Manual / Guide · 1938
Friedman's training text: frequency distributions tallied on cross-section paper, word patterns and "idiomorphism" (DIVISION = ABCBDBEF), probable-word method (76 pp scan; OCR misreads the 1938 imprint as 1918)
,,~·==============~=====================;t WAR DEPARTMENT OFFICE OF THE CHIEF SIGNAL OFFICER WASHINGTON MILITARY CRYPTANALYSIS Par.t I MONOALPHABETIC SUBSTITUTION SYSTEMS By WILLIAM ·F. FRIEDMAN Principal Cryptanal11at Chief of Signal Intelligence Section War Plam and Training Division PREPARED UNDER THE DIRECTION OP THB CHIBP SIGNAL Ol'Ji'ICER - ,,.. trNI'i'ED STA'tlS GOVERNMENT PRINTING OPFICE wA.SlllNGTON I 1918 MILITARY CRYPTANALYSIS, PART I. -MONOALPHABETIC SUBSTITUTION SYSTEMS B1lction Paragraphs Pages I. Introductory remarks..----------------------------------------------------------------------------------- 1- 3 1- 6 II. Fundamental principles---------------------------------------------------------------------------------- 4- 8 7-10 III. Frequency distributions______________________________________________________________________________________ 9-11 11-17 IV. Fundamental uses of the uniliteral frequency distribution_________________________________________ 12-16 18-26 V. Uniliteral substitution with standard cipher alphabets-------------------------------------- 17-22 27-39 VI. Uniliteral substitution with mixed cipher alphabets-------------------------------------------------- 23-34 40-58 VII. Multiliteral substitution with single-equivalent cipher alphabets_________________________________ 35-36 59-62 VIII. Multiliteral substitution with multiple-equivalent cipher alphabets.. ____________________________ 37-40 63-69 IX. Polygraphic substitution systems.. ____________________________________________________ .-------------------- 41-46 70-98 X. Concluding remarks------------------------------------------------------------------------------------------ 47-50 99-104 XI. Appendix---------------------------------------------------------------------------------------------------------------- 105-120 (ID) r SECTION I INTRODUCTORY REMARKS Paragraph Scope of this text.___ ·-.---------------------------------------------------------------------------------------'-1' Mental equipment neceas&ry for cryptanalytic work..----------------------------------------------------------V&lldity of rellult.s of crypt&na.lysia..--------------------------------------------------------------------- 1 2 3 1. Scope of this text.-a.. It is assumed that the student has studied the two preceding texts written by the same author and forming part of this series, viz, Elementary Military Oryptography, and Adronced MiliJary Oryptography. These texts deal exclusively with cryptography as defined therein; that is, with the various types of ciphers and codes, their principles of construction, and their employment in cryptograpbing and decryptographing messages. Particular emphasis was placed upon such means and methods as are practicable for military usage. It is also assumed that the student has firmly in mind the technically precise, special nomenclature employed in those texts, for the terms and definitions therein will all be used in the present text, with essentially the same significances. If this is not the case, it is recommended that the student review bis preceding work, in order to regain a familiarity with the specific meanings assigned to the terms used therein. There will be no opportunity herein to repeat this information and unless he understands clearly the significance of the terms employed, bis progress will be retarded. b. This text constitutes the first of a series of texts on cryptanalysis. Although most of the information contained herein is applicable to cryptograms of various types and sources, special emphasis will be laid upon the principles and methods of solving military cryptograms. Exeept for an introductory discussion of fundamental principles underlying the science of cryptanalytfos, this first text in the series will deal solely with the principles and methods for the analysis of monoalphabetic substitution ciphers. Even with this limitation it will be possible fu discuss only a few of the many variations of this one type; but with a firm grasp upon the general principles no difficulties should be experienced with any variations that may be encountered. c. This and some of the succeeding texts will deal only with elementary types of cipher systems not because they may be encountered in military operations but because their study is essential to an understanding of the principles underlying the solution of the modern, very much more complex types of ciphers and codes that are likely to be employed by the larger governments today in the conduct of their military affairs in time of war. d. All of this series of texts will deal only with the solution of visible secret writing. At some future date, texts dealing with the solution of invisible secret writing, and with secret signalling systems, may be prepared. 