Manual of Cryptography: from the second Italian edition

By Luigi Sacco

Translation of the second (1936) Italian edition by noted American cryptographer Helen Fouché Gaines. The author, a noted European cryptographer, whose Manuale di Crittografia went through three editions in the original Italian, presents - with illustrative examples of enciphering and cryptanalysis - all the cryptosystems proposed or in use through the early 20th century. He also includes, again with examples, description and analysis of the cipher machines in use between the World Wars, including the Enigma which played a major role in World War 2. Finally, he introduces the reader to the mathematical aspect of cryptography, again with extensive examples. Thus this book is a bridge from the ancient origins of the art of cryptography to recent aspects. The only omissions are modern digital cryptosystems developed after WW2, including RSA and public-key systems.

• Language: English
• Publisher: Lulu.com
• Release date: Jul 22, 2020
• ISBN: 9781716717284

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MANUAL OF CRYPTOGRAPHY

INTRODUCTION

1. General Remarks

The need for corresponding by secret methods is as old as the race. Traces of secret writing are encountered in the study of all civilizations, even the most ancient, showing that in every age the corresponding science, cryptography, has had its devotees more or less genial. During the renaissance, the art of encipherment received a notable impulse from favorable political conditions, particularly in Italy and due to the work of the Italians Gerolamo Cardano and G. B. Della Porta, founders of modern cryptography, living in the second half of the 16th century (¹): but it was not until the century just past that studies of a truly scientific and general character began appearing on the subject. A notable flowering of cryptographic works took place in the closing years of that century, followed by a period of almost complete silence. The great war stimulated a notable revival, manifested in special literature and in the appearance of numerous cipher machines: a revival which is justified by the ever-increasing use of radio-telegraphic communication with its fundamental defect - easy interception - offering a vast field for the application of cryptography, particularly for military and political purposes.

Cryptography, in proposing the secrecy of communications which are to pass through unfriendly hands, has in view the safeguarding of the surprise element, a capital factor in every contest. To expose the secret of a message may foil a surprise: it may mean the failure of an enterprise. Hence the battle between cryptography and decryptment, the episodes of which, for the most part unknown, are not always bloodless. Many such episodes took place in the last great war, not all revealed to the public; those which are known, however, suffice to show the perils and injuries overhanging individuals, as well as governments and military commands, who attach too little weight to the weapon, or art, of cryptography. Many sources of very interesting information along this line have been listed in the bibliography at the beginning of this volume.

Here, we are going to concern ourselves with secret writing, that is, with the phase of secret language which is unfolded in written documents, leaving aside the spoken secret language even in its very modern form, secret telephony, or crypto-telephony, by means of which it is proposed that telephone conversations, by wire or radio, shall be rendered incomprehensible during transit.

As a matter of fact, the cryptological processes involved in this very recent branch of secret language are based on artifices pre-eminently technical, and of a nature totally different from those appertaining to secret writing which are to be examined here.

2. Different Kinds of Secret Writing

Secret writing may be classified in four separate categories:

The first three categories are used mainly for purposes of military espionage, or in clandestine correspondence of a politico-revolutionary character.

Sympathetic inks consist in colorless solutions of metallic salts (particularly of silver), or sometimes in organic substances such as the well-known lemon-juice, with which the secret text is hidden; the writing then remains invisible until revealed by some suitable process, such as the application of iodine vapor, which imparts color to the writing. This matter belongs to a special branch of chemistry, and will not further be dealt with.

Conventional writing and dissimulated writing aim at the transmission of a secret message by concealing it, in one of the two ways mentioned, in a plaintext which is apparently innocuous, and of such a nature as to arouse no suspicion on the part of those interested (censorship, police, etc.)

Enciphered writing, proper, comprises texts having quite frankly the appearance of secret and meaningless language, and is used for private, commercial, political and military purposes, especially in connection with telegraphic or radio transmissions.

We are going to begin with the type last mentioned, leaving for Part IV our discussion of other types of secret writing.

PART ONE

ENCIPHERED WRITING

CHAPTER I

GENERAL SURVEY

3. Fundamental Definitions.

a) To ENCIPHER means to translate plain language into enciphered language.

b) A CRYPTOGRAM is the text obtained after the encipherment; it is also referred to as enciphered text, as distinguished from plaintext.

c) CIPHER is the entirety of the documents or of the rules necessary to encipherment. Often, the word is applied only to the principal document, distinguished as the cipher; to this may be added special rules, characterised by conventional words or numbers called keys, or by special encipherment tables.

d) To DECIPHER means to translate enciphered language into plain language, making use of the cipher legitimately in one's possession.

e) DECRYPTMENT is the process equivalent to decipherment, but performed by a person not the intended recipient of the cryptogram and without legitimate possession of the cipher.

