Design of Symmetric Encryption Algorithm

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Design of Symmetric Encryption Algorithm
ECE802-607Cryptography and Network
SecurityInstructor Dr. Jian Ren

• Xiaomei Liu
• Karthik Nandakumar
• Umut Uludag

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Roadmap

• Major Features
• Specifications
• Round Transformation
• Key Schedule
• Performance Analysis
• Security
• Time-complexity
• Summary

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Major Features

• Combines the properties of the simple Feistel
  structure used in DES and the finite field
  operations of AES
• A transformation function F is applied to both
  the left and right branches of the Feistel
  Structure
• Balanced processing allows efficient parallel
  implementation
• Key-dependent S-boxes for byte substitution
• Based on finite field theory
• Complex sub-key generation algorithm compared to
  DES

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Specifications

• Block Size 64 bits
• Key Length 128, 192, or 256 bits
• Number of rounds 16, 24, or 32
• Sub-key Size 64 bits
• IP and IP-1 were randomly selected
• Number of S-boxes 16
• Size of each S-box 16 16

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Encryption and Decryption Structure
General Encryption Structure
General Decryption Structure
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The Round Transformation
Round Decryption
Round Encryption
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Key Schedule Algorithm
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Key Schedule Algorithm (cont.)
Table The key shift schedule based on round
index
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Byte Substitution

• 16 primitive polynomials in GF(28)
• Use the round sub-key to index one of them
• Compute inverse based on that polynomial
• Compute the affine transformation Y MX L
• X is the inverse of the byte to be substituted

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Security Analysis

• Confusion
• Making the relationship between the cipher text
  and the encryption key as complex as possible
• each bit in the encryption key must affect many
  bits in the cipher text
• achieved by complex, non-linear, and
  key-dependent S-box transformations and complex
  sub-key generation algorithm
• Example
• Plain Text AF84FD6A6D263A37
• Key A084FFFF0851C6A9FF1160BA57476773
• Cipher Text 551B35B8E004C9A6
• Invert the bit 4 in the encryption key
• Plain Text AF84FD6A6D263A37
• Key B084FFFF0851C6A9FF1160BA57476773
• Cipher Text 3E05B74136723550
• Number of bit changes in the cipher text 34

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Security Analysis

• Diffusion
• Making the statistical properties of the plain
  text completely obscure
• each bit in the plain text must affect many bits
  in the cipher text
• achieved by repeated permutations (bit shift, mix
  column and addition (exclusive-or) of the left
  part of the intermediate state to the right part
  followed by the interchange of the left and the
  right parts)
• Example
• Plain Text 958E5DDFD17247CB
• Key 1AC02A4FF9593816D6033583042C70F4
• Cipher Text 06B2AC82F760D311
• Invert the bit 33 in the plain text
• Plain Text 958E5DDF517247CB
• Key 1AC02A4FF9593816D6033583042C70F4
• Cipher Text 507779D551120AF1
• Number of bit changes in the cipher text 34

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Security Analysis

• Avalanche Effect
• Strict Avalanche Criterion - a change in bit i
  of the plain text or the encryption key, changes
  the bit j in the cipher text with probability ½
• Example
• Plain Text1 05AACB5FDC6EAF47
• Plain Text2 85AACB5FDC6EAF47
• Key 9A354FEAC1982544
• DF4A0CE745345A12

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Bit Independence Criterion

• When a single input bit i is inverted, the
  output bits j and k should change
  independently, for all i, j, and k.
• Example
• Plain Text1 7D43A15290F83074
• Key1 4DC432786F9A8099526251DE63D0188A
• Cipher Text1 C3A7EAB5F4E08A66
• Invert the bit 33 in the plain text
• Plain Text2 7D43A15210F83074
• Key1 4DC432786F9A8099526251DE63D0188A
• CipherText2 A96D49AE9C9E4E23
• Using a different key
• PlainText1 7D43A15290F83074
• Key2 F968CB3AEEFD54F382CC21E08C4A97A9
• CipherText3 A86588614ACA3AED
• PlainText2 7D43A15210F83074
• Key2 F968CB3AEEFD54F382CC21E08C4A97A9
• CipherText4 98D5FD712B27250D

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Time Complexity Analysis
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Summary

• We have developed a secure and efficient
  symmetric encryption algorithm
• Some of the salient features of the design are
• Balanced processing allowing easy parallelization
• Key-dependent S-boxes
• Complex key schedule algorithm
• We have not analyzed in depth some problems like
  weak-keys and differential cryptanalysis