2. l'fental equipment necessary for cryptanalytic work.-a. Captain Parker Hitt, in the first United States Army manual 1 dealing with cryptography, opens the first chapter of his valuable treatise with the following sentence: Success in dealing with unknown ciphers is measured by these four things in the order named: perseverance, careful methods or analysis, intuition, luck. ,, h !. • . 1 Hitt, Ca.pt. Parker, Manual for the Solution of Mi'litary Ciphers. Army Service Schools Press, Fort Leavenworth, Kansas, 1916. 2d Edition, 1918. (Both out of print.) (1) 2 3 These words are as true today as they were then. There is no royal road to success in the solution of cryptograms. Hitt goes on to say: solved than are isolated cryptograms exchanged between unknown correspondents, dealing with unknown subjects. It is obvious that in the former case there are good data upon which the intuitive powers of the cryptamalyst can be brought to bear, whereas in the latter case· no such data are available. Consequently, in the absence of such data, no matter how good the imagination and intuition of the cryptanalyst, these powers are of no particular service to him. Some writers, however, regard the intuitive spirit as valuable from still another viewpoint, as may be noted in the following: 3 Cipher work will have little permanent attraction for one who expects results at once, without labor, for there is a vast amount of purely routine labor in the preparation of frequency tables, the rearrangement of ciphers for examination, and the trial and fitting of letter to letter before the message begins to appear. The present author deems it advisable to add that the kind of work involved in solving cryptograms is not at all similar to that involved in solving "cross-word puzzles", for example. The wide vogue the latter have had and continue to have is due to the appeal they make to the quite common instinct for mysteries of one sort or another; but in solving a cross-word puzzle there is usually no necessity for performing any preliminary labor, and palpable results become evident after the first minute or two of attention. This successful start spurs the cross-word "addict" on to complete the solution, which rarely requires more than an hour's time. Furthermore, cross-word puzzles are all alike in basic principle and once understood, there is no more to learn. Skill comes largely from the embellishment of one's vocabulary, though, to be sure, constant practice and exercise of the imagination contribute to the ease and rapidity with which solutions are generally reached. In solving cryptograms, however, many principles must be learned, for there are many different systems of varying degrees of complexity. Even some of the simpler varieties require the preparation of tabulations of one sort or another, which many people find irksome; moreover, it is only toward the very close of the solution that results in the form of intelligible text become evident. Often, indeed, the student will not even known whether he is on the right track until he has performed a large amount of preliminary "spade work" involving many hours of labor. Thus, without at least a willingness to pursue a fair amount of theoretical study, and a more than average amount of patience and perseverance, little skill and experience can be gained in the rather difficult art of cryptanalysis. General Givierge, the author of an excellent treatise on cryptanalysis, remarks in this connection: 2 The cryptanalyst's attitude must be that of William the Silent: No need to hope in order to undertake, nor to succeed in order to persevere. b. As regards Hitt's reference to careful methods of analysis, before one can be said to be a cryptanalyst worthy of the name it is necessary that one should have firstly a sound knowledge of the basic principles of cryptanalysis, and secondly, a long, varied, and active practical experience in the successful application of those principles. It is not sufficient to have read tre.atises on this subject. One month's actual practice in solution is worth a whole year's mere reading of theoretical principles. An exceedingly important element of success in solving the more intricate ciphers is the possession of the rather unusual mental faculty designated in general terms as the power of inductive and deductive reasoning. Probably this is an inherited rather than an acquired faculty; the best sort of training for its emergence, if latent in the individual, and for its development is the study of the natural sciences, such as chemistry, physics, biology, geology, and the like. Other sciences such as linguistics and philology are also excellent. Aptitude in mathematics is quite important, more especially in the solution of ciphers than of codes. c. An active imagination, or perhaps what Hitt and other writers call intuition, is essential, but mere imagination uncontrolled by a judicious spirit will more often be a hindrance than a