1. The Caesar cipher
Plain: 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 Cipher key: D E F G H I J K L M N O P Q R S T U V W X Y Z A B C Key = 4 Plain: meet me after the toga Cipher: PHHW PH DIWHU WHK WRJD

2. The Caesar cipher
for a key K=3, plaintext letter: ABCDEF...UVWXYZ ciphtertext letter: DEF...UVWXYZABC
Hence TREATY IMPOSSIBLE is translated into WUHDWB LPSRVVLEOH

3. Substitution Cipher
For each letter, substitute some other letter(randomly)
A key determines what the substitution is
E.g., 4, 8, 1, 26,...
1st letter in the alphabet will be represented by the 4th letter
A  D
2nd letter will be represented by the 8th
B  H
3rd letter will be represented by the 1st
C  A
4th letter will be represented by the 26th
D  Z

4. Shift cipher Two basic properties for a cryptosystem:
1. Each encryption function eK and each decryption dK should be
efficiently computable.
2. An opponent upon seeing a ciphertext string y, should be unable to
determine the key K that was used, or the plaintext string x.
Question: is shift cipher secure?
Of course NOT, since there are only 26 possible keys,
it is easy to be broken by exhaustive key search.
Example: JBCRCLQRWCRVNBJENBWRWN
Plaintext: astitchintimesavesnine (K=9)
On average, a plaintext will be computed after trying 26/2=13 times.

5. Shift Alphabets Cipher (direct)
C(a)=(a+k)mod n=26        encipher
P=(c‐k)mod n=26           decipher
 i.e.  c=(p+k)mod 26, 
     where a =0,…………..z=25 

6. Shift Alphabets Cipher (direct)
Ex : Encrypt the Plain text = THIS with key =3
T= H= I=8 S=18
Ek(T) = (T+KEY ) mod 26 = (19 + 3) mod 25 = 22 mod 26 =22  W
Ek(H) =(H+KEY ) mod 26 = (7 + 3) mod 25 =10 mod 26 =10  K
Ek(I) = (I+KEY ) mod 26 = (8 + 3) mod 25 = 11 mod 26 =11  L
Ek(S) =(S+KEY ) mod 26 = (18 + 3) mod 25 = 21 mod 26 =22  V

7. Shift Alphabets Cipher (direct)
Ex : Decrypt cipher text = WKLV with key =3 DK(W) =(W-KEY) mod 26 = (22-3) mod 26 = 19 mod 26 = 19 T DK(K) =(K-KEY) mod 26 = (10-3) mod 26 = 7 mod 26 = 7 H DK(L) =(L-KEY) mod 26 = (11 - 3) mod 26 = 11 mod 26 =19 I DK(V) =(V-KEY) mod 26 = (21-3) mod 26 = 21 mod 26 = 21  S Plain text = THIS

8. Shift Alphabets Cipher (direct)

9. Standard-Reverse
In this method, the shifting is toward the left side, so use the following form:- For Ciphering C=(K-P) mod 26 For Deciphering P=(K-C) mod 2

10. Standard-Reverse

11. Standard-Reverse Encryption

12. Standard-Reverse Decryption