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1.3. FREQUENCY ANALYSIS 17
A bit more concretely, a, e and i form a set of high frequency letters 4 steps
or letters apart. Next, hi and no are high pairs and rst a high triplet. Finally,
uvwxyz is a set of six very low values that directly follows the rst triplet and
occurs directly before a.
To see how these patterns are used let’s look at an example.
Example: Use frequency analysis to decrypt YPYH NBCM MBILN GYMMUAY XIYM
HIN LYGUCH MYWLYN ZIL FIHA.
We first construct a frequency chart by counting the number of times each
letter appears:
ciphertext
\ \ \
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
The most common letters are M and Y, so one of these is probably e. (Of
course, e might instead be N, H or L, but these are less likely.) If M were e,
we’d expect to find the aei-triple of high counts separated at intervals of four
at IMQ. There are several I’s, but no Q’s. Worse, H would be z, and four z’s is
unlikely. On the other hand, if Y were e, the aei-triple would be at UYC. This
message is very short, so a “high”-triple is not all that high, and so UYC might
be reasonable fit for aei.
Where might rst fit The highest consecutive triple is at LMN. This fits
pretty well, since the low septet uvwxyz would fit at OPQRST. Finally, just before
LMN is a high pair HI, so we might guess that HI is no.
Putting this plaintext guess above the frequency chart will help us see if
everything fits:
plaintext
ciphertext
g h i j k l m n o p q r s t u v w x y z a b c d e f
\ \ \
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
The fit is good – the peaks at e, no, and rst, and the long valley at uvwxyz give
us confidence we’ve done this correctly. Finally, the keyletter is the ciphertext
letter that a becomes, so the key is U. Now we simply decipher to find that the
message is Even this short message does not remain secret for long.
⋄ ⋄ ⋄ ⋄ ⋄ ⋄ ⋄ ⋄ ⋄ ⋄ ⋄ ⋄
A message’s frequency chart will seldom have all of the patterns, but it
should have good evidence of several. When trying to fit the patterns generally
we start with the tallest peaks of e and t, and the long low valley of uvwxyz.
Then we look for the aei and rst triples. Finally, we see if the no pair is present.
If there are several “probably”’s when trying to fit these patterns, then the key
likely is the ciphertext letter posing as a. Try this possible key by deciphering
ten or so letters from the ciphertext. If a message seems to be appearing, we’ve