases, not appear to be a cipher at all. The original Cardan Grille met that aim.
Variations on the Cardano original, however, were not intended to fulfill condition 3 and generally failed to meet condition 2 as well. But, few if any ciphers have ever achieved this second condition, so the point is generally a cryptanalyst's delight whenever the grille ciphers are used.
The attraction of a grille cipher for users lies in its ease of use (condition 1). In short, it's very simple.
Single-letter grilles
In this example, a grille has eight irregularly placed holes – equal to the length of the word tangiers. The grille is placed on a gridded sheet and the letters are written in from top to bottom. Removing the grille, the grid is filled with random letters and numbers.
Not all ciphers are used for communication with others: records and reminders may be kept in cipher for use of the author alone. A grille is easily usable for protection of brief information such as a key word or a key number in such a use.
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 probable loss of all secret correspondence encrypted with that grille. Either the messages cannot be read (i.e., decrypted) or someone else (with the lost grille) may be reading them.
The Elizabethan spymaster Sir Francis Walsingham (1530–1590) is reported to have used a "trellis" to conceal the letters of a plaintext in communication with his agents. However, he generally preferred the combined code-cipher method known as a nomenclator, which was the practical state-of-the-art in his day. The trellis was described as a device with spaces that was reversible. It appears to have been a transposition tool that produced something much like the Rail fence cipher and resembled a chess board.
Cardano is not known to have proposed 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 a regular pattern results.
The encipherer begins with the board in the wrong position for chess. Each successive letter of the message is written in a single square. If the message is written vertically, it is taken off horizontally and vice versa.
After filling in 32 letters, the board is turned through 90 degrees and another 32 letters written (note that flipping the board horizontally or vertically is the equivalent). Shorter messages are filled with null letters (i.e., padding). Messages longer than 64 letters require another turn of the board and another sheet of paper. If the plaintext is too short, 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 satisfactorily secure for anything other than cursory notes.
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 a reverse spiral, together with a specific 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.
A Fleissner grille of dimensions 8x8 before the apertures are cut.
Baron Edouard Fleissner von Wostrowitz, a retired Austrian cavalry colonel, described a variation on the chess board cipher in 1880 and his grilles were adopted by the German army during World War I. These grilles are often named after Fleissner, although he took his material largely from a German work, published in Tübingen in 1809, written by Klüber who attributed this form of the grille to Cardano, as did Helen Fouché Gaines.[3]
Bauer notes that grilles were used in the 18th century, for example in 1745 in the administration of the Dutch Stadthouder William IV. Later, the mathematician C. F. Hindenburg studied turning grilles more systematically in 1796. '[they]are often called Fleissner grilles in ignorance of their historical origin.'
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 placing the 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, even if the total is 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 wide 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 treatise Handbuch der Kryptographie which appeared in 1881.
One of the many variations on a Fleissner grille which can be rotated clockwise or anticlockwise.
Fleissner Grilles were constructed in various sizes during World War I and were used by the German Army at the end of 1916.[4] 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.
In the following examples, 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 ciphertext is then taken off the grid in horizontal lines - but it could equally be taken off vertically.
In 1925 Luigi Sacco of the Italian Signals Corps began writing a 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 DelastelleBifid or Four-Square, with considerable increase in security.
Grille ciphers are also useful device for transposing Chinese characters; they avoid the transcription of words into alphabetic or syllabic characters to which other ciphers (for example, substitution ciphers) can be applied.
After World War I, machine encryption made simple cipher devices obsolete, and grille ciphers fell into disuse except for amateur purposes. Yet, grilles provided seed ideas for transposition ciphers that are reflected in modern cryptography.
Unusual possibilities
The d'Agapeyeff cipher
The unsolved D'Agapeyeff cipher, which was set as a challenge in 1939, contains 14x14 dinomes and might be based on Sacco's idea of transposing a fractionated cipher text by means of a grille.
