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[PDF page 269] CH. XI] CRYPTOGRAPHS 253 whole message is written backwards: tsop yb tnes tnemeerga fo seniltuo smret ruo tpecca yeht. In such a case it is unnecessary to indicate the division into words by leaving spaces between them, and we might divide the letters artifi- cially, as thus: Ts opybtne stne meer gafos eniltu osmret ruot peccaye ht. Systems of this kind which depend on altering the places of letters or lines in some pre-arranged manner have always been common. I quoteacoupleofinstances * fromWilkins’sbooktowhichIhavealready referred—it was a work which seems to have been studied diligently by many of those who took part in the civil disturbances of the 17th century, and gives an excellent account of some of the easier systems of cryptographs and ciphers. The first example I take from him is where the letters which make up the communication are written vertically up or down. Thus the message: The pestilence continues to increasemight be written thus: e i o t n l i t sn t i o e th ac sncnse e r eue cep Again, Wilkins says that the cryptograph may be yet further ob- scured by placing the letters which make up the message in any pre- arranged but discontinuate order. For instance if the message runs to four lines we may put the first letter at the beginning of the first line, the second at the beginning of the fourth line, the third at the end of the first line, the fourth at the end of the fourth line, the fifth at the beginning of the second line, the sixth at the beginning of the third line, the seventh at the end of the second line, the eighth at the end of the third line, and so on. Thus the message: Wee shall make an Irruption upon the Enemie, from the North, at ten of the clock this * Mercury, or the Secret and Swift Messenger, by J. Wilkins, London, 1641, pp. 50–52.

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[PDF page 270] 254 CRYPTOGRAPHS AND CIPHERS. [CH. XI night would read thus: Wm rpeta hhs cteinpke haih fonoih kftoe nil anoerr ocgt tthmnu rl eauo mhtei nlen ettes, where, to obscure the message further, it is divided arbitrarily into what appear to be words. Another instance of a cryptograph of this type may be constructed thus. First, bywritingthemessageinlinesofsomearrangedlength, say, for instance, each containing seventeen letters—the letters in successive lines being arranged vertically under those corresponding to them in the upper line—and either leaving no spaces between the words or in- serting some pre-arranged letter or letters or digits between them, such as j, q, z. The message can be then sent as a cryptograph by writing the letters in order in successive vertical lines. This only comes to say- ing that we write successively the 1st, 18th, 35th letters of the original message, and then the 2nd, 19th, 36th letters, and so on. To confuse the decipherer the final reading may be arbitrarily put into what might represent words. If, however, we know the clue number, sayc, it is easy enough to read the communication. For if it divides into the number of letters n times with a remainderr it suffices to re-write the message in lines putting n + 1 letters in each of the firstr lines, and n letters in each of the last c − r lines, and then the communication can be read by reading the columns downwards. For instance, if the following communication, containing 270 letters, were received:Ahtzeipqhgesoa eouazsesewaeqtmusfdtbenzcesjteottqizyczhtzjioarhqettjrfesftnzmroomoh yearziaqneornbreotlennkaerwizesjuasjodezwjzzszjbrrittjnfjlweuzroqyfoht qayeizsleopjidihaloalhpepkrheanazsrvliimosiadygtpekijscerqvvjqjqajqnyji ntkaehsbhsnbgoaotqetqeuuesayqurntpebqstzamztqrj, and the clue num- ber were17 we should put16 letters in each of the first15 lines and 15 letters in each of the last2 lines. The communication could then be discovered by reading the columns downwards: the lettersj, q, and z marking the ends of words. Another cryptograph of this type may be constructed by arrang- ing the letters cyclically, and agreeing that the communication is to be made by selected letters, as, for instance, every seventh, second, sev- enth, second, and so on. Thus if the communication wereAmmunition

