A simple substitution cipher is one in which each letter of the original text is replaced by a different letter. For example, if you wanted to encipher:

You might replace A with Z, B with Y, C with X and so on until you have a corresponding cipher letter for each plain text letter. The enciphered phrase would then appear as:

Notice that simple enciphered messages, of the sort you find in newspaper puzzle sections and commonly referred to as cryptograms or cryptoquotes, are given in uppercase with spaces between words and with punctuation preserved. You will find that these characteristics, combined with the simple substitution enciphering method make all but the most arduously selected and constructed cryptograms relatively easy to solve.

There are as many ways to create cipher alphabets as there are cryptogram authors. The alphabet employed in our example would appear as:

The P: and C: are conventional in cryptology and refer to Plain (or unenciphered) text and Cipher text. Note that this cipher alphabet is really only useful in enciphering messages. If you were communicating with another person via this cipher alphabet you would also want a deciphering version of the alphabet:

This particular cipher alphabet is known as the reversed alphabet. There is one other well known cipher alphabet named the Caesar cipher after its purported inventor, Julius Caesar:

In the original Caesar cipher, each plain text letter is replaced with the letter that is three further on in the alphabet. If you think of the letters as numbers then this type of substitution can be represented as a mathematical equation involving modular arithmetic:

C = ( P + X ) modulo 26

C represents the cipher text letter, P represents the plain text letter and X represents the number of letter positions to advance. Modulo arithmetic in simple terms means to take the remainder of the number when divided by the modulo number. In our example 1 would be assigned to plain text A, 2 to plain text B and so on. X would be replaced by 3. To encipher the letter A using the equation we would plug 1 in place of P, take its value modulo 26 (or 1), add 3 to it to get 4 and then replace 4 by its corresponding letter or D.

The problem with these cipher alphabets is that they are very well known and easy to spot for experienced puzzlers. Common words such as THE appear as GSV and WKH in the reversed and Caesar cipher alphabets and soon become nearly as recognizable as the unenciphered word itself.

This leads to the construction of unique cipher alphabets for each puzzle that is created or for each pair of correspondents when the cipher alphabet is meant to ensure secrecy. Perhaps the simplest way to create a cipher alphabet is to employ a worksheet that provides the ciphering alphabet consisting of the plain text alphabet from A to Z with an unfilled cipher text alphabet following it. The deciphering alphabet is also given and consists of the cipher text alphabet from A to Z with an unfilled plain text alphabet following it. As each plain text letter is assigned a cipher text letter in the ciphering alphabet, the plain text letter is assigned to the same cipher text letter in the deciphering alphabet.

The easiest way to create a cipher alphabet is to randomly assign cipher text to plain text letters. Here is one such example of this technique:

This technique works very well when constructing cipher alphabets for cryptoquotes and other puzzles but for use in secret communications it is cumbersome because it requires that both parties have the cipher alphabet written down. A cipher alphabet constructed in this manner is simply too difficult to memorize.

Far better a method is for the two parties to agree on an easy to remember key word or phrase and use that to construct the cipher alphabet whenever it is needed. The best key words and phrases involve letter sequences in which no letter is repeated. The longer the word or phrase the better. By way of example, I have selected the phrase "Albacore Tuna". These words give me ten distinct letters from the alphabet once the additional As are struck out. The key phrase remains "Albacore Tuna" but we will only use "ALBCORETUN" as our working key.

Once a word or phrase is decided upon, the correspondents must also agree on how to employ the key during construction of the cipher alphabet. The method I have chosen is to place each letter in the working key in the odd letter positions until I have run out of letters.

This immediately leads to a problem with our example since A would be placed as the cipher text letter for plain text A. I decide therefore, to move any letter that clashes in this fashion to the next position in the alphabet. The initial cipher alphabet will appear as:

To complete the cipher alphabets I work from right to left of the deciphering (second alphabet) and assign each cipher letter that is not yet in use to the first cipher alphabet working left to right. In our example cipher text Z is assigned to plain text A, cipher text Y to plain text D:

And so on. Notice that when a clash occurs (cipher text P goes to plain text P) the problem is handled by skipping to the next unassigned plain text letter (cipher text P goes to plain text R):

Until the alphabets are completed:

Enciphering or deciphering a message is relatively simple provided you have the enciphering and deciphering alphabets available. Let's encipher and then decipher a short message as practice. The message is:

