# 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** **e**k**a**zcy**e** bs se**e**dh**en**pl **ana**ylfvf

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** **e**k**a**zc**le** bs se**e**dh**en**pl **anal**l**s**v**s**

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