Classical Cryptography

Shift Cipher

History and Description

In the first century B.C., Julius Caesar developed the shift cipher. Based on a shift key, each letter in the alphabet is replaced by the new shifted letter. The message which is enciphered by replacing the corresponding new letter is called plaintext, and the new message which is produced by the substitution is called ciphertext. The key gives the number of letters the alphabet is shifted between plaintext and ciphertext.

Example

Encipher
Given: The shift key is 5
Plaintext: I AM A STUDENT

The corresponding ciphertext letter is computed for each letter in the plaintext as follows
I + Shift(5) = N

A + Shift(5) = F
M + Shift(5) = R

A + Shift(5) = F

S + Shift(5) = X
T + Shift(5) = Y
U + Shift(5) = Z
D + Shift(5) = I
E + Shift(5) = J
N + Shift(5) = S
T + Shift(5) = Y

Therefore, the ciphertext is NFRFXYZIJSY.

Decipher
We decipher NFRFXYZIJSY. by computing the corresponding plaintext letter for each letter in the ciphertext as follows
N - Shift(5) = I

F - Shift(5) = A
R - Shift(5) = M

F - Shift(5) = A

X - Shift(5) = S
Y Shift(5) = T
Z - Shift(5) = U
I - Shift(5) = D
J - Shift(5) = E
S - Shift(5) = N
Y - Shift(5) = T

Therefore, the plaintext is IAMASTUDENT.

Disadvantages

As there are 26 letters in alphabet, each letter can be shifted up to 25 places. To break the ciphertext, we can list all the possible plaintext and choose the most reasonable message.

For example, if we have the ciphertext which is NFRFXYZIJSY, possible corresponding plaintexts are:

Shift Plaintext
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
MEQEWXYHIRX
LDPDVWXGHQW
KCOCUVWFGPV
JBNBTUVEFOU
IAMASTUDENT
HZLZRSTCDMS
GYKYQRSBCLR
FXJXPQRABKQ
EWIWOPQZAJP
DVHVNOPYZIO
CUGUMNOXYHN
BTFTLMNWXGM
ASESKLMVWFL
ZRDRJKLUVEK
YQCQIJKTUDJ
XPBPHIJSTCI
WOAOGHIRSBH
VNZNFGHQRAG
UMYMEFGPQZF
TLXLDEFOPYE
SKWKCDENOXD
RJVJBCDMNWC
QIUIABCLMVB
PHTHZABKLUA
OGSGYZAJKTZ

By locating the only reasonable message, we can decide that the shift key is 5 and the plaintext is IAMASTUDENT.