A Third-Party Grille: the crossword puzzle
A crossword grid taken from a 1941 newspaper
The distribution of grilles, an example of the difficult problem of key exchange, can be eased by taking a readily-available third-party grid in the form of a newspaper crossword puzzle. Although this is not strictly a grille cipher, it resembles the chessboard with the black squares shifted and it can be used in the Cardan manner. The message text can be written horizontally in the white squares and the ciphertext taken off vertically, or vice versa.
Again, following Sacco's observation, this method disrupts a fractionating cipher such as Seriated Playfair.
Crosswords are also a possible source of keywords. A grid of the size illustrated has a word for each day of the month, the squares being numbered.
Cryptanalysis
The original Cardano Grille was a literary device for gentlemen's private correspondence. Any suspicion of its use can lead to discoveries of hidden messages where no hidden messages exist at all, thus confusing the cryptanalyst. Letters and numbers in a random grid can take shape without substance. Obtaining the grille itself is a chief goal of the attacker.
But all is not lost if a grille copy can't be obtained. The later variants of the Cardano grille present problems which are common to all transposition ciphers. Frequency analysis will show a normal distribution of letters, and will suggest the language in which the plaintext was written.[5] The problem, easily stated though less easily accomplished, is to identify the transposition pattern and so decrypt the ciphertext. Possession of several messages written using the same grille is a considerable aid.
Gaines, in her standard work on hand ciphers and their cryptanalysis, gave a lengthy account of transposition ciphers, and devoted a chapter to the turning grille.[3]
In cryptography, a cipher is an algorithm for performing encryption or decryption—a series of well-defined steps that can be followed as a procedure. An alternative, less common term is encipherment. To encipher or encode is to convert information into cipher or code. In common parlance, "cipher" is synonymous with "code", as they are both a set of steps that encrypt a message; however, the concepts are distinct in cryptography, especially classical cryptography.
Cryptanalysis refers to the process of analyzing information systems in order to understand hidden aspects of the systems. Cryptanalysis is used to breach cryptographic security systems and gain access to the contents of encrypted messages, even if the cryptographic key is unknown.
In cryptography, the one-time pad (OTP) is an encryption technique that cannot be cracked, but requires the use of a single-use pre-shared key that is larger than or equal to the size of the message being sent. In this technique, a plaintext is paired with a random secret key. Then, each bit or character of the plaintext is encrypted by combining it with the corresponding bit or character from the pad using modular addition.
In cryptography, a substitution cipher is a method of encrypting in which units of plaintext are replaced with the ciphertext, in a defined manner, with the help of a key; the "units" may be single letters, pairs of letters, triplets of letters, mixtures of the above, and so forth. The receiver deciphers the text by performing the inverse substitution process to extract the original message.
In cryptography, a transposition cipher is a method of encryption which scrambles the positions of characters (transposition) without changing the characters themselves. Transposition ciphers reorder units of plaintext according to a regular system to produce a ciphertext which is a permutation of the plaintext. They differ from substitution ciphers, which do not change the position of units of plaintext but instead change the units themselves. Despite the difference between transposition and substitution operations, they are often combined, as in historical ciphers like the ADFGVX cipher or complex high-quality encryption methods like the modern Advanced Encryption Standard (AES).
In cryptography, a Caesar cipher, also known as Caesar's cipher, the shift cipher, Caesar's code, or Caesar shift, is one of the simplest and most widely known encryption techniques. It is a type of substitution cipher in which each letter in the plaintext is replaced by a letter some fixed number of positions down the alphabet. For example, with a left shift of 3, D would be replaced by A, E would become B, and so on. The method is named after Julius Caesar, who used it in his private correspondence.
Symmetric-key algorithms are algorithms for cryptography that use the same cryptographic keys for both the encryption of plaintext and the decryption of ciphertext. The keys may be identical, or there may be a simple transformation to go between the two keys. The keys, in practice, represent a shared secret between two or more parties that can be used to maintain a private information link. The requirement that both parties have access to the secret key is one of the main drawbacks of symmetric-key encryption, in comparison to public-key encryption. However, symmetric-key encryption algorithms are usually better for bulk encryption. With exception of the one-time pad they have a smaller key size, which means less storage space and faster transmission. Due to this, asymmetric-key encryption is often used to exchange the secret key for symmetric-key encryption.
