Slater's Telegraphic Code and Secrecy

Slater's Telegraphic Code was compiled not for brevity, the usual reason for most public codes, but rather for secrecy.

First published prior to February 1st, 1870 when the telegraph system throughout the United Kingdom came under control of the government, Slater’s went through nine editions without variation. The ninth edition was published in 1938 and the code is known to have been used well into the 1950s.

Slater's Code consists of a vocabulary of 25,000 words arranged 100 words to a page in two columns. The first 24,000 words comprise a dictionary in alphabetical order. The final 1,000 expressed proper names, geographic names and even names of deities and heroes (presumably because ships were often named after mythological characters). Each word was assigned a five-digit number from 00001 through 25000. It was by the manipulation of these five digit numbers followed by the replacement of the original words with the words corresponding to the resulting five digit numbers that Slater's sought to ensure secrecy in the resulting communication.

Figure 1 – A page from Slater’s Code

How secure was Slater's Code? Without actual examples of messages employing Slater's Code the answer to this question must inevitably involve speculation as to how innovative the correspondents were with the manipulation of the code numbers.

Slater's provides nine examples of how one might manipulate the numbers. Each example is based on the illustrative sentence:

This paper will examine these examples in order to show the cryptographic weaknesses inherent in each and will also attempt to show how the structure of the actual code book lends itself to additional weaknesses arising from a less than rigorous application of the methods provided in the examples.

Example I illustrates the addition of a key number to encode the message.

Figure 2 – Example of an additive key

The essential weakness of this example is that the normal word frequency is completely unaffected by the arithmetic operation. The word "the" appears three times in the example sentence and its corresponding encode of "bounteous" also appears three times. Solving this type of encoding amounts to little more than acquiring a message of reasonable length and knowledge of the frequencies of common words. Creating two worksheets facilitates the solution.

The first contains the actual message with the corresponding code numbers for the code words written beneath each word:

The second worksheet contains the words most frequently found in English text with each word's number underneath. I have chosen the six most common words found in 1000 words of English text based on the studies of Merle E. Ohaver, an expert on the solution of cryptograms:

Based on the recurrence of the word bounteous, the first step in the solution would be to look up its number (02868) in Slater's. Write the number beneath each number on the second worksheet:

Next subtract the number (adding 25000 when necessary):

The resulting numbers are the most likely candidates for the key number used by the correspondents.

The final step in the solution consists of adding each candidate key in turn to the numbers representing the other code words in the message and seeing if any number results in sensible text. As the worksheet suggests the most likely candidates in order, we would proceed in that order, adding the number to see if it provided a solution and continuing on through the candidates until a solution presented itself or we exhaust the possibilities.

Thus, our first attempt at a solution is to add 19445 (adjusting the result by subtracting 25000 when the result exceeds 25000) and looking up the corresponding word in Slater's:

Adding 19445 thus presents us with an intelligible message.

Having derived the key of 19445 we are now in a position to read additional messages exchanged between the correspondents as readily as they did.

A key of 19445 works when the original key was 5555 because of the modular nature of Slater's. Note that 5555 plus 19445 give a sum of 25000. In other words, the addition of 5555 to the original code number followed by the addition of 19445 brings the resulting number one full cycle through the set of code numbers and back to the original number.

If none of the candidate keys provides satisfactory results then the exercise could be repeated by selecting other code words from the original message and attempting to match them up with THE, AND, OF, TO, A or IN. According to Ohaver, these six words make up fully 20% of the words found in each 1000 words in English text. If none of these words leads to a solution the exercise can be expanded to Ohaver's complete list of 50 words that he determined comprise nearly 50% of the words in 1000 words of English text.

One shortcoming of this method is if the correspondents couched their communications in something other than "normal" English text. This is certainly a possibility given that "telegraphic" text tended to eliminate many common words for economy's sake.

The method can be extended to a specialized vocabulary based on the probable text of the message. For example, if it is known that the message is between a retailer and his purchasing agent, then it is highly probable that words relating to the particular market, buying, selling, shipping, commissions, drafts and other financial matters will be included in the text.

Example II involves subtracting a key number to encode the message and is therefore cryptographically identical to Example I.

The same weaknesses found in Example I are present in Example II. The method of solution outlined in Example I is therefore applicable to Example II.

Example III involves the transposition of the third, fourth and fifth digits of each code number.

Figure 3 – Example of a transposition

The first two digits cannot participate in the transposition scheme since the first is limited to values 0 through 2 and the second is limited to values 0 through 5 when the first digit is 2. Only digit positions that encompass the entire range of values (i.e. 0 through 9) can be transposed to form a valid code number.

