2. Terms:
Plaintext
Is a message to be communicated.
Ciphertext
A disguised version of a plaintext.
Encryption
The process of turning Plaintext into Ciphertext.
Decryption
The process of turning Ciphertext into Plaintext.
3. Caesar Cipher
One of the earliest known examples of substitution cipher.
Said to have been used by Julius Caesar to communicate with his army (secretly).
Each character of a plaintext message is replaced by a character n position down in the alphabet.
Belongs to Substitution Cipher.
4. Caesar Cipher
Example:
The first row denotes the plaintext
Second row denotes the ciphertext
The ciphertext is obtained by "shifting" the original letter by the N position to the right.
In this example, it is shifted by 3 to the right.
A becomes D
B becomes E
X becomes A, and so on...
A B C D E … … X Y Z
D E F G H … … A B C
5. Caesar Cipher
Suppose the following plaintext is to be encrypted:
ATTACK AT DAWN
By shifting each letter by 3, to the right. Then the resulting ciphertext would be:
DWWDFN DW GDZQ
A B C D E … … X Y Z
D E F G H … … A B C
6. Caesar Cipher
One could shift other than 3 letters apart.
The offset (Number of shifts) is called the "Key"
Decryption Process:
Given that the key is known, just shift back N letter to the left.
Example:
Ciphertext: WJYZWS YT GFXJ
Key used: 5
Plaintext: RETURN TO BASE
7. Caesar Cipher
Math Behind Encryption:
This can be represented using modular arithmetic.
Assume that : A = 0, B = 1, C = 2, ..., Y = 24, Z = 25.
Encryption process can be represented as:
Such that: e(x) = (x + k) (mod 26)
X → the plaintext.
K → the number of shifts (offset).
26 → There are 26 letters in the alphabet (English alphabet).
8. Caesar Cipher
Math Behind Decryption:
Can be represented using modular arithmetic.
Assume that : A = 0, B = 1, C = 2, ..., Y = 24, Z = 25.
The decryption process can be represented as:
Such that: e(x) = (x - k) (mod 26).
X → the plaintext.
k → the key (number of shifts or offset).
26 → There are 26 letters in the alphabet (English alphabet).
9. Example
A B C D E F G H I J K L M N O P Q R S T U V W X Y Z
0 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
A B C D E F G H I J K L M N O P Q R S T U V W X Y Z
F G H I J K L M N O P Q R S T U V W X Y Z A B C D E
Then have Caesar cipher as:
c = E(p) = (p + k) mod (26) 12%26 12 = M
p = D(c) = (c – k) mod (26) 7%26 7 = H
Example: HOWDY (7,14,22,3,24) encrypted using key k (i.e a shift of 5) is MTBID
Can Define Transformation as:
Mathematically Give Each Letter a number :
