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1.3. FREQUENCY ANALYSIS 15
PX PBEE FXXM TM FBWGBZAM
QY QCFF GYYN UN GCXHCABN
RZ RDGG HZZO VO HDYIDBCO
SA SEHH IAAP WP IEZJECDP
TB TFII JBBQ XQ JFAKFDEQ
UC UGJJ KCCR YR KGBLGEFR
VD VHKK LDDS ZS LHCMHFGS
WE WILL MEET AT MIDNIGHT
XF XJMM NFFU BU NJEOJHIU
YG YKNN OGGV CV OKFPKIJV
Figure 1.2: Decrypting a Caesar cipher by running down the alphabet
etc. There is no mixing of the alphabet – every letter moves the exact same
distance. This is why Caesar ciphers are not very secure ones.
Examples: Decrypt the following ciphertexts by running down the alphabet.
(1) NQYFP YIWFI WE.
(2) MBZXK. 13
⋄ ⋄ ⋄ ⋄ ⋄ ⋄ ⋄ ⋄ ⋄ ⋄ ⋄ ⋄
Since before long we will have ways of enciphering that have hundreds of keys,
rather than only twenty-six, the method of exhaustion will be too exhausting to
do by hand. To develop a better method for decrypting ciphers we must think
more carefully about the ciphertext message we are trying to read.
1.3 Frequency Analysis
Let’s reconsider the situation in which we have captured a message written in
cipher. What might we be able to figure out about this message without reading
it Well, first, we probably know that it is in English (as all of our messages will
be) and we know a lot about English. For instance, that e, t, and a are all very
common, and that x, z and q are among the least common letters in English.
Abraham Sinkov, an important codebreaker during World War II, made a count
of the letters appearing in 16410 words, and Figure 1.3 contains the results.
What do we see in this chart First, the two most common letters are e
and t. Nearly 13% of all letters in an English text are e’s, and over 9% are t’s.
Almost always, e or t will be the most common letter in a text.
13 (1) twelve o’clock. This took six steps, so the key is −6 = 20. (2) Sorry, but it’s a trick.
Either a shift of 3 to produce pecan, or a shift of 7 to give tiger.