Introduction

Two Types of Cipher

1. stream cipher
   • prone to error or loss
2. block cipher
   • partial errors don't affect entire data

N-bits Encryption

• example: n=2

  00 => 11
  01 => 10
  10 => 00
  11 => 01
  

• It needs a table of 2^n * n bits

Feistel Cipher

• Encryption

Input: n=32
[ LE0 | RE0 ]

Round 1:
    LE1 = RE0
    t = F(RE0, K1)
    RE1 = LE0 XOR t

[ LE1 | RE1 ]

Round 2:
    LE2 = RE1
    t = F(RE1, K2)
    RE2 = LE1 XOR t

[ LE2 | RE2 ]

...
Round 16:

[ LE16 | RE16 ]

Last (swap):
    LE17 = RE16
    RE17 = LE16

[ LE17 | RE17]

• Input size and round iteration can be optimized
• Decryption

[ LD0 | RD0 ] (= LE17, RE17)

    LD1 = RE17
    t = F(RE17, K16)
    RD1 = LE17 XOR t

[ LD1 | RD1 ]

...

[ LD16 | RD16 ]

    LD17 = RD16
    RD17 = LD16

[ LD17 | RD17 ] (Plaintext)

• Explain

  LD1 = RD0 = LE16 = RE15
  RD1 = LD0 XOR F(RD0, K16)
    = RE16 XOR F(LE16, K16)
    = LE15 XOR F(RE15, K16) XOR F(LE16, K16)
    = LE15 XOR F(RE15, K16) XOR F(RE16, K16)
    = LE15 XOR 0
    = LE15
  

Simplified DES (SDES)

• Example

  • Input: 8-bit
  • Key: 10-bit; additional keys can be derived

• SDES Practice

  • Plaintext = 0111 0010
  • Key = 10100 00010

Sub-key generation

• P10
  • change position
  • 1 2 3 4 5 6 7 8 9 10 -> 3 5 2 7 4 10 1 9 8 6
• LS-1
  • left shift 1 (LSB will be at RSB)
• P8
  • 6 3 7 4 8 5 10 9 (1, 2 not used)
• LS-2
  • left shift 2 (LS-1 twice)

Encryption

• IP; initial permutation
  • change position (like P10)
• E/P; extend permutation
  • 1 2 3 4 -> 4 1 2 3 2 3 4 1
• S0-box
  • with a 4*4 matrix
  • xyzw -> xw, yz
  • output = matrix[xw][yz]
  • 0b0110 => matrix[0b00][0b11]
• S1-box; same but different matrix
• SW; swap
• IP^-1
  • 4 1 3 5 7 2 8 6

Decryption

• same but using keys in reversed order