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

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