4. Fundamental Elements and Operations of Encipherment

Elements of plaintext, to which encipherment rules may be applied, are: single letters, syllables, groups of two or more consecutive letters, words and phrases, or, finally, even fractions or parts of letters.

From the cryptographic standpoint, encipherment operations fall into two classes fundamentally different:

a) Transposition, in which the plaintext elements become transposed, that is disarranged in such a way as to make immediate reconstruction of the plaintext impossible for any person not in possession of the rule which governs the transposition.

b) Substitution, in which elements of plaintext are replaced with other elements, according to suitable lists or rules.

Both operations, of course, can be applied several times in succession, either separately or jointly. Normally, however, transposition is applied only to single letters, or to fractions of letters.

5. Literal Systems and Codes.

In the discussion of encipherment systems, these are generally grouped under two major classifications:

a) Literal systems, in which the elements undergoing change are letters, fractions of letters, or groups of letters of a given length, to which is applied the operation of transposition, or of substitution, or of both.

b) Code systems, applied to syllables, words and phrases of the plaintext by means of a simple substitution, which may or may not be followed by a second encipherment (called superencipherment) applied to the enciphered elements just obtained; this superencipherment, in its own turn may be either substitution or transposition.

This division will be adopted in the study which we are about to begin.

CHAPTER II

PRINCIPAL SYSTEMS OF LITERAL ENCIPHERMENT

6. The Make-up of Cipher Groups.

In the literal encipherment systems, single letters are altered to produce cryptograms made up of letters or figure without apparent meaning. If the cryptogram is to be transmitted by letter, it is immaterial whether or not the enciphered text consists of letters rather than of numbers or of some other symbol; but if, as is usually the case, the cryptogram is to be sent by wire or radio, matters are different. In this case it becomes necessary that cipher groups, in so far as is possible, be homogeneous, so as to avoid errors in transmission; and that that the cryptograms consist of groups containing a number, possibly constant, of letters only, or of figures only, all other symbols being, as a rule, excluded, as is also the intermingling of letters with figures. Normally, cipher groups will have a maximum of five letters or figures, this being the maximum permitted by telegraphic tariffs so that each group may be charged for as a single word. In order to eliminate uncertainties, literal cryptograms are always transcribed in printed capital letters.

7. Encipherment of Numbers and Punctuation Marks.

At this point the problem arises of obtaining homogeneous cipher groups from normal plaintexts which are heterogeneous, that is, consisting of words, numbers, and punctuation marks. For this purpose, a special convention is necessary, which could, as an example, be the following:

Remembering the fact that in Italian the letters K, W, X, Y are never used except in an occasional proper name, it is agreed that whenever a plaintext includes numbers or punctuation marks, this text, prior to encipherment, is to be prepared in the following way:

a) The letter K is placed before and after the numbers, and these, in turn, are replaced by the beginning letters of the alphabet which occupy the corresponding serial positions, that is: 1 equals A; 2 equals B; 3 equals C;......; 9 equals I and 0 equals J.

b) The period and the comma are replaced, respectively, by X and Y.

c) Whenever the letters K, X, Y, are to be used with their true significance instead of the conventional one shown above, the letter W is placed before them.

By such a plan, numbers and punctuation marks can be enciphered like any other plaintext letters and will provide cipher groups homogeneous with those derived from the other letters.

Example: Having to encipher giunti alle 13, 14, sul Krn, we first transform the text to read giunti alle kacydjk sul wkrn, and thus provide a text composed entirely of letters.

It is possible, of course, to establish other conventions which will permit the restoration of the original numbers and punctuation marks by the person who must afterwards decipher.

8. Numerical and Literal Keys

In a very large number of cryptographic systems, secrecy is entrusted to a special convention which is individuated by means of a key, usually an easily-remembered word or phrase, which directly governs the operation of encipherment, or which serves for operations necessary to the encipherment. Often such keys must first be transformed into numerical keys of a specific length.

The simplest method for converting a mnemonic key into a numerical key consists in numbering the successive letters of the key according to their order of succession in the normal alphabet.

For instance, take the key-word Montevideo:

5 7 6 9 2 10 4 1 3 9

M O N T E V I D E O

The number 1 is placed above the letter D, which is the first letter of the normal alphabet to be found in the key; the number 2 is placed above the first E, the number 3 above the second E, and so on.

The resulting numerical key is 5, 7, 6, 9, 2, 10, 4, 1, 3, 8.

