Feistel Cipher Structure

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

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 ofprocessing then combine to produce the cipherblock.• Each round has as input and derived from

the previous round as well as a sub-key derived from the overall

00 and RL

iKK

i

i 1iL 1iR

Feistel Cipher Structure (1973)

All rounds have the same structureA 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.

F

Classical Feistel Network

Classical Feistel Network

Design Features of Feistel Network

Block Size: (larger block means greater security) 64 bits.

Key Size:56-128 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.

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.

Feistel Encryption and Decryption

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).

Simplified DES Scheme

Overview

• We can express the encryption algorithm as a composition function:

IP-1fk2 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)))))

Key Generation for S-DES

Key Generation for S-DES

• First permute the key in the following way:

• Ex: (1010000010)is permuted to (1000001100)• Perform a circular left shift to each bits of the key:• Ex: (1000001100)(0000111000)• Next apply P8

• This yields K1=(10100100)

P10

3 5 2 7 4 10 1 9 8 6

P8

6 3 7 4 8 5 10 9

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=(01000011)

S-DES Encryption

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{(10110101)}=(01111100)• IP-1 {01111100}=(10110101)

IP

2 6 3 1 4 8 5 7

IP-1

4 1 3 5 7 2 8 6

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)=(LF(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 (10111101) and

F(1101,SK)=(1110) for some SK then

fk(10111101)=(1011) (1110)=(0101)

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 2 3 4 1

n4 n1 n2 n3

n2 n3 n4 n1

n4+K11 n1+ K12 n2 +K13 n3 +K14

n2 +K15 n3 +K16 n4 +K17 n1 +K18

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

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

3012

0103

3102

3210

1,

2313

3120

0123

2301

0 SS

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.