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[PDF page 271] CH. XI] CRYPTOGRAPHS 255 too low to allow of a sortie, which consists of32 letters, the successive significant letters would come in the order7, 9, 16, 18, 25, 27, 2, 4, 13, 15, 24, 28, 5, 8, 20, 22, 1, 6, 21, 26, 11, 14, 32, 10, 31, 12, 17, 23, 3, 29, 30, 19—the numbers being selected as in the decimation problem given above on pages 19–20, and being struck out from the32 cycle as soon as they are determined. The above communication would then read Ttriooalmolaoonmsueoawotnliotifw. This is a good cryptograph, but it is troublesome to construct, especially if the message is long, and for that reason is not to be recommended. A cryptograph of the second type is one in which the message is expressed in ordinary writing, but in it are introduced a number of dummies or non-significant letters or digits thus concealing which of the letters are relevant. One way of picking out those letters which are relevant is by the use of a perforated card of the shape of (say) a sheet of note-paper, which when put over such a sheet permits only such letters as are on certain portionsofittobevisible. Suchacardisknownasa grille. Anexample of a grille with four openings is figured below. A communication made in this way may be easily concealed from anyone who does not possess A B C D a card of the same pattern. If the recipient possesses such a card he has only to apply it in order to read the message. The use of the grille may be rendered less easy to detect if it be used successively in different positions, for instance, with the edgesAB and CD successively put along the top of the paper containing the message. On the next page, for instance, is a message which, with the aid of the grille figured above, is at once intelligible. On applying the grille to it with the lineAB along the top HK we get the first half of the communication, namely,1000 rifles se. On applying the grille with the line CD along the top HK we get the rest of the message,

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[PDF page 272] 256 CRYPTOGRAPHS AND CIPHERS. [CH. XI namely, nt to L to-day. The other spaces in the paper are filled with non-significant letters or numerals in any way we please. Of course any one using such a grille would not divide the sheet of paper on which the communication was written into cells, but in the figure I have done so in order to render the illustration clearer. 981 264 070 523 479 100 N T T ORI SON SON AHY DT C BF S P U M OLT KF E LJ O EGX AEU QJ T EGO F LE HV E W LA F M L AES REM REM ODA SSE Y ZZ EP D QJ C EKS T IM OEF H K We can avoid the awkward expedient of having to use a perforated card, which may fall into undesired hands, by introducing a certain pre-arranged number of dummies or non-significant letters or symbols between those which make up the message. Thus, to take an extreme case, we might arrange that only every101st letter should form our communication, and the intervening100 letters should be written at random. But such a communication would be101 times longer than the message, a nearly fatal objection if it had to be written in a hurry or telegraphed. Abettermethod, andonewhichisnoteasilydiscoveredby astranger, istoarrangethat(say)onlyeveryalternatesecondandthird letter shall be relevant. Thus the first, third, sixth, eighth, eleventh, etc., letters are those that make up the message. Such a communication would be only two and a half times as long as the message, but even that might be a great disadvantage if time in sending the message was of importance. For a message written at leisure this need not matter much, and in such a code the introduction of a sufficient number of unnecessary letters in some pre-arranged manner gives an effectual means of conveying a message in secret. We can also avoid the use of a perforated card if it be arranged that everynth word shall give the message, the other words being non- significant, though of course inserted as far as possible so as to make the complete communication run as a whole. But the difficulty of compos- ing a document of this kind and its great length render it unsuitable for any purpose except an occasional communication composed at leisure

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[PDF page 273] CH. XI] CRYPTOGRAPHS 257 and sent in writing. This method is said to have been used by the Earl of Argyle when plotting against James II. Similarly any system that rests on picking out certain letters in a document, which letters form a communication in ordinary writing, is a cryptograph. Thus a communication conveyed by a newspaper, in which the letters making up the message are indicated by pen dots or pin pricks or in some other agreed way, is a cryptograph. A kind of secret writing which may perhaps be considered to con- stitute a third type of cryptograph is a communication on paper which is legible only when the paper is folded in a particular way. An example is a message written across the edges of a strip of paper wrapped spiral- wise round a stick called ascytale. When the paper is unwound and taken off the stick the letters appear broken, and may seem to consist of arbitrary signs, but by wrapping the paper round a similar stick the message can be again read. This system is said to have been used by the Lacedemonians*. The concealment can never have been effectual against an intelligent reader who got possession of the paper. The defect of the method is that the broken letters at once attract attention and suggest the system used. If the fact can be concealed that the visible symbols are parts of letters the cryptograph would be much improved. As an illustration take the appended communication which is said to have been given to the Young Pretender during his wanderings after Culloden. If it be creased along the lines BB and CC (CC being along the second line of the second score), and then folded over, with B inside, so that the crease C lies over the line A (which is the second line of the first score) thus leaving only the top * For references, see Wilkins, supra, p. 38.