help. In practical cryptanalysis the imaginative or intuitive faculties must, in other words, be guided by good judgment, by practical experience, and by as thorough a knowledge of the general situation or extraneous circumstances that led to the sending of the cryptogram as is possible to obtain. In this respect the many cryptograms exchanged between correspondents whose identities and general affairs, commercial, social, or political, are known are far more readily ' Givierge, CMn~ral M"1"cel, Cour3 de Cryptographie, Paris, 1925, p. 301. UlllllUlllllUlllllUlllllUlllllUlllllUlllllUlllllUlllllUlllllUlllllUlllllUlllllUlllllUlllllUlllllUlllllUlllllUlllllUlllllUlllllUlllllUI I Intuition, like a fl.ash of lightning, lasts only for a second. It generally comes when one is tormented by · a difficult decipherment and when one reviews in his mind the fruitless experiments already tried. Suddenly the light breaks through and one finds after a few minutes what previous days of labor were unable to reveal. This, too, is true, but unfortunately there is no way in which the intuition may be sumtnoned at will, when it is most needed.' There are certain authors who regard as indispensable the possession of a somewhat rare, rather mysterious faculty that they designate by the word "flair", or by the expression "cipher brains." Even so excellent an authority as General Givierge,6 in referring to this mental facility, uses the following words: "Over and above perseverance and this aptitude of mind which some authors consider a special gift, and which they call intuition, or even, in its highest manifestation, clairvoyance, cryptographic studies will continue more and more to demand the qualities of orderliness and memory." Although the present author believes a special aptitude for the work is essential to cryptanalytic success, he is sure there is nothing mysterious about the matter at all. Special aptitude is prerequisite to success in all fields of endeavor. There are, for example, thousands of physicists, hundreds of excellent ones, but only a handful of world-wide fame. Should it be said, then, that a physicist 1 Lange et Soudart, TraiU de Cryptographie, Librairie.Felix Alean, Paris, 1925, p. 104. · ' The following extracts are of interest in this connection: The fact that the scientific investigator works 50 per cent of his time by non-rational means is, it seems, quite insufficiently recognized. There is without the least doubt an instinct fot research, and often the most successful investigators of nature are quite unable to give an account of thek reasons for doing such and such an experiment, or for placing side by side two apparently unrelated facts. Again, one of the most salient traits in the character of the succeBSful scientific worker is the capacity for knowing that a point is proved when it would not appear to be proved to an outside intelligence functioning in a purely rational manner; thus the investigator feels that some proposition is true, and proceeds at once to the next set of experiments without waiting and wasting time in the elaboration of the formal proof of the point which heavier minds would need. Questioriless such a scientific intuition may and does sometimes lead investigators astray, but it is quite certain that if they did not widely make use of it, they would not get a quarter as far as they do. Experiments confirm each other, and a false step is usually soon discovered. And not only by this partial replacement of reason by intuition does the work of science go on, but also to the born scientific worker-and emphatically they cannot be made-the structure of the method of research is as it were given, ·he cannot explain it to you, though he may be brought to agree a postiori to a formal logical presentation of the way the method works.-Excerpt from Needham, Joseph, The Sceptical Biologist, London, 1929, p. 79. The e88ence of scientific method, quite simply, is to try to see how data. arrange themselves into causal configurations. Scientific problems are solved by collecting data. and by "thinking about them all the time." We need to look at strange things until, by the appearance of known configurations, they seem familiar, and to look at familiar things until we see novel configurations which make them appear strange. We must look at events until they become luminous. That is scientific method . . . Insight is the touchstone . , . The application of insight as the touchstone of method enables us to evaluate properly the role of imagination in scientific 111ethod. The scientific process is akin to the artistic process: it is a process of selecting out those elements of experience which fit together and recombining them in the mind. Much of this kind of research is simply a ceaseless mulling over, and even the physical scientist has considerable need o( an armchair .. , Our view of scientific method as a struggle to obtain insight forces the admission that science is half art . . • Insight is the unknown quantity which has eluded students of scientific method.