DATA ENCRYPTION ALGORITHM

DES ENCRYPTION

Plainext is broken into blocks of length 64 bits.Encryption is blockwise.
A message block is first gone through an initial permutation IP,then divided into two parts L₀,where L₀ is the left part of 32 bits and R₀ is the right part of the 32 bits
Round i has input L_i-1,R_i-1 and output L_i,R_i

L_i = R_i-1,R_i = L_i-1 ⊕ f(R_i-1,K_i)

and K_i is the subkey for the 'i'th where 1 ≤ i ≤ 16

L₁ = R₀, R₁ = L₀ ⊕ f(R₀,K₁)

L₂ = R₁, R₂ = L₁ ⊕ f(R₁,K₂)

L₃ = R₂, R₃ = L₂ ⊕ f(R₂,K₃)

................ ..........................

L₁₆ = R₁₅, R₁₆ = L₁₅ ⊕ f(R₁₅,K₁₆)

After round 16,L₁₆ and R₁₆ are swapped,so that the decryption algorithm has the same structure as the encrption algorithm.
Finally,the block is gone through the inverse the permutation IP^-1 and then output
One round of DES in very simple way during encryption

DES DECRYPTION

Observation:In encryption,we have

L_i = R_i-1,R_i = R_i = L_i-1 ⊕ f(R_i-1,K_i)

and K_i is the subkey for the 'i'th round.Hence

R_i-1 = L_i,L_i-1 = R_i ⊕ f(L_i,K_i) for each 'i'

Due to swap operation after the 16th round encryption,the output of encryption is IP^-1(R₁₆,L₁₆)
Equation(1) as follows:

R₁₅ = L₁₆, L₁₅ = R₁₆ ⊕ f(L₁₆,K₁₆)

R₁₄ = L₁₅, L₁₄ = R₁₅ ⊕ f(L₁₅,K₁₅)

R₁₃ = L₁₄, L₁₃ = R₁₄ ⊕ f(L₁₄,K₁₄)

................ ..........................

R₁ = L₂, L₁ = R₂ ⊕ f(L₂,K₂)

If we give IP^-1(R₁₆,L₁₆) as the input for the same algorithm with round subkeys(K₁₆,K₁₅,......K₁),then the output is IP^-1(L₀,R₀),the original message block
Decryption is performed using the same algorithm,except the K₁₆ is used as the first round,K₁₅ in the second,and so on,with K₁ used in the 16th round
One round of DES in very simple way during decryption

Difference between encryption and decryption in very simple way

Initial permutations

DES has an initial permutation and final permutation after 16 rounds
these permautations are inverse of each other and operate on 64 bits.
They have no cryptographic significance.
The designers did not disclose their purpose

The initial permutation will look like this
Input and Output of the permutation layer

(X₁,X₂,......,X₆₄)------->(X_IP(1),X_IP(2),-------->,X_IP(64)) Initial permutation

The final permutation will look like this

(X₁,X₂,......,X₆₄)------->(X_IP(1)^-1,X_IP(2)^-1,-------->,X_IP(64)^-1)

One round of the DES

DES Expansion

Input 32 bits

Output 48 bits

DES S-Box(substitution box)

8 "SUbstitution boxes" or S-boxes
Each S-box maps 6 bits to 4 bits

S-Box(1)

Row Index:The combination of first and last bit gives the row number
Column Index:Remaining 4 bits gives the column number
What is the output if input is 101000?

Row = 10 = 2 ,Column = 0100 = 4

we have to look at 2nd row and 4th column,then Output is 13
here you can feel the importance of S-box.It takes 6 bits as input and gives 4 bits as output

Properties of the S-box

There are several properties
We highlight some:

-The rows are permutations

-The outputs are a non-linear combination of the inputs

-Change one bit of the input,and half of the output bits change(Avanlanche Effect)

-Each output bit is dependent on all the input bits

The Function f(x,k)

This is called fiestal function or round function
Function f is nothing but mixing of X and K

DES p-box(Permutation Box)

Input 32 bits

Output 32 bits
The output bits are just Transposition of bits

DES subkey

Input Key size:64 bits,of which 8 are parity bits
56 bit DES key,0,1,2,........55

Parity Check bits For Error Detection

Definition:For any binary string a₁a₂.........a_n,append another bit a_n+1 = a₁ ⊕ a₂........ ⊕ a_n, obtaining a₁a₂.........a_na_n+1.This new sequence can detect one error

Adding 8 parity check bits in DES key

Each P_i in position 8i is the parity check bit of the previous 7 bits

Permuted choice 1

PC-1:The permutation PC-1(permuted choice 1)discards the parity bits and transposes the remaining 56 bits as below:

Key Permutation PC-1:

with out positions 8,16,24,32,40,48,56,64 marked with "F"
Simply given as PC-1 is a permutation of {1,2,3......,64}-{8,16,24,32,40,48,56,64}

Left shift operation

LS_i:Each LS_i is a circular shift of some positions.The number of shifted positions is given below

For rounds 1,2,9 and 16 the shifts is 1,and for the remaining all the rounds shifts are 2
PC-2:Permuted choice 2 selects 48 bits from the 56 bit input

PC-2

final 48 bits obtained after the permuted choice is the Key