The Rijndael Block Cipher

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The Rijndael Block Cipher

• By Vincent Leith

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Basics of Cryptography

• Encryption turning plaintext into unreadable
  nonsense
• Plaintext Regular type or data to be encrypted
• Ciphertext converted plaintext
• Cipher algorithm used to encrypt and decrypt
  plaintext and ciphertext.

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Introduction

• Created by Joan Daemen and Vincent Rijmen
• American National Institute of Standards and
  Technology
• Trying to create a new Advanced Encryption
  Standard (AES)
• Held a contest to create a new encryption standard

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Design

• Resistance against all known attacks
• Speed and code compactness on a wide range of
  platforms
• Design simplicity

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Finite Field Arithmetic

• Rijndael operates in a GF(28) finite field
• The field is byte based and expressed in Hex
• b7X7 b6X6 b5X5 b4X4 b3X3 b2X2 b1X1
  bo
• Example
• X7 X6 X4 X3 X2 1 11011101

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Finite Field Arithmetic (cont.)

• 0000 0
• 0001 1
• 0010 2
• 0011 3
• 0100 4
• 0101 5
• 0110 6
• 0111 7
• 1000 8
• 1001 9

• 1010 A
• 1011 B
• 1100 C
• 1101 D
• 1110 E
• 1111 F

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Finite Field Arithmetic (cont.)

• Addition done using bitwise EXOR
• Example 57 83 D4
• (X6 X4 X2 X 1) (X7 X 1) X7 X6
  X4 X2
• Multiplication using modulo X8 X4 X3 X 1
• Example 57 ? 83 C1
• (X6 X4 X2 X 1) (X7 X 1)
• X13 X11 X9 X8 X6 X5 X4 X3 1 mod
• X7 X6 1

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ByteSub Transformation

• Transformation is a non-linear byte substitution,
  operating on each of the Statebytes
  independently.

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ShiftRow Transformation

• The rows of the State are cyclically shifted over
  different offsets.
• Row 0 is not shifted, Row 1 is shifted over C1
  bytes, row 2 over C2 bytes and row 3 over C3
  bytes.

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MixColumn Transformation

• The columns of the State are considered as
  polynomials over GF(28) and multiplied modulo X4
  1 with a fixed polynomial c(X)
• b(X) c(X) a(X)

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Round Key Addition

• Applied to the State by a simple bitwise EXOR.

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The Round Transformation

• Matrix implementation of key addition and
  MixColumn
• For ShiftRow and ByteSub transformations

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The Round Transformation (cont.)

• Using Substitution and taking the column indices
  to modulo Nb
• Matrix multiplication of a linear combination of
  vectors

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The Round Transformation (cont.)

• Perform a table lookup for input bytes ai,j in
  the S-box table S256 for multiplication factors
• Using the above 4 tables the round transformation
  can now be expressed

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Example of Encryption

• 128 bit cipher
• Key E8E9EAEBEDEEEFF0F2F3F4F5F7F8F9FA
• Plaintext 014BAF2278A69D331D5180103643E99A
• Ciphertext 6743C3D1519AB4F2CD9A78AB09A511BD 
• 192 bit cipher
• Key 04050607090A0B0C0E0F10111314151618191A1B1D1E1
  F20
• Plaintext 76777475F1F2F3F4F8F9E6E777707172
• Ciphertext 5D1EF20DCED6BCBC12131AC7C54788AA 
• 256 bit cipher
• Key 08090A0B0D0E0F10121314151718191A1C1D1E1F21222
  324262728292B2C2D2E
• Plaintext 069A007FC76A459F98BAF917FEDF9521
• Ciphertext 080E9517EB1677719ACF728086040AE3

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For Example of Actual Code

• http//msdn.microsoft.com/en-us/library/system.sec
  urity.cryptography.rijndael.aspx

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Acknowledgements

• http//www.eng.tau.ac.il/yash/crypto-netsec/rijnd
  ael_files/rijnov.gif
• http//msdn.microsoft.com/en-us/library/system.sec
  urity.cryptography.rijndael.aspx
• http//www.hanewin.net/encrypt/aes/aes-test.htm
• AES Proposal Rijndael by Joan Daemen, Vincent
  Rijmen