-Excerpts from an article entitled lmiqht anq Scientific Method, by Willard Waller, in The American Journal of Sociology, VQl, XL, 1934, I Op. cit., p. 302. I IUlllllUlllllUlllllUlllllUlllllUlllllUlllllUlllllUlllllUlllllUlllllUlllllUlllllUlllllUlllllUllll~lllllUlllllUlllllUlllllUlllllUll,IU 4 I: I. : who has achieved very notable success in his field has done so because he is the fortunate posesssor of a mysterious faculty? That he is fortunate in possessing a special aptitude for his subject is granted, but that there is anything mysterious about it, partaking of the nature of clairvoyance (if, indeed, the latter is a reality) is not granted. While the ultimate nature of any mental process seems to be as complete a mystery today as it has ever been, the present author would like to see the superficial veil of mystery removed from a subject that has been shrouded in mystery from even before the Middle Ages down to our own times. (The principal and easily understandable reason for this is that governments have always closely guarded cryptographic secrets and anything so guarded soon becomes "mysterious.") He would, rather, have the student approach the subject as he might approach any other science that can stand on its own merits with other sciences, because cryptanalytics, like other sciences, has a practical importance in human affairs. It presents to the inquiring mind an interest in its own right as a branch of knowledge; it, too, holds forth many difficulties and disappointments, and these are all the more keenly felt when the nature of these difficulties is not understood by those unfamiliar with the special circumstances that very often are the real factors that led to success in other cases. Finally, just as in the other sciences wherein many men labor long and earnestly for the true satisfaction and pleasure that comes from work well-done, so the mental pleasure that the sueeeesful cryptanalyst derives from his accomplishments is very often the only reward for much ot the drudgery that he must do in his daily work. General Givierge's words in this connection are well worth quoting:• · Some studies will last for yeii.rs before bearing fruit. In the case of others, cryptanalysts undertaking them never get any result. But, for a cryptanalyst who likes the work, the joy of discoveries effaces the memory of his hours of doubt and impatience. d. With his usual deft touch, Hitt says of the element of luck, as regards the role it plays in analysis: As to luck, there is the old miners' proverb: "Gold is where you find it." The cryptanalyst is lucky when one of the correspondents whose ciphers he is studying makes a blunder that gives the necessary clue; or when he finds two cryptograms identical in text but in different keys in the same system; or when he finds two cryptograms identical in text but in different systems, and so on. The element of luck is there, to be sure, but the cryptanalyst mmt be on the alert if he is to profit by these lucky "breaks." e. If the present author were asked to state, in view of the progress in the field since 1916, what elements might be added to the four ingredients Hitt thought essential to cryptanalytic success, he would be inclined to mention the following: (1) A broad, general education, embodying interests covering as many fields of practical knowledge as possible. This is useful because the cryptanalyst is often called upon to solve messages dealing with the most varied of human activities, and the more he knows about these activities, the easier his task. (2) Access to a large library of current literature, and wide and direct contacts with sources of collateral information. These often afford clues as to the contents of specific messages. For example, to be able instantly to have at his disposal a newspaper report or a personal report of events described or referred to in a message under investigation goes a long way toward simplifying or facilitating solution. Government cryptanalysts are sometimes fortunately situated in this respect, especially where various agencies work in harmony. (3) Proper coordination of effort. This includes the organization of cryptanalytic personnel into harmonious, efficient teams of cooperating individuals. • Op. cit., p. 301, (4) Under mental equipment he would also include the faculty of being able to concentrate on a problem for rather long periods of time, without distraction, nervous irritability, and impatience. The strain under which cryptanalytic studies a.re necessarily conducted is quite severe and too long-continued application has the effect of draining nervous energy to an unwholesome degree, so that a word or two of caution may not here be out of place. One should continue at work only so long as a peaceful, calm spirit prevails, whether the work is fruitful or not. ·But just as soon as the mind becomes wearied with the exertion, or just as soon as a feeling of hopelessness