By the same procedure, it is possible to derive from the same keyword numerical keys of various lengths, as 6 or 15:

6-digit key:

2 4 3 5 1 6

M O N T E V

15-digit key:

6 10 8 13 2 15 5 1 3 11 7 12 9 14 4

M O N T E V I D E O M  O N  T E

CHAPTER III

LITERAL TRANSPOSITION SYSTEMS

9. General Remarks.

Methods are very numerous indeed for enciphering by transposition that is, by alteration of the natural sequence of letters in a text, but many of these are extremely simple and others much too complicated, so that the number of systems practical for use is limited to three or four, or specifically to: simple transposition, key transposition, grille transposition, and double transposition.

We will show one example of each of these.

10. Simple Transposition

With the aid of quadrille paper, the letters of the plaintext are written successively into the cells of a given rectangle and are then taken off in an order different from that in which they were written.

Example: The number of cells per line is to be nine; a 45-letter text will result in five lines, and the letters of the block thus formed can be taken off in various ways, as: by columns from right to left, by columns from left to right, by reversed columns, by alternate columns, by diagonals from left or right and from top or bottom, and so on, thus producing various different cryptograms of which two examples are shown:

1 2 3 4 5 6 7 8 9

R I N F O R Z I G

I U N G E R A N N

O S T A N O T T E

Q U O T A K B J K

G E N T I L O N I

RIOQG – IUSUE – NNTON – FGATT – OENAI – RROKL – ZATBO – INTJN - GNEKI

RIIOU – NQSNF – GUTGO – EOAER – NTNRZ – TAOAI – IKTNG – LBTNO - JENKI

In case the rectangle does not come out complete, the empty cells resulting on the last line are to be filled with meaningless incoherent letters. The person receiving the cryptogram must, of course, be informed of the method, in order to decipher. Knowing this, as well as the fixed number of letters per line and the number of letters in the cryptogram, he need merely ascertain how many lines are to be used, thus fixing the dimensions of the rectangle in which the cryptogram must be contained; all that then remains is to fill the rectangle, using the agreed method, and read the text, which must come out normally arranged.

11. Key Transposition

With the plaintext written into a rectangle whose width, expressed in letters, is equal to the number of letters in the key, the cryptogram is taken off by columns following the order indicated in the numerical key, which, for that purpose, will be written out at the top of the rectangle. That is, we begin by taking off the column indicated by the number 1 of the key, and continue by taking off the 2nd, the 3rd, etc. When the rectangle does not come out complete, it can either be completed with incoherent letters or to be left incomplete. In the latter case, the difficulties of the correspondent who deciphers it are slightly increased, since he must deduce from the number of letters the number of cells to be left vacant in order to decipher.

Example of completed rectangle:

D:\LIBRARY\Sacco\Sacco Images\2020_07_05\8_0002.tif

Cryptogram to be transmitted:

CEIOU ENCBD SNNQT IUCUN IOOOK HMOSA DIOIO SIROY EZRTX

To decipher, taking into account the fact that the key has 9 letters and the text 45, all that is needed is a rectangle of nine columns, each with five cells (45), to be filled with the enciphered text, taking successively column 1, 2, 3... of the key; at the end od the operation the plaintext appears, written in normal order.

Example of incomplete rectangle:

D:\LIBRARY\Sacco\Sacco Images\2020_07_05\8_0003.tif

Cryptogram to be transmitted:

EAAPO AFOLR ABTEE IOUSI IMEBI TCFTG ARITR RT

To decipher, the recipient, finding that the text has 37 letters, and knowing that the key has 7, prepares a rectangle with five complete lines plus a final one having only two cells (2 equals remainder from division of 37 by 7); he then writes the key across the top and begins filling the rectangle as follows:

D:\LIBRARY\Sacco\Sacco Images\2020_07_05\9_0002.tif

and continues until it is completed; the text comes out in normal order.

12. Grille Transposition

Grilles for effecting transpositions have been devised in great numbers. We will describe the two principle types, that is, the rotating grille and the indefinite grille. Both of these consist of a card, or a sheet of thin metal, marked off into squares, and pierced irregularly with holes; cryptograms are prepared by writing the letters of the plaintext into the successive openings of the grille.

13. Rotating Grilles

The square rotating grille is the oldest known (Cardano, 16th century); in this, one-fourth of the available cells (excluding the central, when there is one) are cut out, and the arrangement of these openings is such that if the grille be placed over a corresponding square of paper and rotated in a succession of 90 degree angles, the successive turns of the grille will in the end expose the total number of cells on the lower square. Thus, if the apertures exposed during the successive rotations be filled with plain-text letters, it is found at the end of the operation that on the square beneath are grille all the cells have been filled in, but in an apparently incoherent manner. Afterward, the taking-off can be accomplished by any one of the conventional routes, that is, by normal lines, by direct or reversed columns, by diagonals, or even with a numerical key of the kind shown under No. 11.