The Vigenère cipher is a method of encrypting alphabetic text where each letter of the plaintext is encoded with a different Caesar cipher, whose increment is determined by the corresponding letter of another text, the key.
In cryptography, a scytale is a tool used to perform a transposition cipher, consisting of a cylinder with a strip of parchment wound around it on which is written a message. The ancient Greeks, and the Spartans in particular, are said to have used this cipher to communicate during military campaigns.
The Playfair cipher or Playfair square or Wheatstone–Playfair cipher is a manual symmetric encryption technique and was the first literal digram substitution cipher. The scheme was invented in 1854 by Charles Wheatstone, but bears the name of Lord Playfair for promoting its use.
In cryptography, ciphertext or cyphertext is the result of encryption performed on plaintext using an algorithm, called a cipher. Ciphertext is also known as encrypted or encoded information because it contains a form of the original plaintext that is unreadable by a human or computer without the proper cipher to decrypt it. This process prevents the loss of sensitive information via hacking. Decryption, the inverse of encryption, is the process of turning ciphertext into readable plaintext. Ciphertext is not to be confused with codetext because the latter is a result of a code, not a cipher.
A null cipher, also known as concealment cipher, is an ancient form of encryption where the plaintext is mixed with a large amount of non-cipher material. Today it is regarded as a simple form of steganography, which can be used to hide ciphertext.
A straddling checkerboard is a device for converting an alphanumeric plaintext into digits whilst simultaneously achieving fractionation and data compression relative to other schemes using digits. It also is known as a monôme-binôme cipher.
In cryptography, a ciphertext-only attack (COA) or known ciphertext attack is an attack model for cryptanalysis where the attacker is assumed to have access only to a set of ciphertexts. While the attacker has no channel providing access to the plaintext prior to encryption, in all practical ciphertext-only attacks, the attacker still has some knowledge of the plaintext. For instance, the attacker might know the language in which the plaintext is written or the expected statistical distribution of characters in the plaintext. Standard protocol data and messages are commonly part of the plaintext in many deployed systems, and can usually be guessed or known efficiently as part of a ciphertext-only attack on these systems.
In cryptography, the ADFGVX cipher was a manually applied field cipher used by the Imperial German Army during World War I. It was used to transmit messages secretly using wireless telegraphy. ADFGVX was in fact an extension of an earlier cipher called ADFGX which was first used on 1 March 1918 on the German Western Front. ADFGVX was applied from 1 June 1918 on both the Western Front and Eastern Front.
The Polybius square, also known as the Polybius checkerboard, is a device invented by the ancient Greeks Cleoxenus and Democleitus, and made famous by the historian and scholar Polybius. The device is used for fractionating plaintext characters so that they can be represented by a smaller set of symbols, which is useful for telegraphy, steganography, and cryptography. The device was originally used for fire signalling, allowing for the coded transmission of any message, not just a finite number of predetermined options as was the convention before.
In classical cryptography, the bifid cipher is a cipher which combines the Polybius square with transposition, and uses fractionation to achieve diffusion. It was invented around 1901 by Felix Delastelle.
In cryptography, a classical cipher is a type of cipher that was used historically but for the most part, has fallen into disuse. In contrast to modern cryptographic algorithms, most classical ciphers can be practically computed and solved by hand. However, they are also usually very simple to break with modern technology. The term includes the simple systems used since Greek and Roman times, the elaborate Renaissance ciphers, World War II cryptography such as the Enigma machine and beyond.
The Cardan grille is a method of writing secret messages using a grid.
The Two-square cipher, also called double Playfair, is a manual symmetric encryption technique. It was developed to ease the cumbersome nature of the large encryption/decryption matrix used in the four-square cipher while still being slightly stronger than the single-square Playfair cipher.
↑ Kahn, David (1996). The Codebreakers — The Comprehensive History of Secret Communication from Ancient Times to the Internet. pp.308–309. ISBN0-684-83130-9.
This page is based on this Wikipedia article Text is available under the CC BY-SA 4.0 license; additional terms may apply. Images, videos and audio are available under their respective licenses.