Start by printing out the message with adequate space between the letters, more space between the words and if the message continues to additional lines with plenty of blank space between the lines as well:

Next, consult the enciphering alphabet and write each cipher text letter below the plain text letter in the message. I usually take the first letter of the message, look up its cipher text equivalent and then write the cipher text letter beneath all occurrences of the plain text letter. This makes enciphering the messages go quite a bit faster. So enciphering this message employing the "Albacore Tuna" key would proceed as follows:

The enciphered message would be sent to your correspondent as:

Your correspondent would reverse the process using the deciphering alphabet:

In order to read the message:

Solving a message in the absence of a key

Solving enciphered messages requires knowledge of the characteristics of the language. The most basic characteristic of a language is the relative frequency of each letter in the alphabet of that language and the positioning of the letters in relationship to each other as words are formed. In addition, the types of messages that appear as cryptograms or cryptoquotes supply additional context in the form of word breaks and punctuation. Because this is a very basic tutorial I am going to supply only the most basic information about letter usage in English. In addition I will supply information about some of the more common digraphs (letter pairs) and the most common short words. This information should give you enough knowledge to solve most cryptoquotes that you will encounter.

Letter frequency is the most important feature of the language that we will use. Letter frequencies have been derived for most languages and we will rely on a summary of frequencies that I have taken from a number of sources. The letters are divided into three groups, high, moderate and low frequency as follows with a rough count of the number of times you can expect to see the letter in any 100 letters taken from normal written English:

Letter frequencies per 100 letters

Digraphs, or letter pairs, are much more complex to analyze so I will only mention the two most common digraphs as they are clearly delineated in frequency from all other digraphs. In a sample of 1,000 letters the "th" digraph will normally appear about 4% of the time and the "he" digraph about 3% of the time. These digraphs appear more frequently than others because of their occurrence in many common words such as "the", "then", "that" and "when". Note that both digraphs appear in "the" and "then".

The following list contains the fifty most common short words as compiled by Merle E. Ohaver in his booklet "Cryptogram Solving". Ohaver maintained that these words "make up nearly one-half of the words in ordinary reading matter". Ohaver was a renowned cryptogram solver and his abilities as a cryptanalyst was even acknowledged by no less an authority than William Friedman, who was foremost among the many fine cryptanalysts employed by the United States during World War II. The counts beside each word are the number of occurrences of the word in 1000 words of normal English text.

Word frequencies per 1000 words

An Example

Suppose you are confronted with the following enciphered message:

Start by copying over the message leaving plenty of room for doodling with pencil.

You may wish to create a form that has the standard alphabet at the top and then make a number of copies of the form with the enciphered message added. As you assign cipher text letters to plain text letters you can use the standard alphabet as a guide:

The first step in solving a cryptogram is to make a frequency count of the letters so that we can attempt some preliminary cipher text to plain text matches.

Next, we arrange the letters by frequency:

Letter frequencies in example cryptogram

Given our frequency table of high frequency letters it is a fair first assumption that the cipher text letters R, A, N, Q, F, G, O, U, H, I, L, P, and T contain most if not all of the nine most frequently appearing plain text letters. A fair second assumption would be that the remaining cipher text letters J, S, W, X and Y encompass most if not all of the moderate and low frequency plain text letters.

Perhaps we can nail the solution quickly by seeing if the four most frequent cipher text letters, R, A, N and Q correspond to the four most frequent plain text letters, E, T, A and O.

Obviously we are off on the wrong foot. AFN might be TEA but then cipher text R could not represent plain text E. What really shoots down this tentative solution however is the two letter word enciphered as AR deciphering to TE.

One interesting possibility presents itself at this point based on the failure of AR to translate as TE. And that is that this two letter word appears twice and is separated by a four letter word. Let's consult our list of frequent two letter words and see if one of these words does not fit the pattern of AR HRON AR. The most frequent two letter words are OF, TO, IN and IT. Since T is the second most common letter, let's try TO in place of AR and then IT in place of AR:

This seems so promising that I will ignore AR to IT for the moment. But not before writing a note to resume with the AR to IT possibility if the AR to TO possibility doesn't play out.

