When a substitution key (a pair of alphabets) is being used for cipher purposes, the letters which make up the cipher alphabet cannot be chosen at random; the key must be of such a nature that any one of the several correspondents, desiring to make use of it, will have it at his disposal. Word-divisions are usually concealed, or, occasionally, falsified. Punctuation, if used at all, must don the apparel worn by the rest of the text; no limitations can be placed on length, and no word whatever can be barred, where the intention is that of conveying actual messages; and it is not at all uncommon to find that one or more letters are serving as their own substitutes.
In discussing keys, we will make some arbitrary rulings of our own, but only in the interests of clarity. We will assume, for all cases, that the two necessary alphabets are always written horizontally, as several are shown in Fig. 59; that wherever the two complete alphabets appear, the upper of the pair is always the one in which plaintext letters must be found, so that the lower one is always the cipher alphabet. Thus, whenever the two alphabets are written out in full, the substitute for any given plaintext letter will be the letter standing immediately below it; and the original of any cipher letter will be the letter standing just above it. Wherever it seems advisable to show a distinction, the cipher letters will be expressed as capitals and the plaintext letters will appear in lower case.
Among the oldest cipher alphabets ever used for practical purposes are those of the type called “Caesar,” one such alphabet having been used by Julius Caesar, and another by Octavius. As may be seen at (a) of Fig. 59, this type of cipher alphabet is no more than a simple shifting of the normal alphabet to a new point of beginning. Using this particular example, the word “Caesar” will be enciphered as F D H V D U; or, if the word R Y H U is found in a cryptogram, it deciphers as “over.”
At (b) of the same figure, we have a pair of inverse normal alphabets. Here, it is not necessary to specify that one of the pair is a plaintext alphabet and the other a cipher alphabet; whenever a plaintext alphabet is merely reversed and allowed to serve as its own cipher alphabet, the encipherment becomes reciprocal; that is, whenever Z is the substitute for A, then A will also be the substitute for Z, and so for other letters. Thus, we need not write down more than half of the key shown at (b); and, in any other case of reciprocal alphabets, only enough of it to make sure that we have all 26 of the letters; after that, we may find them where we please, both for encipherment and for decipherment. Simple reciprocal alphabets are also ancient. The one just mentioned, and also the one shown at (c), are both said to have been used in parts of the Bible. The two inverse alphabets of (b) may, of course, be shifted with reference to each other; that is, one or the other may be caused to begin at any desired letter, just as is done with the ordinary alphabet in deriving one of the “Caesars.” It is also possible, as indicated at (d), to divide the
| Figure 59 Some Simple Substitution Keys(a) A shifted, or "Caeser," alphabet: Plaintext: 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 CIPHER: D E F G H I J K L M N O P Q R S T U V W X Y Z A B C (b) A pair of inverse alphabets: A B C D E F G H I J K L N N O P Q R S T U V W X Y Z Z Y X W V U T S R Q P O N M L K J I H G F E D C B A Other examples of the RECIPROCAL alphabet: (c) A B C D E F G H I J K L M (e) C U L P E R A B D F G H I N O P Q R S T U V W X Y Z Z Y X W V T S Q O N M K J (d) A B C D E F G H I J K L M (f) C U L P E R A B D F G H I T S R Q P O N Z Y X W V U J K M N O Q S T V W X Y Z |
normal alphabet into its two halves, and shift one of the halves; in this case the encipherment would be reciprocal whether or not the shifted portion runs in reverse order. At (e) and (f), we have mixed (or interverted) alphabets which, though crude, are more in line with modern practice than those which precede them, since both of these are based on the key-word CULPEPER.
The usual plan for deriving cipher alphabets from key-words is as follows: First, all repeated occurrences of any same letter, such as the second P and the second E of the word CULPEPER, are discarded. The unrepeated letters of the key-word, as C U L P E R, are placed at the beginning of the cipher alphabet, and the rest of the 26 letters are made to follow these, usually in their normal alphabetical order. If an adequate key-word be chosen, for instance the word UNCOPYRIGHTABLE, a well-mixed alphabet results; but, in order to have a cipher alphabet which is truly incoherent, and hard for the decryptor to reconstruct, we may write this already-mixed alphabet into block form and subject it to a transposition of some kind. Several examples of this may be examined in Fig. 60. In example (a), the repeated letters of the key-word have merely been discarded, while example (b) retains these two positions in order to produce more and shorter columns, with three different lengths. In both cases, the columns of the block have been taken out by descending verticals to form cipher alphabets (a) and (b), but the transposition may follow any desired route or other process. Example (c) suggests further uses for key-words. Still another process (not shown) consists in writing the key-numbers above a block, exactly as in example (c), and allowing them to govern the lengths of rows. In the writing-in of the alphabet, normal or mixed, the first row of letters is made to end under key-number 1, the second row under key-number 2, and so on, so that the completed block contains rows of different lengths; it may then be taken off by columns, or otherwise. Numerous other devices exist, but it should be plain from the foregoing that we have an unlimited field in which to derive well-scrambled cipher alphabets, so that there is no need whatever for forming one at random and later being unable to set it up again.
| Figure 60 Some Methods for Forming a Keyword-Mixed Alphabet Keyword: CULPEPER (a) (b)* (c) C U L P E R C U L P E * * R C U L P E P E R A B D F G H A B D F G H I J 1 8 4 5 2 6 3 7 I J K M N O K M N O Q S T V A B C D E F G H Q S T V W X W X Y Z I J K L M N O P Y Z Q R S T U V W X *)(An OHAVER Method). Y Z (a) Plaintext: 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 CIPHER: C A I Q Y U B J S Z L D K T P F M V E G N W R H O X (b) Plaintext: 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 CIPHER: C A K W U B M X L D N Y P F O Z E G Q H S I T R J V (c) Plaintext: 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 CIPHER: A I Q Y E M U G O W C K S D L T F N V H P X B J R Z |
For the encipherment of substitution cryptograms, the plaintext is first written out in full with enough space between its lines to allow for the later insertion of cryptogram-letters. The correct substitute for each letter is then written below it, after which, these substitutes are nearly always marked off into five-letter groups, and the groups are taken off on another sheet to form the finished cryptogram. It is sometimes recommended that plaintext and cipher letters be written in two different
| Figure 61 "Running Down the Alphabet" Cryptogram: Y B P R O B Q L... Z C Q S P C R M... A D R T Q D S N... Plaintext: B E S U R E T O... |