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[PDF page 274] 258 CRYPTOGRAPHS AND CIPHERS. [CH. XI and bottom of the piece of paper visible, it will be found to readconceal yourself, your foes look for you. I have seen what purports to be the original, but of the truth of the anecdote I know nothing, and the desirability of concealing himself must have been so patent that it was hardly necessary to communicate it by a cryptograph. I proceed next to some of the more common types of ciphers. It is immaterial whether we invent characters to denote the various letters; or whether we employ special symbols to represent them, such as the symbol ( fora, the symbol : forb, and so on; or whether we use the letters in a non-natural sense, such as the letterz for a, the lettery for b, and so on. The rules for reading the cipher will be the same in each case. In early times it was a common practice to invent arbitrary symbols torepresenttheletters. Ifthesymbolsareinventedforthepurposethey provoke attention, hence it would seem that preferably we should use symbols which are not likely to attract special notice. For instance, the symbols may be musical notes, in which case the message would appear as a piece of music. Geometrical figures have also been used for the same purpose. It is not even necessary to employ written signs. Natural objects have often been used, as in a necklace of beads, or a bouquet of flowers, where the different shaped or coloured beads or different flowers stand for different letters or words. An even more subtle form of disguising the cipher is to make the different distances between consecutive knots or beads indicate the different letters. Of all such systems we may say that a careful scrutiny shows that different symbols are being used, and as soon as the various symbols are distinguished one from the other no additional complication is in- troduced, while for practical purposes they are more trouble to send or receive than those written in symbols in current use. Accordingly I confine myself to ciphers written by the use of the current letters and numerals. It is convenient to divide ciphers into four classes. The first class comprises ciphers in which the same letter or word is always represented by the same symbol, and this symbol always represents the same letter or word. The second class comprises ciphers in which the same letter or word is, in some or all cases, represented by more than one symbol, and this symbol always represents the same letter or word. The third class comprises ciphers in which the same symbol represents sometimes

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[PDF page 275] CH. XI] CIPHERS 259 one letter or word and sometimes another. The fourth class comprises ciphers in which each letter or word is always represented by the same symbol, but more than one letter or word may be represented by the same symbol. A cipher of the first type then is one in which the same letter or word is always represented by the same symbol, and this symbol always represents the same letter or word. Perhaps the simplest illustration of a cipher of this type is to em- ploy one language, but written as far as practical in the alphabet of another language. It is said that during the Indian Mutiny messages in English, but written in Greek characters, were used freely, and suc- cessfully baffled the ingenuity of the enemy, into whose hands they fell. If this is true, the intelligence of the Hindoos must have been much less than that with which they are usually credited. The device, how- ever, is an old one, for we are told* that Edward VI was accustomed to make notes in cipher “with Greek characters, to the end that they who waited on him should not read them.” A common cipher of this type is made by using the actual letters of the alphabet, but in a non-natural sense as indicating other letters. Thus we may use each letter to represent the one immediately following it in the natural order of the alphabet—the letters being supposed to be cyclically arranged—a standing forb wherever it occurs,b standing for c, and so on, and finallyz standing for a. Or more generally we may write the letters of the alphabet in a line, and under them re-write the letters in any order we like. For instance a b c d e f g h i j k l m n o p q r s t u v w x y z o l k m a z s q x e u f y r t h c w b v n i d g j p In such a scheme, we must in our communication replacea by o, b by l, etc. The recipient will prepare a key by rearranging the letters in the second line in their natural order and placing under them the corresponding letter in the first line. Then wherevera comes in the message he receives he will replace it bye; similarly he will replaceb by s, and so on. A cipher of this kind is not uncommonly used in military signalling, the order of the letters being given by the use of a key-word. If, for instance, Pretoria is chosen as the key-word, we write the letters in * Sir John Hayward, Life of Edward VI., edition of 1636, p. 20.

