Hack 70. Break Codes with Etaoin Shrdlu

You never know when you will have to decipher a cryptic message, whether it's one intercepted by your man, James Bond, or one scribbled illegibly onto a prescription pad by your doctor. Here are all the statistical tricks you'll need, Agent 003.14159.

You might have noticed that certain keys on your computer keyboard get dirty or wear out more quickly than others. That's because you hit them more often than the others. You might also notice that these letters tend to be in the middle of the keyboard or, more correctly, in small circles near where your hands are when they are centered on a keyboard.

Both the wear and tear on your keys and the placement of them in a standard typewriter (a.k.a. QWERTY, for the first six letters on the top row) pattern are based on their frequency of use in English. Different letters in the alphabet are used with different frequencies in the spelling of words in a language. By applying the known frequency of these letters, along with other statistical tricks, you can quickly decode classified documents, whether they are Leonardo da Vinci's diary, a puzzle in the newspaper, or big, bright letters being turned by Vanna White on TV.

Single Substitution Ciphers

The simplest and oldest type of letter-based code is the single substitution format. In these codes, some message is transformed from the actual letters in the words to other letters in the alphabet. In the simplest form of this type of coding, the same letter substitutes for the same letter throughout the message. For example, a simple cipher might use the substitution pattern shown in Table 6-18, in which the letters on the top row (the plain text) are replaced by the letters on the bottom row (the cipher text).

Table A single substitution cipher
Plain text 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

With a code like the one shown in Table 6-18, the following plain-text passage:

Tom appeared on the sidewalk with a bucket of whitewash and a long-handled brush.

appears in cipher text like this:

Jut nhhpnipb ug jdp wrbpynfs yrjd n axospj uc ydrjp yhwd ngb u fugq-dngbfpb aixwd.

The passage looks like nonsense, but with the key shown in Table 6-18, anyone could easily replace the nonsense letters with the original letters, causing the opening sentence of the second paragraph in Chapter Two of Tom Sawyer to reveal itself.

Using Probability to Decode Substitution Ciphers

Of course, the real task when deciphering ciphers is to do it without access to the code key. Real-life code breakers and winning contestants on Wheel of Fortune use the same tool to solve their problems: they apply the known distribution of letters in English language words.

The advent of computers, computer analysis, and electronic copies of millions of books has made the calculation of exact probabilities for each letter of the alphabet possible, though cryptographers (code makers and breakers) have known the basics for some time. Here are some of these basics:

  • The most common letter, in terms of usage in English, is E.

  • The least commonly used letter is Z.

  • The most common consonant is T.

  • J and X are rarely used, as is Q.

  • When Q is used, it is almost always followed by U.

  • Only A and I are used as one-letter words in English.

With even just these basic probability facts, you could begin to tackle decoding a cipher such as our Mark Twain passage. The most commonly appearing letters in the garbled version are P and N. Because N is used as a single-letter word, it cannot be E (N is most likely A), so a good first guess for P is that it substitutes for E.

With just a little knowledge of letter distribution, we have already identified the substitutes for E and A. We can't be sure we are right, but like any good statistician, we think we are probably right. Table 6-19 shows the likely distribution for each letter of the alphabet.

Table Frequency distribution of letters in English
A8.04 percent
B1.54 percent
C3.06 percent
D3.99 percent
E12.51 percent
F2.30 percent
G1.96 percent
H5.49 percent
I7.26 percent
J0.16 percent
K0.67 percent
L4.14 percent
M2.53 percent
N7.09 percent
O7.60 percent
P2.00 percent
Q0.11 percent
R6.12 percent
S6.54 percent
T9.25 percent
U2.71 percent
V0.99 percent
W1.92 percent
X0.19 percent
Y1.73 percent
Z0.09 percent


The strange phrase "ETAOIN SHRDLU" is a mnemonic device (memory tool) for remembering the most frequently occurring letters. These 12 letters account for over 80 percent of total letter frequency.

You might notice that the order of letters in ETAOIN SHRDLU is not exactly the rank order of popularity shown in Table 6-19. It is close enough, though, and easier to pronounce than if it were exactly correct. Another thing to remember is that any "definitive" list of letter probability depends on the source material for the letter count. You can find many different lists of letter order and frequency, and some differ slightly from others.

For example, one organization that produced a list of statistical distributions of letters in English text relied on a computer analysis and actual count of letter occurrence in seven literary classics, such as Jane Eyre and Wuthering Heights. Two of these seven books were Tarzan novels. I'm guessing that if we were to compare that table of letter distributions with others, we would find that the proportional number of times the letter Z appeared was greater than if other sources were used. For the common letters, thoughsuch as E, T, and Athere is wide agreement on their use as best first guesses for code breaking.

Wheel of Fortune Strategy

On the TV game show Wheel of Fortune, before solving the big puzzle at the end, the producers are nice enough to provide certain letters and show whether they appear in the hangman-type phrase. They provide R, S, T, L, N, and E. These are given, of course, because they are common letters, and are in our top 12: ETAOIN SHRDLU. The player is allowed to choose three more consonants and another vowel. Using our statistical knowledge of letter frequency, a good basic strategy would be to pick A as the vowel and the three most common consonants not yet shown: H, D, and C.

Statistical Analysis of Coded Texts

Here's how you might use these letter stats in real life to decode a secret message or solve a puzzle. This method works best if the coded text is lengthy, but it works surprisingly well even for shorter passages. Calculate the distribution of the coded, substitute letters (the cipher text), and then compare it to the distribution shown in Table 6-19.

Figure 6-8 shows how this process might look graphically. Only the first 10 most common letters are shown, but the analysis would use all the letters. This example pretends that there is a lot of coded text and that the substitute cipher shown in Table 6-18 is being used.

Figure 6-8. English letter frequency (left) and coded letter frequency (right)

Because the most common substitute letters are P, followed by J, a good guess for breaking the code would be to see whether P could really be E and J could really be T. These first guesses can be made all the way down the line for each letter. By starting with the most frequently appearing letters and moving down the list, a code breaker can quickly see whether these first hypotheses are right or wrong and change guesses around until English words start to appear.

Other Common Letter Patterns

Beyond just knowing the frequency of individual letters appearing, good code breakers use probability information about other patterns of letters:

  • Words are most likely to start with T, O, A, W, or B.

  • Most words end with an E, T, D, or S.

  • If two letters are doubled in a word, they are most likely to be SS, EE, TT, FF, or LL.

  • Frequently appearing two-letter words include of, to, in, it, and is.

  • By far, the most common three-letter words are the and and. Other common three-letter words include for, are, and but.

  • Letters that tend to come in pairs include TH, HE, AN, IN, and ER.

  • The most frequently used words are the, of, and, to, in, a, is, that, be, and it.

  • Perhaps indicating what people tend to write about, the top 100 most-used words in written texts include dollars, great, general, and public. Debts just barely failed to make the top 100, but it is surprisingly common.

See Also

  • A good explanation of single substitution ciphers can be found under the entry for frequency analysis at http://en.wikipedia.org/wiki/Frequency_analysis.

  • Some of the statistics reported in this hack were found at http://www.data-compression.com and http://www.scottbryce.com. Good information and advice for solving cryptograms and other codes using statistics can be found at those sites.

Statistics Hacks
Statistics Hacks: Tips & Tools for Measuring the World and Beating the Odds
ISBN: 0596101643
EAN: 2147483647
Year: 2004
Pages: 114
Authors: Bruce Frey

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