or mental fatigue intervenes, it is better to stop completely and turn to other activities, rest, or play. It is essential to remark that systematization and orderliness of work are aids in reducing nervous tension and irritability. On this account it is better to take the time to prepare the data carefully, rewrite the text if necessary, and so on, rather than work with slipshod, incomplete, or improperly arranged material. (5) A retentive memory is an important asset to cryptanalytic skill, especially in the solution of codes. The ability to remember individual groups, their approximate locations in other messages, the associations they form with other groups, their peculiarities and similarities, saves much wear and tear of the mental machinery, as well.as much time in looking up these groups in indexes. j. It may be advisable to add a word or two at this point to prepare the student to expect slight mental jars and tensions which will almost inevitably come to him in the conscientious study of this and the subsequent texts. The present author is well a.ware of the complaint of students that authors of texts on cryptanalysis base much of their explanation upon their foreknowledge of the "answer"-which the student does not know while he is attempting to follow the solution with an unbiased mind. They complain too that these authors use such expressions as "obviously", "naturally", "of course", "it is evident that", and so on, when the circumstances seem not at all to warrant their use. There is no question but that this sort of treatment is apt to discourage the student, especially when the point elucidated becomes clear to him only after many hours' labor, whereas, according to the book, the author noted the weak spot at the first moment's inspection. The present author can only promise to try to avoid making the steps appear to be much more simple than they really are, and to suppress glaring instances of unjusti· fia.ble "jumping at conclusions." At the same time he roust indicate that for pedagogical reasons in many cases a. message has been consciously "manipulated" so as to allow certain principles to become more obvious in the illustrative examples than they ever are in practical work. During ·the course of some of the explanations attention will even be directed to cases of unjustified inferences. Furthermore, of the student who is quick in observation and deduction, the author will only ask that he bear in mind that if the elucidation of certain principles seems prolix and occupies more space than necessary, this is occasioned by the author's desire to carry the explanation forward in very short, easily-comprehended, and plainly-described steps, for the benefit of students who are perhaps a bit slower to grasp but who, once they understand, are able to retain and apply principles slowly learned just as well, if not better than the students who learn more quickly. 3. Validity of results of cryptanalysis.-Valid, or authentic cryptanalytic solutions cannot and do not represent "opinions" of the cryptanalyst. They are valid only so far as they are wholly objective, and are susceptible of demonstration and proof, employing authentic, objective methods. It should hardly be necessary (but an attitude frequently encountered among laymen makes it advisable) to indicate that the validity of the results achieved by any serious cryptanalytic studies on authentic material rests upon the same sure foundations and are reached by the same general steps as the results achieved by any other scientific studies; viz, observation, hypothesis, deduction and induction, and confirmatory experiment. Implied in the latter is the I i i i II I i Ii ~ I 6 possibility that two or more qualified investigators, each working independently upon.the same material, will achieve identical (or practically identical) results. Occasion~y a ps.eudo-~rypt a.nalyst offers "solutions" which cannot withstand such tests; a second, unbiased, mvestiga~r working independently either cannot consistently apply the methods alleged to ha~e been applied by the pseudo-cryptanalyst, or else, if he can apply them ~t ~ll, the. results (pla~-t~xt translations) a.re far different in the two cases. The reason for this is that m such cases it is generally found that the "methods" are not clear-cut, straightforward or mathematical in charac.ter. Instead,. they often involve the making of judgments on matters t~o tenuou~ to measure'. we~gh, or otherwise subject to careful scrutiny. In such cases, the conclusion to which the unpre1udiced observer is forced to come is that the alleged "solution" obtained by the first investigator, the pseudo-cryptanalyst, is purely subjective. In nearly all c8:8es wh~re this ~s happened (and they occur from time to time) there has been uncovered nothing which can ill a'!1y war b~ used to impugn the integrity of the pseudo-cryptanalyst. The wors~ that can be s~d of_him is that he has become a victim of a special or peculiar form of self-delusion, and that his desire to solve the problem, usually in accord with some previously-formed opinion, or notion, has over-balanced, or undermined, his judgment and good sense.7 . 