1. Feistel Cipher Structure
Horst Feistel devised the feistel cipher
based on concept of invertible product cipher
partitions input block into two halves
process through multiple rounds which:
perform a substitution on left data half
based on round function of right half & sub key
then have permutation swapping halves
implements Shannon’s substitution-permutation network concept

2. Feistel Cipher Structure (1973)
Virtually all conventional block encryption algorithms including data encryption standard (DES) are based on Feistel Cipher Structure.
The plaintext is divided into two halves
Then the two halves pass through n rounds of
processing then combine to produce the cipher
block.
Each round has as input and derived from the previous round as well as a sub-key derived from the overall

3. Feistel Cipher Structure (1973)
All rounds have the same structure
A substitution is performed on the left half of the data. This is done by applying a round function to the right half of the data followed by the XOR of the output of that function and the left half of the data.

4. Classical Feistel Network

5. Classical Feistel Network

6. Design Features of Feistel Network
Block Size: (larger block means greater security) 64 bits.
Key Size: bits.
Number of Rounds: a single round offers inadequate security, a typical size is 16 rounds.
Sub-key Generation Algorithms: greater complexity should lead to a greater difficulty of cryptanalysis.
Round function: Again, greater complexity generally means greater resistance to cryptanalysis.

7. Design Features of Feistel Network.
Round function: Again, greater complexity generally means greater resistance to cryptanalysis.
Fast Software encryption/Decryption: the speed of execution of the algorithm is important.
Ease of Analysis: to be able to develop a higher level of assurance as to its strength
Decryption: use the same algorithm with reversed keys.

8. Feistel Encryption and Decryption

9. Simplified DES (S-DES)
Developed by Prof. Edward Schaefer of Santa Clara University 1996.
Takes 8 bit block of plain text and 10 bit key as input and produce an 8 bit block cipher text output.
The encryption algorithm involves 5 functions: initial permutation (IP); a complex function fk which involves substitution and permutation depends on the key; simple permutation function (switch) SW; the function fk again and final inverse of the initial permutation( IP-1).

10. Simplified DES Scheme

11. Overview
We can express the encryption algorithm as a composition function:
IP-1fk2 SW fk1 IP
OR ;
Ciphertext=IP-1(fk2(SW(fk1(IP(plaintext)))))
Where,
K1=P8(shift(P10(key)))
K2 =P8 (shift(shift(P10(key))))
The decryption algorithm is:
Plaintext=IP-1 (fk1(SW(fk2(IP(Ciphertext)))))

12. Key Generation for S-DES

13. Key Generation for S-DES
First permute the key in the following way:
Ex: ( )is permuted to ( )
Perform a circular left shift to each bits of the key:
Ex: (1000001100)(0000111000)
Next apply P8
This yields K1=( )
P10 3 5 2 7 4 10 1 9 8 6 P8 6 3 7 4 8 5 10 9

14. Continue…
Then perform again 2 bit circular shift left on each of the five bits:
(00001)(11000)(00100)(00011)
Finally apply again P8:
Then K2=( )

15. S-DES Encryption

16. S-DES Encryption
The i/p 8-bit block plaintext is first permuted using the IP function:
At the end of the algorithm the inverse permutation is used :
IP-1(IP(X))=X;
Ex: IP{( )}=( )
IP-1 { }=( ) IP 2 6 3 1 4 8 5 7
IP-1 4 1 3 5 7 2 8 6

17. The Function fk
Let L and R be the left most 4 bits and rightmost 4 bits of the 8 bits input
fk (L, R)=(LF(R,SK),R)
Where SK is a sub key and the  is bit-by-bit XOR function.
Ex: if the o/p of the IP is ( ) and
F(1101,SK)=(1110) for some SK then
fk( )=(1011) (1110)=(0101)

18. Continue…
Recall the first operation is an expansion and permutation to first 4 bits as follows:
We can depict the result as :
The 8 bit key K1is added to this value using XOR:
E / P 4 1 2 3 n4 n1 n2 n3
n4+K11
n1+ K12
n2 +K13
n3 +K14
n2 +K15
n3 +K16
n4 +K17
n1 +K18

19. Continue… Let us rename these bits:
The first row of the matrix 4 bits are fed into the S-box S0 to produce 2 bit o/p and the remaining 2 bits are fed to S1 to produce another 2 bits
P0,0
P0,1
P0,2
P0,3
P1,0
P1,1
P1,2
P1,3

20. S-Box
The s-box operates as follows: (P0,0,P0,3 ) determine the row of the S0 matrix and (P0,1,P0,2 )determine the column:
Ex: if (P0,0,P0,3 ) =(00), (P0,1,P0,2 )=(10) then the o/p is from row 0 and column 2 in S0 which is equal to 3, i.e., (11) in binary.
In a similar way we can produce the other two bits

21. The Switch Function (SW)
SW interchange the left and right 4 bits so that the second instance of fK operates on a different 4 bits.