Again, the recurrence of words provides the cryptanalyst with a vital entry into the structure of the code. In this case, the cryptanalyst need only compare the final three digits of the code number, represented in ascending order of its digits against a list of the code numbers of frequent or probable words arranged in a similar manner:

As "talking" appears three times in the message and its last three digits in ascending order are 133, we readily find a match with "the". Determining the precise order of transposition may require multiple trials as the repeated 3 in the code number for "the" may be transposed in multiple ways to obtain the code number for "talking".

Obviously, when a simple transposition is suspected, the quickest method is to search for probable words whose code number does not contain repeats in the final three digits. The words "in" and "of" in our probable word list are the best suited for this purpose as they contain no repeated digits.

At most, only five distinct permutations of the final three digits need to be examined. Since the 345 permutation is in fact not a transposition it has already been dealt with. Thus, only the following transpositions need to be analyzed:

Example IV combines addition of a key number followed by a transposition.

Figure 4 – Example of transposition followed by additive key

Again, the recurrence of words provides the cryptanalyst with an entry into the structure of the code.

The transposition of digits however, introduces difficulties in the solution. The number deduced for the additive based on the method outlined for solving Example I is 19625 for the word "the". When solution is attempted by adding 19625 we get the following:

Once the probable word technique is exhausted we resort to the comparison of the ordered digits of "blundered" to our list of probable words in digit order. When this also fails to yield a solution we begin to suspect a combination of an additive and transposition.

The preponderance of the code word "blundered" indicates that an additive is involved and that the additive is constant but that the number has been transposed either prior to or following application of the additive.

Solving an additive/transposition method requires shrewd guesses as to the probable words within the message followed by exhaustive testing of the five possible transpositions of the final three digits in the code number.

If the original digit order of the code word's number is 12345 then one could proceed to apply each of the five combinations in turn:

Note that although the five transpositions reduce to three additive cases and therefore only three additives to test against the entire message, there are still five distinct transpositions that must be tested against the entire message.

As case 3 is the correct transposition we can expect to solve the message when we test for this case.

Example V is essentially the same as Example IV. Instead of adding a key number before transposing, Slater subtracts the key number and then transposes. The method of solution for Example V is identical to the method described for Example IV.

Example VI shows the splitting of the stream of code number digits into groups of four.

Figure 5 – Example of grouping code number digits by four

This type of manipulation is easily detected by the fact that the resulting four digit code numbers all translate to words ranging from "A" (00001) to "Glen" (09999).

Another clue to the nature of the manipulation can be found by looking up the code number of the final word. This number will end with at least as many zero digits as the modulo five value of the count of code words in the message multiplied by four.

In this example the count of code words in the message is twelve. Twelve multiplied by four gives forty-eight and a value of three modulo five:

12 * 4 = 48 and 48 modulo 5 = 3

The code number for the final word "few" is 09000 which has three trailing zeros.

The solution to this example is essentially one of recognizing the splitting of the code numbers into groups of four digits. Once recognized it is a simple matter of grouping the digits from the code words back into their original groups of five digits.

Note that this is the first example that begins to suppress the normal word frequency of messages. However, any plain text words repeated at intervals of zero modulo four or at intervals of one modulo four produce a repeated code word.

Because each four plain text words produce five code words the repeated code words will be found at intervals of zero modulo five or one modulo five.

This characteristic is illustrated in the example with the second and third occurrences of "the" encoding to "beneath". The second "the" is the fourth word in the plain text and appears at zero modulo four in the original message while the third "the" is the eighth word in the plain text and also appears at zero modulo four in the original message. The code word "beneath" appears as the fifth and the tenth words in the coded message and these positions are both zero modulo five.

Another flaw is the repetition of any phrase of two or more plain text words where the first words of the repeated plain text share the same modulo four value. At least one repeated code word will result from this type of coincidence and two repeated code words will result when the first plain text word is zero modulo four.

Example VII combines the splitting technique of the previous example with a subsequent transposition.

Figure 6 – Code digits grouped in fours and then transposed

This example is characterized by the code words in the range of "A" through "glen" implying four digit code words; by the recurrence of the code word "bays" at zero modulo five; and by the code number of 9000 for the word "few" at the end of the message with its three trailing zeros matching the code word count times four modulo five calculation. Solution of this message and its technique is a combination of the techniques illustrated in Examples III and VI.

Example VIII combines the splitting technique followed by a transposition and finally a variable additive.

Figure 7 – Grouping code digits by fours, transposing and then adding a variable key

This is certainly the most difficult example provided by Slater. The variable additive blunts the common words frequency attack. However it is not completely obscured because the additive varies in a predictable way.

Notice that the second and third encodes of the final four digits of the code number for "the" produce code words (beaconage and beaker) whose code numbers (2138 and 2143) differ by five. This coupled with the fact that beaker appears five words after beaconage serves as an important clue to the variability of the additive.