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[PDF page 276] 260 CRYPTOGRAPHS AND CIPHERS. [CH. XI this order, striking out any which occur more than once, and continue with the unused letters of the alphabet in their natural order, writing the whole in two lines thus: p r e t o i a b c d f g h z y x w v u s q n m l k j Then in using the cipherp is replaced byz and vice versâ, r by y, and so on. A long message in such a cipher would be easily discoverable, but it is rapidly composed by the sender and read by the receiver, and for some purposes may be useful, especially if the discovery of the purport of the message is, after a few hours, immaterial. A summary of the usual rules for reading ciphers of this type, whether written in English, French, German, Italian, Dutch, Latin, or Greek, was given by D.A. Conradus in 1742*; and similar rules have been given by various later writers. In English the letter which occurs most frequently ise. The next most common letters are said to bet, a, o, andi; thenn; thenr, s, andh; thend and l; thenc, w, u, andm; then f, y, g, p, andb; thenv and k; and thenx, q, j, andz. The most common double letters areee, ll, oo, and ss; while in more than half the cases of a double letter at the end of a word, the letter is eitherl or s. Also, t and h form a common conjunction. I need not, however, go here into further details of this kind. Assuming that the division into words is given, that non-significant symbols are not introduced, and that the problem is not complicated by the avoidance of the use of common words, a communication of any considerable length can usually be read with but little difficulty. The hints given by Conradus will at once suggest certain hypotheses as to which letters stand for which. Taking one of these hypotheses we write the message, replacing the symbols by the letters we conjecture that they represent and replace the others by dots. If the hypothesis is tenable, the arrangement will probably suggest some of the missing letters. If, for example, we find two words emphs-all and empht-e where the missing letter is represented by the same symbol, the first word shows us that the missing letter ish, m, ort, and the second word shews us that it must bee, h, i, oro, hence it must beh. Every fresh letter so determined makes the hypothesis more probable and renders * Gentleman’s Magazine, 1742, vol.xii, pp. 133–135, 185–186, 241–242, 473–475. See also theCollected Works of E.A. Poein 4 volumes, vol.i, p. 30et seq.

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[PDF page 277] CH. XI] CIPHERS 261 it easier to guess what the remaining symbols represent. The chief difficulty is to get a working hypothesis for the first few letters—if it is the true solution, probably the puzzle will be readily solved—but to make up a working hypothesis for even a few letters requires patience. Ciphers of this class in which the division between the words is given are to be avoided. If we leave a space between such words a would-be decipherer is given an immense help. He will naturally try if a word denoted by a single symbol can be ani or ana, while the words of two or three letters will often stand revealed and so provide a definite groundwork on which he can construct the key. A long word may also betray the secret. For instance, if the decipherer has reason to suspect that the message related to something connected with Birmingham, and he found that a particular word of ten letters had its second and fifth letters alike, as also its fourth and tenth letters, he would naturally see how the key would work if the word represented Birmingham, and on this hypothesis would at once know the letters represented by eight symbols. With reasonable luck this should suffice to enable him to tell if the hypothesis was tenable. The effect of this can be avoided by leaving no spaces between the words, but this might lead to confusion and is not to be recommended. We can also use letters which occur but rarely, such asj, q, x, z, to separate words, and probably this is the best method. Ciphers of this type suggest themselves naturally to those ap- proaching the subject for the first time, and are commonly made by merely shifting the letters a certain number of places forward. If this is done we may decrease the risk of detection by altering the amount of shifting at short (and preferably irregular) intervals. Thus it may be agreed that if initially we shift every letter one place forward then whenever we come to the letter (say)n we shall shift every letter one more place forward. In this way the cipher changes continually, and is essentially changed to one of the third class; but even with this im- provement it is probable that an expert would decode a fairly long message without much difficulty. We can have ciphers for numerals as well as for letters: such ciphers are common in many shops. Any word or sentence containing ten different letters will answer the purpose. Thus, an old tradesman of my acquaintance used the excellent preceptBe just O Man—the first letter representing 1, the second2, and so on. In this cipher the price10/6

