Feistel Cipher Structure

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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 Shannons substitution-permutation
  network concept

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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

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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.

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Classical Feistel Network
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Classical Feistel Network
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Design Features of Feistel Network

• Block Size (larger block means greater security)
  64 bits.
• Key Size56-128 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.

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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.

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Feistel Encryption and Decryption
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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).

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Simplified DES Scheme
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Overview

• We can express the encryption algorithm as a
  composition function
• IP-1?fk2 ?SW ?fk1 ?IP
• OR
• CiphertextIP-1(fk2(SW(fk1(IP(plaintext)))))
• Where,
• K1P8(shift(P10(key)))
• K2 P8 (shift(shift(P10(key))))
• The decryption algorithm is
• PlaintextIP-1 (fk1(SW(fk2(IP(Ciphertext)))))

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Key Generation for S-DES
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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 (10000?01100)?(00001?11000)
• Next apply P8
• This yields K1(10100100)

P10 P10 P10 P10 P10 P10 P10 P10 P10 P10
3 5 2 7 4 10 1 9 8 6
P8 P8 P8 P8 P8 P8 P8 P8
6 3 7 4 8 5 10 9
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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)

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S-DES Encryption
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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 IP IP IP IP IP IP IP
2 6 3 1 4 8 5 7
IP-1 IP-1 IP-1 IP-1 IP-1 IP-1 IP-1 IP-1
4 1 3 5 7 2 8 6
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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 (10111101) and
• F(1101,SK)(1110) for some SK then
• fk(10111101)(1011) ?(1110)(0101)

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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 E / P E / P E / P E / P E / P E / P E / P
4 1 2 3 2 3 4 1
n4 n1 n2 n3
n2 n3 n4 n1
n4K11 n1 K12 n2 K13 n3 K14
n2 K15 n3 K16 n4 K17 n1 K18
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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
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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

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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.