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DES - Overview and Encryption
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A [http://www.projectrhea.org/learning/slectures.php slecture] on [[Cryptography]] by student Divya Agarwal and Katie Marsh

Partly based on the [[2015 Summer Cryptography Paar|Cryptography Summer 2015]] lecture material of Prof. Paar.
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=== '''Overview of DES Algorithm''' ===

[[File:DES_Overview.png|500px|thumb|left|Fig 1: Overview of the DES Algorithm]]

* DES is a Symmetric cipher: uses same key for encryption and decryption
* Uses 16 rounds which all perform the identical operation
* Different subkey(48 bit) in each round derived from main key

=== '''Internal structure of DES''' ===

1.  '''Initial Permutaion(IP)''' : This is the first thing that is seen in the expanded view of DES block in Fig 1. 

* IP is a bitwise permutation or simple crosswiring in hardware.
* The corsswiring is done according to the table(left) given in Fig 2.
* The IP has no effect on the DES security at all.

[[File:IPFP.png|500px|thumb|left|Fig 2: Initial Permutation(left) and the Final Permutation(right) tables ]]
 
2.  '''DES Encryption Round - Feistel Networks'''

* DES structure is a Feistel network
* Advantage: encryption and decryption differ only in keyschedule( explained later )

[[File:FN.png|500px|thumb|left|Fig 3: Encryption block round 1 - Feistel Networks]]

* The encryption block for round 1 in Fig 3 takes an input of 64 bit data permuted in the IP
* Plaintext is split into 32-bit halves <math>L_i</math> and <math>R_i</math>
* <math>R_i</math> is fed into the '''function f''', the output of which is then XORed with <math>L_i</math>
* Left and right half halves are swapped at the end of one encryption round
* Each encryption round can be expressed as :

<math>L_i = R_{i-1}</math>

<math>R_i = L_{i-1} \oplus f(R_{i-1},k_i)</math> 

[[File:FNfinal.png|500px|thumb|left|Fig 4: Encryption block final round - Feistel Networks]]

* And as seen in Fig 1, we have sixteen such rounds.
* And the Left and Right side bits are swapped again before the Final Permutation(FP) as shown in Fig 4.

3. '''The f-funtion(inside the feistel network)'''

[[File:f_fucntion.png|300px|thumb|left|Fig 5: The f-function block]]

* Main operation of DES
* Inputs to f function are <math>R_{i-1}</math> and round key <math>k_i</math>
* It has 4 main steps in Fig 5 :

  ** Expansion block E
  ** XOR with round key
  ** S-box substitution (eight of them)
  ** Permutation

3.1 The Expansion fucntion E

* The main purpose of the expansion funtion is to increase diffusion in the input <math>R_{i-1}</math> bits.
* It is done using the table shown in Fig 6.

[[File:expansion.png|400px|thumb|left|Fig 6: The expansion block table(top) and bitwise explanation(bottom)]]

3.2 XOR with round key 

* Bitwise XOR of the round key <math>k_i</math> and the output of the expansion function E
* We take a 48-bit expanded message bit and XOR with 48-bit key input and the output data is also 48-bit (Fig 5)
[Round keys are derived from the main key in the DES keyschedule later in the notes]


3.3 The DES S-Box substitution

* Eight substitution tables which form the core security of DES (Refer book)
* Take 6 bits of input and gives 4-bit output
* Non-linear and resistant to differential cryptanalysis

3.4 The Permutation P

* This is the last step in the f-fucntion in Fig 5.
* It is also bitiwse permutation, which introduces diffusion using the table in Fig 7.
* Output bits of one S-Box effect several S-Boxes in next round.
* Diffusion by E, S-Boxes and P guarantees that after Round 5 every bit is a function of each key bit and each plaintext bit.

[[File:P.png|200px|thumb|left|Fig 7: The Permutation table P]]

The complete lecture on DES by Prof. Paar can be found [https://www.youtube.com/watch?v=kPBJIhpcZgE here].
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== References==
* C. Paar. Understanding Cryptography. Lecture Notes. Dept. of Electr. Eng. and Information Sciences, Ruhr University.
* C. Paar and J. Pelzl. Understanding Cryptography. A textbook for Student and Practitioners. Springer 2010.
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==[[2015_Summer_Cryptography_Paar_Divya Agarwal_comments | Questions and comments]]==
If you have any questions, comments, etc. please post them [[2015_Summer_Cryptography_Paar_Divya Agarwal_comments|here]].
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