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Section 2.3 Falconer's Approach

In 1685 John Falconer, who we met briefly in Section 1.1, wrote the second ever published text in English on the subject of cryptology; it has the rather lengthy title Cryptomenysis patefacta; or, the art of secret information disclosed without a key. containing plain and demonstrative rule, for decyphering. Beyond this work little is known about him for certain. A descendant of his writing in the nineteenth century claimed that John was the personal cipher keeper for King James II and followed the king into exile in France where he died. In slim support of this the book is dedicated to King James II and addressed to the king's secretary of state. However, no readily available documented evidence exists to independently corroborate his descendant's claims, and in fact there are some tax records for John and his wife, Mary Dalmahoy, in Edinburgh Scotland, from 1695, over six years after James fled to France. [13]

In his text John Falconer presents a wide variety of ciphers and, for most of them suggestions, for how we might attack them. In this section we will focus on his directions for how to break, or attempt to break, what we now call monoalphabetic substitution ciphers.

Subsection 2.3.1 Step 1:

First, Distinguish the Vowels from the Consonants.
  1. And first, the vowels generally discover themselves by their frequency; for because they are but few in number, and no word made up without some of them, they must frequently be used in any writing.
  2. Where you find any character or letter standing by it self, it must be a vowel.
  3. If you find any character doubled in the beginning of a word, in any language it is a vowel, as Aaron, Eel, Jilt, Oogala, Vulture, etc., except for some English proper names, as Llandaff or Lloyd.
  4. In monosyllables of two letters you may distinguish it from the consonant joined with it by its frequency.
  5. In a word of three letters beginning and ending in the same letter the vowel is probably included.
  6. When you find a character doubled in the middle of a word of four letters, `tis probably the vowel e or o.
  7. In Polysyllables, where a character is double in the middle of the word, it is for the most part a consonant; and if so, the precedent letter is always a vowel, and very often the following.[4, pp. 8-9]

Comprehension Check:

  • Do some of these sound familiar from what you read in Section 2.1?
  • Which of these are new? Do any of those seem strange to you?
  • In what ways does Falconer say that one, two, and three letter words can help us?
  • According to Falconer when might we expect a double letter to be a vowel and when might it be a consonant?
  • Try to find out why Falconer says “Jilt” and “Vulture” begin with a double vowel.

For the following Checkpoints find a large sample of normal English text (you can use the one you found for the chekpoints in Section 2.1, but something bigger may be better). You will also want to use the n-gram counting and word counting tools below.

In your text, what letters are most common? How many vowels are there? How many consonants are there?

What are the one, two, and three letter words in the text you found to analyze? Do they follow the pattern that Falconer described? Are any of them more common than others?

Look at your text for words with double letters, do they behave the way that Falconer says they should?

N-Gram Counter:

Figure 2.3.4. N-Gram Analysis Tool

String Analyzer:

Figure 2.3.5. String Analyzer Tool

Word Counter:

Figure 2.3.6. Word Counter Tool

Subsection 2.3.2 Step 2:

Secondly, Distinguish the Vowels from Themselves..
  1. Compare their frequency, and e, as we observed before, is generally the most used in the English tongue, next o, then a and i; but u and y are not so frequently used as some of the consonants.
  2. It is remarkable that amongst the vowels, e and o are often doubled, the rest seldom or never.
  3. e is very often a terminal letter, and y terminates words, but they are distinguishable, because there is no proportion to their frequency: o is not often in the end of words, except in monosyllables.
  4. e is the only vowel that can be doubled in the end of an English word, except o in too, etc.
  5. You may consider which of the vowels, in any language, can stand alone, as a, i, and sometimes o in English, a, e, o, in Latin or i the imperative of eo.[4, pp. 9-10]

Comprehension Check:

  • Do you agree with his comments about e, o and the other vowels? Why or why not?
  • Can you think of examples of or exceptions to his third and fourth comments above?
  • Can you think of or find an example of o standing alone in English?

Test out Falconer's observations about vowels using the same sample of text that you analyzed in exercise Checkpoint 2.3.1. Do his statements hold true or has the language changed since 1685?

Subsection 2.3.3 Step 3:

Distinguish the Consonants Amongst Themselves..
  1. As before observe their frequency. Those of most use in English are d, h, n, r, s, t, and next to those may be reckoned c, f, g, l, m, w, in third rank may be placed b, k, p, and lastly q, x, z...
  2. You may consider which consonants may be doubled in the middle or end of words.
  3. What are terminal letters, etc.
  4. The number and nature of consonants and vowels that fall together, or do usually fall together.[4, p. 10]

What consonnts does Falconer say are most common? In the text you have been analyzing which are most common?

Consider statement two above and look at the same text you used previously, which consonants are commonly doubled in the middle and at the end of words?

In your sample of text which consonants do you commonly see at the end of words? Are there some that, when they do show up, are almost always at the end of a word? Are there any that are almost never at the end of a word?

Falconer's first three pieces of advice are similar to what we have looked at before; his fourth comment is something a little new. Using the same text which you analyzed before set the n-gram counter to count two letter combinations in your text (\(N=2\)). Once you have the count take note of which combinations of letters appear most often and for each vowel which two or three consonants it is most often paired with.

Subsection 2.3.4 Step 4:

Additional Observations.
  1. A word of three letters, beginning and ending with the same, may be supposed did
  2. A word consisting of four characters, with the same letter in the beginning and end, is probably that or hath
  3. A word consisting of five letters, when the second and last are the same, is commonly which, though it may be otherways, as in known, serve, etc. And you may judge of the truth of such suppositions by the frequency of the letters in the word supposed.

Next you may compare words one with another, as on and no, each being the other reversed; so of and for, the last being the first reversed with the addition of a letter; for and from will discover each other, etc.

You may also likewise observe some of the usual propositions and terminations of words, such as com, con, ing, ed, etc. Note that t and h are often joined in the beginning and end of English words, and sometimes in the middle.[4, pp. 11-12]

Comprehension Check:

  • Can you think of more examples of three or four letter words beginning and ending with the same letter?
  • What about five little words in which the second and last letters are the same?
  • How many words like on and no or of and for can you think of?
  • Compared with other suggestions we have looked at, how practical do these seem? Do they seem a little too subtle?

Looking one last time at the text which you have been using identify common prefixes and suffixes (what Falconer called propositions and terminations) within the text. Are you finding any of the examples which he gave?

To see how we can pull these ideas together take a look at Appendix E.