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[PDF page 278] 262 CRYPTOGRAPHS AND CIPHERS. [CH. XI would be markedbn/t. This is an instance of a cipher of the first type. A cipher of the second type is one in which the same letter or word is, in some or all cases, represented by more than one symbol, and this symbol always represents the same letter or word. Such ciphers were uncommon before the Renaissance, but the fact that to those who held the key they were not more difficult to write or read than ciphers of the first type, while the key was not so easily discovered, led to their common adoption in the seventeenth century. A simple instance of such a cipher is given by the use of numerals to denote the letters of the alphabet. Thusa may be represented by 11 or by 37 or by 63, b by 12 or by 38 or by 64, and so on, and finally z by 36 or by 62 or by 88, while we can use89 or 90 to signify the end of a word and the numbers91 to 99 to denote words or sentences which constantly occur. Of course in practice no one would employ the numbers in an order like this, which suggests their meaning, but it will serve to illustrate the principle. I have deliberately used numbers of only two digits, as the recipient can then point off the symbols used in twos, and will know that each pair of symbols represents a letter, word, or sentence in the message. A disadvantage of this cipher is that since each letter is denoted by two symbols the length of the message is doubled by putting it in cipher. The cipher can be improved by introducing after every (say) eleventh digit a non-significant digit. If this is done the recipient of the message must erase every twelfth digit before he begins to read the message. With this addition the difficulty of discovering the key is considerably increased. The same principle is sometimes applied with letters instead of numbers. For instance, if we take a word (say) ofn letters, preferably all different, and construct a table as shown below ofn2 cells, each cell is defined by two letters of the key-word. Thus, if we choose the word smoking-cap we shall have100 cells, and each cell is determined uniquely by the two letters denoting its row and column. If we fill these cells in order with the letters of the alphabet we shall have a system similar to that explained above, wherea will be denoted byss or og or no, and so for the other letters. The last22 cells may be used to denote the first 22 letters of the alphabet, or better, three or four of them may be used after the end of a word to show that it is ended, and the rest may be used to denote words or sentences which are likely

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[PDF page 279] CH. XI] CIPHERS 263 S M O K I N G C A P S a b c d e f g h i j M k l m n o p q r s t O u v w x y z a b c d K e f g h i j k l m n I o p q r s t u v w x N y z a b c d e f g h G i j k l m n o p q r C s t u v w x y z A P to occur frequently. Like the similar cipher with numbers this can be improved by in- troducing after every mth letter any single letter which it is agreed shall be non-significant. To decipher a communication so written it is necessary to know the clue-word and the clue-number. Here for instance is a communication written in the above cipher with the clue-wordsmoking-cap, and with7 as the clue-number:ngmk sigrioicpssamckscakqignassnxmigpoasuiamnocmpaminscnogcpncisyiksk amsssgnncaekknoomkhscpcmscbgpngsiawssgiggndiica 1. In this sentence the letters denoting the 79th, 80th, 81st, and 82nd cells have been used to denote the end of a word, and no use has been made of the last 18 cells. Another cipher of this type is made as follows*. The sender and recipientofthemessagefurnishthemselveswithidenticalcopiesofsome book. Inthecipheronlynumeralsareused, andthesenumeralsindicate the locality of the letters in the book. For example, the first letter in the communication might be indicated by 79–8–5, meaning that it is the 5th letter in the 8th line of the 79th page. But though secrecy might * The method is well known. It is mentioned by E.A. Poe, Collected Works, vol. iii, pp. 338–9, but is much older. 1. The original text read ...sssgnnn..., which leads to gobbledegook in the deci- phered message.
