2.5 Sherlock Holmes

Cryptography has appeared in many places in literature, for example, in the works of Edgar Allen Poe (The Gold Bug), William Thackeray (The History of Henry Esmond), Jules Verne (Voyage to the Center of the Earth), and Agatha Christie (The Four Suspects).

Here we give a summary of an enjoyable tale by Arthur Conan Doyle, in which Sherlock Holmes displays his usual cleverness, this time by breaking a cipher system. We cannot do the story justice here, so we urge the reader to read The Adventure of the Dancing Men in its entirety. The following is a cryptic, and cryptographic, summary of the plot.

Mr. Hilton Cubitt, who has recently married the former Elsie Patrick, mails Sherlock Holmes a letter. In it is a piece of paper with dancing stick figures that he found in his garden at Riding Thorpe Manor:

An illustration shows stick diagram of 15 stick figures in various positions.

Two weeks later, Cubitt finds another series of figures written in chalk on his toolhouse door:

An illustration shows stick diagram of 9 figures in various positions.

Two mornings later another sequence appears:

An illustration shows stick diagram of 9 stick figures in various positions.

Three days later, another message appears:

An illustration shows stick diagram of 5 stick figures in various positions.

Cubitt gives copies of all of these to Holmes, who spends the next two days making many calculations. Suddenly, Holmes jumps from his chair, clearly having made a breakthrough. He quickly sends a long telegram to someone and then waits, telling Watson that they will probably be going to visit Cubitt the next day. But two days pass with no reply to the telegram, and then a letter arrives from Cubitt with yet another message:

An illustration shows a stick diagram of 24 stick figures in 2 rows, each row including 12 stick figures in various positions.

Holmes studies it and says they need to travel to Riding Thorpe Manor as soon as possible. A short time later, a reply to Holmes’s telegram arrives, and Holmes indicates that the matter has become even more urgent. When Holmes and Watson arrive at Cubitt’s house the next day, they find the police already there. Cubitt has been shot dead. His wife, Elsie, has also been shot and is in critical condition (although she survives). Holmes asks several questions and then has someone deliver a note to a Mr. Abe Slaney at nearby Elrige’s Farm. Holmes then explains to Watson and the police how he decrypted the messages. First, he guessed that the flags on some of the figures indicated the ends of words. He then noticed that the most common figure was

An illustration shows a stick diagram of 1 stick figure.

so it was likely E. This gave the fourth message as –E–E–. The possibilities LEVER, NEVER, SEVER came to mind, but since the message was probably a one word reply to a previous message, Holmes guessed it was NEVER. Next, Holmes observed that

An illustration shows a stick diagram of 5 stick figures in various positions.

had the form E– – –E, which could be ELSIE. The third message was therefore – – – E   ELSIE. Holmes tried several combinations, finally settling on COME ELSIE as the only viable possibility. The first message therefore was – M   –ERE   – – E   SL– NE–. Holmes guessed that the first letter was A and the third letter as H, which gave the message as AM HERE A–E SLANE–. It was reasonable to complete this to AM HERE ABE SLANEY. The second message then was A–   ELRI–ES. Of course, Holmes correctly guessed that this must be stating where Slaney was staying. The only letters that seemed reasonable completed the phrase to AT ELRIGES. It was after decrypting these two messages that Holmes sent a telegram to a friend at the New York Police Bureau, who sent back the reply that Abe Slaney was “the most dangerous crook in Chicago.” When the final message arrived, Holmes decrypted it to ELSIE –RE–ARE TO MEET THY GO–. Since he recognized the missing letters as P, P, D,  respectively, Holmes became very concerned and that’s why he decided to make the trip to Riding Thorpe Manor.

When Holmes finishes this explanation, the police urge that they go to Elrige’s and arrest Slaney immediately. However, Holmes suggests that is unnecessary and that Slaney will arrive shortly. Sure enough, Slaney soon appears and is handcuffed by the police. While waiting to be taken away, he confesses to the shooting (it was somewhat in self-defense, he claims) and says that the writing was invented by Elsie Patrick’s father for use by his gang, the Joint, in Chicago. Slaney was engaged to be married to Elsie, but she escaped from the world of gangsters and fled to London. Slaney finally traced her location and sent the secret messages. But why did Slaney walk into the trap that Holmes set? Holmes shows the message he wrote:

An illustration shows a stick diagram of 14 stick figures in various positions.

From the letters already deduced, we see that this says COME HERE AT ONCE. Slaney was sure this message must have been from Elsie since he was certain no one outside of the Joint could write such messages. Therefore, he made the visit that led to his capture.

Comments

What Holmes did was solve a simple substitution cipher, though he did this with very little data. As with most such ciphers, both frequency analysis and a knowledge of the language are very useful. A little luck is nice, too, both in the form of lucky guesses and in the distribution of letters. Note how overwhelmingly E was the most common letter. In fact, it appeared 11 times among the 38 characters in the first four messages. This gave Holmes a good start. If Elsie had been Carol and Abe Slaney had been John Smith, the decryption would probably have been more difficult.

Authentication is an important issue in cryptography. If Eve breaks Alice’s cryptosystem, then Eve can often masquerade as Alice in communications with Bob. Safeguards against this are important. The judges gave Abe Slaney many years to think about this issue.

The alert reader might have noticed that we cheated a little when decrypting the messages. The same symbol represents the V in NEVER and the Ps in PREPARE. This is presumably due to a misprint and has occurred in every printed version of the work, starting with the story’s first publication back in 1903. In the original text, the R in NEVER is written as the B in ABE, but this is corrected in later editions (however, in some later editions, the first C in the message Holmes wrote is given an extra arm and therefore looks like the M). If these mistakes had been in the text that Holmes was working with, he would have had a very difficult time decrypting and would have rightly concluded that the Joint needed to use error correction techniques in their transmissions. In fact, some type of error correction should be used in conjunction with almost every cryptographic protocol.

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