Example of the square grille:

Text to be enciphered: Missione compiuta riento subito Cap. Rota.

Successive positions of the grille:

D:\LIBRARY\Sacco\Sacco Images\page 11_0001.tif

Successive inscription of the square:

D:\LIBRARY\Sacco\Sacco Images\page 11_0002.tif

Cryptogram to be sent (taken off by lines, from the left):

T M E I O      S N C O A      S M P T I P R R I O       O O N U T

S T A A E      U R B C I      I

To form grilles which will satisfy the essential condition of exposing, in four successive positions, the entire number of cells on the square beneath, one may proceed very simply by first calculating arbitrarily the position of one aperture, then cancelling with a mark the three cells which can be occupied by that aperture in the three remaining positions; this done, another aperture may be selected arbitrarily from among the un-cancelled cells, and its three corresponding cells cancelled; this may continue until a number of apertures has been selected which is equal to one-fourth of the cells of the grille. Mathematical rules, too, have been formulated for the purpose, of which it is hardly worth to speak, inasmuch as the system does not present a sufficient guaranty of secrecy.

D:\LIBRARY\Sacco\Sacco Images\page 12.tif

With grilles, too, it can be agreed either to fill with nulls any cells which remain in excess of the number required by the text to be transmitted, or to leave the grille incomplete. In the latter case, however, it is necessary, before beginning the encipherment, to count the letters of the text and cancel the cells which are to remain vacant on the last lines, covering these, say, with black or red chalk, so that when they become exposed during the rotations of the grille, they will not be used.

Should the length of the text exceed the capacity of one grille, it can be agreed to use the same grille a second or a third time, or to reverse it by turns, then leaving the last grille incomplete.

Example of the incomplete grille. Having to transmit the text: Urgone munizioni mitragliatrici: since the text has 29 letters while the grille has 36 cells, the last seven cells are to be cancelled. The rest are then filled in the usual way.

D:\LIBRARY\Sacco\Sacco Images\page 13.tif

Cryptogram to be sent (taken off by column from the left):

M M I R Z      N A I C A      L R U N I      U T T I G      I G N O O      I R O I

Other rotating grilles can be obtained with other regular figures (triangles, pentagons, hexagons, etc.). One ingenious type was originated by Collon, called cubic from its appearance of perspective, which is enclosed in three positions of the grille. This can also be obtained of double a capacity by dividing the cells transversely in two.

The subjoined figure gives an example of the single cubic grille.

D:\LIBRARY\Sacco\Sacco Images\page 13c.tif

To decipher the cryptograms resulting from rotating grilles the figures resulting from the figures resulting from the agreed method must first be filled, using the enciphered text, after which the plaintext is read from these by placing the grilles above them in its various prescribed positions.

To avoid any ambiguity, it is necessary to point out by means of special indicators the various positions which a grille may assume (for the square grille, 4 direct, 4 reserved), so that the citing of one of these indicators at the beginning of a cryptogram can show which of these positions has been assumed as the first.

14. Indefinite Grilles (Sacco)

These are rectangular grilles with the height fixed and the length arbitrary. Each column carries a fixed number of apertures, which are disposed at random.

The writing in of the plaintext is done by columns and the taking off by lines, the resulting cryptogram being written in groups the length of which equals the number of apertures per column. In deciphering, it suffices to know the number of groups, since this number equals the number of columns engaged, into which the cryptogram must be written in order to read the plaintext from the columns.

Example of grille with three apertures per column:

D:\LIBRARY\Sacco\Sacco Images\page 14.tif

Example of encipherment. - Text to be enciphered:

Ripiegare subito sulla posizione di partenza.

D:\LIBRARY\Sacco\Sacco Images\page 15.tif

Cryptogram to be sent: taken off by lines from the left, top:

I Z I  L I I S T R O N R A S S I R E P N O A I P

E T U U D E E B P A Z G L O A

There are thirteen groups, indicating the engagement of thirteen columns. To decipher, it is sufficient to write the cryptogram in lines, beginning at the top, left, through the aperture of the grille, stopping at the thirteenth column, since there are thirteen groups, and then to read the plaintext by columns, beginning at the left.

Indefinite grilles may take 4 positions (two right-side up and two reversed), and these can be distinguished by four designations, the mention of which in the cryptogram will indicate the one used.

15. Double Transposition with Key.

This consists in applying twice in succession the single transposition shown under No. 11, the enciphered text obtained from the first encipherment being treated as a plaintext which now receives a second encipherment with the same key, or, if desired, with a different key.