7 Specific reference can be made to the following typ~cal "case histories": Donnelly, Ignatius, The Great Cryptogra.m. Chicago, 1888. · owen_ Orville W., Sir Frtmeis Bacon's Cipher Story. Detroit, 1895. 'Gallu~, Elizabeth Wells, Francia &COf&'B Bililera.l Cipher. Detroit, 1900. Maigaliquth, ,D. 8., The Homer of ArWotle. Oxford, 1923. . . Newbold William Romaine, The Cipher of Roger Bacon. Philadelphia, 1928. (For a scholarly and · com~lete demolition of Professor Newbold's work, see an article entitled Roger Bacon and the Voynich MS, by John M. Manly, in SpeculUm, Vol. VI, No. 3, July 1931.) Arensberg, Walter Conrad, The Cryptography of Shakespeare. Los Angeles, 1922. The Shakespearean Mystery. Pittsburgh, 1928. The Baconian Keys. Pittsburgh, 1928. Feely, Joseph Martin, The Shakespearean Cypher. Rochester, N. Y., 1931. Deciphering Shakespeare. Rochester, N. Y., 1934. SECTION II FUNDAMENTAL PRINCIPLES Paragraph The four basic operations in cryptanalysis-----------------------------------------------------------------------------------·-The determination of the language employed---------------------------------------------·-----------.----------------------·-The determination of the general system-------------------------------·-------------------------------------------------------The reconstruction of the specific keY-------------------------------·--------------·--------------------------------------------The reconstruction of the plain text------------------------------------------------------------------------------------·---------· 4 5 6 7 8 4. The four basic operations in cryptanalysis.-a. The solution of practically every cryptogram involves four fundamental operations or steps: (1) The determination of the language employed in the plain-text version. (2) The determination of the general system of cryptography employed. (3) The reconstruction of the specific key in the case of a cipher system, or the reconstruction, partial or complete, of the code book, in the case of a code system; or both, in the case of an enciphered code system. (4) The reconstruction or establishment of the plain text. b. These operations will be taken up in the order in which they are given above and in which they usually are performed in the solution of cryptograms, although occasionally the second step may precede the first. 6. The determination of the language employed.--a. There is not much that need be said with respect to this operation except that the determination of the language employed seldom comes into question in the case of studies made of the cryptograms of an organized enemy. By this is meant that during wartime the enemy is of course known, and it follows, therefore, that the language he employs in his messages will almost certainly be his native or mother tongue. Only occasionally nowadays is this rule broken. Formerly it often happened, or it might have indeed been the general rule, that the language used in diplomatic correspondence was not the mother tongue, but French. In isolated instances during the World War, the Germans used English when their own language could for one reason or another not be employed. For example, for a year or two before the entry of the United States into that war, during the time America was neutral and the German Government maintained its embassy in Washington, some of the messages exchanged between the Foreign Office in Berlin and the Embassy in Washington were cryptographed in English, and a copy of the code used was deposited with the Department of State and our censor. Another instance is found in the case of certain Hindu conspirators who were associated with and partially financed by the German Government in 1915 and 1916; they employed English as the language of their cryptographic messages. Occasionally the cryptograms of enemy agents may be in a language different from that of the enemy. But in general these are., as has been said, isolated instances; as a rule, the language used in cryptograms exchanged between members of large organizations is the mother tongue of the correspondents. Where this is not the case, that is, when cryptograms of unknown origin must be studied, the cryptanalyst looks for any indications on the cryptograms themselves which may lead to a conclusion as to the language employed. Address, signature, and plain-language words in the preamble or in the body of the text all come under careful scrutiny, as well as all extraneous circumstances connected with the manner in which the cryptograms were obtained, the person on whom they were found, or the locale of their origin and destination. (7) 111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111.11111111111111 ii=-mm iiiii U~i ! ! 