Examination of the final word "fiddler" and its code number of 9012 in conjunction with a count of twelve code words in the message lends further proof to the additive being simply the number of the code word in the message.

Examination of the message indicates that the code numbers were split into four digits as all code words are in the "A" through "glen" range.

Once the alteration from five to four digits and the nature of the additive have been determined this example reduces by steps to a trial and error for the order of transposition.

Example IX simply transposes the original message text before applying the techniques used in Example VIII.

Figure 8 – Transposing original message followed by techniques employed in Example VIII

Why Slater would provide this as the ultimate example is mystifying since transposing clauses in the sentence provides no additional security. The transposition does eliminate the repetition of "the" at modulo four but this is deceptive, as it is just as likely to create a repetition as it is to eliminate a repetition.

The repeat of "the" at critical modulo four positions in the original is lost due to the transposition of the message but the "A" through "glen" crib is still evident. As is the nature of the additive due to the 012 ending value of the final code word of "cupping."

Conclusions

All of the techniques illustrated by Slater readily succumb to methodical cryptanalysis.

In addition, the techniques combining additives and transpositions appear complex enough so as to discourage their use in favor of the much simpler additive technique. Indeed, while the author is in possession of several editions of Slater's containing notations of constant additive key values he is unaware of even a single example where any other method mentioned by Slater was ever employed.

Figure 9 – Examples of additive keys from code books

With the additive technique correspondents may have introduced simplifications to allow for rapid encoding and decoding and further eroded the security achieved by Slater's.

A large additive requires constant referral to Slater's. It is not unlikely that some correspondents would choose to simply pick the word across from the plain text word (Slater's arranged the vocabulary in two columns of fifty words each per page), in effect adding or subtracting fifty from the original word's code number. Or the correspondents might choose a smaller additive that would not require turning forward or backward more than a single page during encoding and decoding. Another possibility is to employ an additive of 10, 100, 1000 or 10,000 or a multiple of any in order to simplify the additive process.

The lack of a relatively easy means of encoding words that were not in Slater's is a serious flaw that is overlooked in the examples but rather quickly comes to light when the code is employed. When a message contains a word not in Slater's the encoder has limited choices, either to leave the word in clear or to encode the word one letter at a time.

If the word is suffixed, with the root in Slater's, then another possibility exists, namely to encode the root and affix the suffix to the resulting code word.

I suspect that when confronted with these situations, most opted to leave the word in clear since the bulk of the message was being hidden. However, mixing plain text and code gives the cryptanalyst a readily exploited entry into the code.

Slater's, employed in a manner suggested by the examples, is obviously not secure. How might Slater have improved the security of the code?

A more secure technique might draw on some commonly available sets of figures in order to introduce an irregular variable additive. Slater might have published supplements to the book that would provide correspondents with unique or semi unique additive streams. At the least, Slater might have suggested the method of an irregular variable additive.

Another technique to increase security would be to employ different orders of transposition from one word to the next based again on a key.

Slater might also have improved security by expanding the code to 100,000 word (numbered 00000 through 99999) so that all five digits in the code numbers might be employed in transpositions, thereby expanding the number of possible transpositions from five to one hundred nineteen. Expansion of the vocabulary would also have the additional benefit of reducing the number of words that would have to be encoded letter by letter or left in clear. The resulting code book would quadruple in size but would still have been very manageable at 4" by 6½" by about 2¾" thick.

Slater might also have improved the code by providing a section of the code where the words might be re-assigned in any manner the correspondents desired. This type of re-assignment of code numbers was actually employed by a number of users. The author has in his possession copies of the code in which numbers towards the end of the code are re-assigned to proper names frequently employed by the correspondents. The author assumes that the original word in Slater's was still used in actual messages with the re-assigned word taking its place (depending on context) when the message was written or decoded.

Figure 10 – Re-assignment of words

Slater has very little to say about altering the original text to achieve greater security. He might have advised correspondents to drop common words such as "the" from the message in order to increase security as fewer common words in the encode would be available for analysis.

Paraphrasing the original message would possibly provide additional security if the vocabulary of the message were somewhat specialized. Paraphrasing has the advantage of concealing the more obvious known word or known phrase attacks.

Ultimately all three techniques, addition of a constant or regularly varying additive, transposition and "splitting" are seriously flawed in terms of security. Employed alone they are easy to see through and analyze. Employed in conjunction they certainly would appear to make the message insolvable to any not possessing the key but it would appear that a determined effort would still provide for a solution.

Example VIII with its use of a variable additive comes closest to some real security but falls short because the additive varies in a simple and predictable manner.

In summation, Slater's code gives the impression of security and appears to have been used regularly for the better part of eight decades. The majority of correspondents opted for the additive encoding method and chose keys for convenience rather than security making their communications nearly transparent to anyone who might surreptitiously gain access to the messages.