Example: The text considered under No. 11, keyword Venezia, is to be enciphered: the cryptogram already enciphered there is taken and enciphered again with the same key:

Mnemonic Key                  V E N E Z I A

Numerical Key                  6 2 5 3 7 4 1

Text from 1st encipherment

E A A P O A F

O L R A B T E

E I O U S I I

M E B I T C F

T G A R I T R

R T

Cryptogram to be transmitted:

F E I F R      A L I E G      T P A U I      R A T I C      T A R O B

A E O E M      T R O B S      T I

For decipherment, of course, the incomplete rectangle must be prepared twice, taking into consideration the number of letters in the cryptogram and the number of letters in the key.

Transposition systems, generally speaking, are not advisable alone, because, as we shall see, they do not afford sufficient of secrecy. They are, however, process quite useful in conjunction with other systems, and in necessary operations, or those of superencipherment.

CHAPTER IV

LITERAL SUBSTITUTION SYSTEMS

16. General Remarks

In literal substitution systems, each letter of plaintext becomes replaced with a conventional symbol, which may be another letter or any other symbol whatever. But for telegraphic correspondence, only those systems are used which result in homogeneous groups, of letters or of numbers. We shall often make use of the expressions plaintext letter and substitute, or cipher letter, in order to distinguish between the unenciphered letter and the corresponding symbol which represents it in cipher.

Literal substitution systems can be distinguished as appertaining to two general classes: monoalphabetic and polyalphabetic.

In monoalphabetical systems, two alphabetic lists are prepared, one called the plaintext alphabet, or deciphering list, which contains the 26 letters of the alphabet arranged in normal order (and sometimes the ten digits and a few punctuation marks); and a second list, called the cipher alphabet, or enciphering list, adjacent to the first and comprising the symbols which are to correspond to the systems of the plaintext alphabet. Sometimes the system is completed with another pair of lists to be used for deciphering, in which it is the cipher alphabet that is rearranged in alphabetic order and the plaintext alphabet in the order consequent upon this.

In polyalphabetical systems, instead of the single cipher alphabet, there are several, each used in turn according to suitable conventions or keys.

Leaving aside those systems, extremely numerous, in which the cipher alphabet is composed of more or less cabalistic signs and which are useful, if at all, only in epistolary correspondence, we may confine our observations to those in which the cipher alphabet comprises letters only or numbers only.

Concerning those of numbers only, it may be noted at once that, with only 10 digits and at least 21 letters, it is impossible that each letter be represented by a single digit, so that texts enciphered in this way must have a length greater that of the plaintext, a fact which, generally speaking, renders them less desirable.

This was the type of the portable military cipher (²*) formerly used in our own army, of which mention will be made in the material that follows.

We have noted elsewhere that any occasional numbers and punctuation marks which must be enciphered can be replaced, prior to encipherment, by the use of suitable conventions of the kind pointed out under No. 7, so as to make the enciphered text consists entirely of letters; this is very advisable for the avoidance of errors in transmission by telegraph or radio.

17. Rules for forming Cipher Alphabets.

Since literal systems, as a rule, must be used without recourse to handy books or instructions, the problem is at once presented of forming cipher alphabets with the assistance of rules which are simple and easily remembered. Let us, then examine some of these rules:

a) The shifted alphabet. Example:

Plaintext alphabet A B C D E F G H I J K L M N O P Q R S T...

Cipher alphabet K L M N O P Q R S T U V W X Y Z A B C D...

With this list, the plaintext letter A is to be replaced, in the cryptogram, by the letter K: B by L, etc. This kind of cipher alphabet may be identified by some single letter, for instance the one which corresponds to A of the plaintext. In the given example, the K-alphabet is being used.

b) The reversed and shifted alphabet. Example:

Plaintext alphabet ABCDEFGHIJKLMNOPQRSTUVWXYZ

Cipher alphabet PONMLKJIHGFEDCBAZYXWVUTSRQ

Here, A is to be enciphered with P, B with O, etc. This second method is characterized by a reciprocal correspondence between letters of the two alphabets: that is, if A is enciphered with P, then P will be enciphered with A, etc. In this case, too, the cipher alphabet is effectively identified by naming the letter which corresponds to A of the plaintext alphabet, in the given example, P.

c) The use of a numerical key, that is, one derived from a mnemonic key, applied in the manner shown under No. 11 for transposition with a key.

Example:

Mnemonic key                                    J U G O S L A V I A

Numerical Key                                    5 9 3 7 8 6 1 10 4 2

Normal alphabet                              A B C D E F G H I