In the course of exploring the AR to TO matchup I notice that the message also has a three letter word AFN and a five letter word that begins with AFN. This letter combination is in all probability THE as THE is by far the most frequent three letter word. This supposition gives us FN to HE:

Nothing seems farfetched about the letter assignments so far. Of the high frequency letters E, T, A, O, N, I, R, S and H we have tentatively identified E, T, O and H. Let's try to use the remaining two letter words to identify more letters. We still have QW with no matches and RL matched to O?. Referring to the two letter frequent word list we have three possible solutions for RL to O?, namely RL to OF, RL to ON and RL to OR. Note that cipher L appears in only one other place in the message as the initial letter in a three letter word whose middle letter has been identified as O. So the matchup of L with F will produce FO? and OF; the matchup of L with N will produce NO? and ON; and the matchup of L with R will produce RO? and OR. FO? might be FOR, NO? might be NOW and RO? might be ROW. After noting the three possibilities let's pursue each in turn.

Starting with RL to OF we see that LRU becomes FO?. This suggests U matches R. Cipher U is a high frequency letter and plain text R is a high frequency letter not yet idetified. We update the worksheet with L to F and U to R:

T H E   R     O     T R

U to R suggests that the Q in AFNQU is I and AFNQU matches to THEIR. Let's add the Q to I matchup:

At some point in any solution, things start to click. In this particular case you may have already reached that point. As you analyze the plain text that your assumptions and trial matchups provide words begin to appear and also plausible phrases. This is the EUREKA point when you realize that the message is a well know quote or phrase and you read it aloud without bothering to proceed with a rigorous solution. This is fine for most cryptograms but caution should be used when deciphering a message for which you do not possess the key and for certain cryptograms which have been carefully constructed to snare you in careless leap of faith as the message becomes apparent to you.

Let's continue with a rigorous solution. AQON to TI?E suggests a number of possible plaintext letters for cipher text O. An easy way to ensure you have all the possibilities is to list all of the words that can be created by selecting plain text letters not yet assigned:

THE TIDE FOR
THE TILE FOR
THE TIME FOR
THE TINE FOR
THE TIRE FOR

O to M giving THE TIME FOR is the obvious choice:

Continuing this process we match ONG to MEN and HRON to COME:

Continuing this process we match QW to IS and HRYGAUJ to COUNTRY:

Continuing this process we match GRX to NOW and recalling the familiar quotation we complete the solution matching PTT to ALL, SRRI to GOOD and PQI to AID:

Note that we are unable to completely reconstruct the cipher alphabet because the message does not contain all twenty six letters. However, enough letters are recovered to indicate that the cipher alphabet is not based on any obvious keyword or phrase.

Solving a cryptogram is a bit like an impromptu juggling act. A slavish adherence to any particular methodology will often result in a tedious and unnecessarily long solution or even a failure to solve a cryptogram.

My solution to the example is by no means the only solution and in fact, if I were to solve the example again I undoubtedly would have proceeded differently. I might have performed a visual inspection of the cryptogram before attempting any matchups. A visual inspection would probably have caused me to notice the repeated AFN word and I might have started off by assuming the AFN to THE matchup.

An interesting exercise for a post mortem is to compare the high frequency letters in the cryptogram to the standard letter frequency for normal English:

Standard Example

Note that the high frequency letters A and S do not appear among the high frequency letters in the example; that the order of frequency in the example does not match the standard; and that the letter M, a moderate frequency letter has snuck into the high frequency group.

The lesson here is that the shorter the cryptogram (the example contains only 53 letters) the more likely that there will be significant divergences from the standards based on analysis of large volumes of letters and words.

Cryptogram Solving by M. E. Ohaver

Solving Simple Substitution Ciphers by Frances A. Harris

An Invitation to Cryptograms by Eugenia Williams

The following pages provide some cryptoquotes as exercises for you to work on. Each cryptoquote is arranged as though it were already transcribed to a worksheet. Each cryptoquote employs a different cipher alphabet and none use the reversed or Caesar cipher alphabets. Two of the examples employ alphabets constructed through the use of a key word or phrase and two of the examples employ alphabets constructed randomly.

Many cryptoquotes include the author's name and sometimes the source at the end of the quote. I have deliberately left this information out of the cryptograms in order to add a bit more complexity to the solutions.

Most of all...Enjoy!

Exercise # 1 (202 letters, 43 words)

Exercise # 2 (179 letters, 35 words)

Exercise # 3 (63 letters, 16 words)

Exercise # 4 (56 letters, 13 words)