8 9 b. In special cases, or under special circumstances a clue to the language employed is found in the nature and composition of the cryptographic text itself. For example, if the letters K and Ware entirely absent or appear very rarely in messages, it may indicate that the language is Spanish, for these letters are absent in the alphabet of that language and are used only to spell foreign words or names. The presence of accented letters or letters marked with special signs of one sort or another, peculiar to certain languages, will sometimes indicate the language used. The Japanese Morse telegraph alphabet and the Russian Morse telegraph alphabet contain combinations of dots and dashes which are peculiar to those alphabets and thus the interception of messages containing these special Morse combinations at once indicates the language involved. Finally, there are certain peculiarities of alphabetic languages which, in certain types of cryptograms, viz, pure transposition, give clues as to the language used. For example, the frequent digraph C H, in German, leads to the presence, in cryptograms of the type mentioned, of many isolated C's and H's; if this is noted, the cryptogram may be assumed to be in German. c. In some cases it is perfectly possible to perform certain steps in cryptanalysis before the language of the cryptogram has been definitely determined. Frequency studies, for example, may be made and analytic processes performed without this knowledge, and by a cryptanalyst wholly unfamiliar with the language even if it has been identified, or who knows only enough about the language to enable him to recognize valid combinations of letters, syllables, or a few common words in that language. He may, after this, call to his assistance a translator who may not be a cryptanalyst but who can materially aid in making necessary assumptions based upon his special knowledge of the characteristics of the language in question. Thus, cooperation between cryptanalyst and translator results in solution. 1 6. The determination of the general system.-a. Except in the case of the more simple types of cryptograms, the determination of the general system according to which a given cryptogram has been produced is usually a difficult, if not the most difficult, step in its solution. The reason for this is not hard to find. b. As will become apparent to the student as he proceeds with his study, in the.final analysi,s, the solution of every cryptogram involving a form of substitution depends upon its reduction to monoalphabetic terms, if it is not originally in those terms. This is true not only of ordinary substitution ciphers, but also of combined substitution-transposition ciphers, and of enciphered code. If the cryptogram must be reduced to monoalphabetic terms, the manner of its accomplishment is usually indicated by the cryptogram itself, by external or internal phenomena which become apparent to the cryptanalyst as he studies the cryptogram. If this is impossible, or too difficult the cryptanalyst must, by one means or another, discover how to accomplish this reduction, by bringing to bear all the special or collateral information he can get from all the sources at his command. If both these possibilities fail him, there is little left but the long, tedious, and often fruitless process of elimination. In the case of transposition ciphers of the more complex type, the discovery of the basic method is often simply a matter of long and tedious elimination of possibilities. For cryptanalysis has unfortunately not yet attained, and may indeed never attain, the precision found today in qualitative analysis in chemistry, for example, where the analytic process is absolutely clear cut and exact in its dichotomy. A few words in explanation of what is meant may not be amiss. When a chemist seeks to determine the identity of an unknown substance, he applies certain specific reagentB to the substance and in a specific sequence. The first reagent tells him definitely into which of two primary classes the unknown substance falls. He then applies a second test with another specific reagent, which tells him again quite definitely into which of two secondary classes the unknown substance falls, and so on, until finally he has reduced the unknown substance to its simplest terms and haa found out what it is. In striking contrast to this situation, cryptanalysis affords exceedingly few "reagents" or tests that may be applied to determine positively that a given cipher belongs to one or the other of two systems yielding externally similar results. And this is what makes the analysis of an isolated, complex cryptogram so difficult. Note the limiting adjective "isolated" in the foregoing sentence, for it is used advisedly. It is not often that the general system fails to disclose it.self or cannot he discovered by painstaking investigation when there is a great volume of text accumulating from a regular traffic between numerous correspondents in a large organization. Sooner or later the system becomes known, either because of blunders