Frequency Analysis

Frequency analysis is the first tool that cryptanalysts use in the analysis of a ciphertext. Frequency analysis is observing the number of times a character appears in a ciphertext and comparing that to the corresponding plaintext letter frequency. For instance, in the ciphertext:

Na rknzcyr bs serdhrapl nanylfvf

it can be observed that there are: 4-n's, 3-a's, and 4-r's. If we observe some of the most used English letters (E, T, N), and arbitrarily assign these letters such that r = e, n = a, a = n; we can reduce the ciphertext to:

An ekazcye bs seedhenpl anaylfvf

Since there are 2-y's and 2-f's, if we arbitrarily assign them to the common letters "S" and "L" (respectively), we reduce the ciphertext to:

An ekazcle bs seedhenpl anallsvs

Further iteration reveals the plaintext to be:

An example of frequency analysis

For reference, the cipher used above is simple Rot-13.

Normalized Frequency Distribution

Normalized Frequency Distribution

Frequency Distribution
Letter Normalized Distribution Distribution
A 0.643 8.17%
B 0.117 1.49%
C 0.219 2.78%
D 0.335 4.25%
E 1.000 12.70%
F 0.175 2.23%
G 0.159 2.02%
H 0.480 6.09%
I 0.548 6.97%
J 0.012 0.15%
K 0.061 0.77%
L 0.317 4.03%
M 0.189 2.41%
N 0.531 6.75%
O 0.591 7.51%
P 0.152 1.93%
Q 0.007 0.10%
R 0.471 5.99%
S 0.498 6.33%
T 0.713 9.06%
U 0.217 2.76%
V 0.077 0.98%
W 0.186 2.36%
X 0.012 0.15%
Y 0.155 1.97%
Z 0.006 0.07%

Reference:
http://www.central.edu/homepages/LintonT/classes/spring01/cryptography/letterfreq.html