and carelessness on the part of the personnel entrusted with the cryptographing of the messages, or because the accumulation of text itself makes possible the determination of the general system by cryptanalytic studies. But in the caae of a single or even a few isolated cryptograms concerning which little or no information can be gained by the cryptanalyst, he is often unable, without a knowledge of, or a shrewd guess as to the general system employed, to decompose the heterogeneous text of the cryptogram into homogeneous, monoalphabetic text, which is the ultimate and essential step in analysis. The only knowledge that the cryptanalyst can bring to his aid in this most difficult step is that gained by long experience and practice in the analysis of many different types of systems. c. On account of the complexities surrounding this particular phase of cryptanalysis, and because in any scheme of analysis baaed upon successive eliminations of alternatives the cryptanalyst can only progress so far as the extent of his own knowledge of all the possible alternatives will permit, it is necessary that detailed discussion of the eliminative process be postponed until the student has covered most of the field. For example, the student will perhaps want to know at once how he can distinguish between a cryptogram that is in code or enciphered code from one that is in cipher. It is at this stage of his studies impracticable to give him any helpful indications on his question. In return it may be asked of him why he should expect to be able to do this in the early stages of his studies when often the experienced expert cryptanalyst is baftled on the same score I d. Nevertheless, in lieu of more precise testB not yet discovered, a general guide that may he useful in cryptanalysis will be built up, step by step as the student progresses, in the form of a series of charts comprising what may be designated An Analytical Key For Oryptanalysi,s. (See Par. 50.) It may be of assistance to the student if, as he proceeds, he will carefully study the charts and note the place which the particular cipher he is solving occupies in the general cryptanalytic panorama.. These charts admittedly constitute only very brief outlines, and can therefore be of but little direct assistance to him in the analysis of the more complex types of ciphers he may encounter later on. So far as they go, however, they may be found to be quite useful in the study of elementary cryptanalysis. For the experienced cryptanalyst they can serve only as a means of assuring that no possible step or process is inadvertently overlooked in attempts to solve a difficult cipher. e. Much of the labor involved in cryptanalytic work, as referred to in Par. 2, is connected with this determination of the general system. The preparation of the text, itB rewriting in different forms, sometimes being rewritten in a half dozen ways, the recording of letters, the establishment of frequencies of occurrences of letters, comparisons and experiments made with known material of similar character, and so on, constitute much labor that is most often indispensable, but which sometimes turns out to have been wholly unnecessary, or in vain. In a 1 The writer has seen in print statements that "during the World War . . . decoded messages in Japanese and Russian without knowing a word of either language." The extent to which such statements are exaggerated will soon become obvious to the student. Of course, there are occasional instances in which a mere clerk with quite limited experience may be able to "solve" a message in an extremely simple system in a language of which he has no knowledge at all; but such a "solution" calls for nothing more arduous than the ability to recognize pronounceable combinations of vowels and coneonants--an ability that hardly deserves to be rated as "cryptanalytic" in any real sense. To say that it is possible to solve a cryptogram in a foreign language "without knowing a word of that language" is not quite the same as to say that it is possible to do so with only a slight knowledge of the language; and it may be stated without cavil that the better the cryptanalyst's knowledge of the language, the greater are the chances for his succese and, in any case, the easier is hie work. Hill lmmt1 11111 10 recent treatise 2 it is stated quite boldly that "this work once done, the determination of the system is often relatively easy." This statement can certainly apply only to the simpler types of ciphers; it is entirely misleading as regards the much more frequently encountered complex cryptograms of modern times. T. The reconstruction of the specific key.-a. Nearly all practical cryptographic methods require the use of a specific key to guide, control, or modify the various steps under the general system. Once the latter has been disclosed, discovered, or has otherwise come into the possession of the cryptanalyst, the next step in solution is to determine, if necessary, a