AES Equivalent Decryption Algorithm

Cryptography Tutorials - Herong's Tutorial Examples

∟Introduction to AES (Advanced Encryption Standard)

∟AES Equivalent Decryption Algorithm

The equivalent decryption algorithm of the AES-128 encryption is provided. It follows the same sequence of applying transformation procedures as the encryption algorithm, but uses modified round keys.

The second type of AES decryption algorithms is called "Equivalent Inverse Cipher" in the FIPS publication, "Announcing the ADVANCED ENCRYPTION STANDARD (AES)" at http://csrc.nist.gov/publications/fips/fips197/fips-197.pdf in 2001.

The difference of equivalent decryption algorithms and standard decryption algorithms can be summarized as:

Standard decryption algorithms use same round keys as the encryption algorithm, but applies transformation procedures in a different sequence.
Equivalent decryption algorithms have the same sequence of applying transformation procedures as the encryption algorithm, but uses modified round keys.

Here is the equivalent decryption algorithm for a single block of 128-bit ciphertext with a 128-bit cipher key:

Input: 
   C: 128 bits of ciphertext
   K: 128 bits cipher key

   InvS[]: Inverse substitution box of 16x16 byte values
   InvKeyExpansion(): Inverse procedure to expand cipher key
   AddRoundKey(): Add round key procedure
   InvShiftRows(): Inverse shift rows procedure
   InvSubBytes(): Inverse substitution of bytes procedure
   InvMixColumns(): Inverse mix columns procedure

Output:
   T: 128 bits of plaintext

Algorithm:
   InvKeyExpansion(K,ik[])       # expanding K to 11 round keys:

   state = C                     # copying ciphertext to state
   AddRoundKey(State, ik[10])    # adding last round key

   for i = 9 to 1                # loop to repeat 9 rounds backward
      InvSubBytes(state)         # performing reverse substitution
      InvShiftRows(state)        # performing reverse byte shifting
      InvMixColumns(state)       # reversely mixing columns in state
      AddRoundKey(state, ik[i])  # adding next round key
   end for                       # end of loop

   InvSubBytes(state)            # performing reverse substitution
   InvShiftRows(state)           # performing reverse byte shifting
   AddRoundKey(state, ik[0])     # adding first round key

   T = state                     # copying state to plaintext

All procedures used in this equivalent decryption algorithm are identical to the standard decryption algorithm except for the InvKeyExpansion() procedure. Comparing with the KeyExpansion procedure, the InvKeyExpansion() procedure only has 1 extra step at the end as shown below:

Procedure Name: 
   InvKeyExpansion(K,ik[])

Input:
   K: 128 bits cipher key
   Rcon[]: Round constant array
   SubWord(): Word substitution procedure
   RotWord(): Word rotation procedure

Output:
   ik[11]: 11 round keys as 4x4 byte arrays

Algorithm:
   w[4*11]              # a word array holding 11 round keys
   w[0..3] = K          # setting cipher key as the first round key
   
   for i = 4 to 43      # computing words of other round keys
      temp = w[i-1]     # copying previous word to a temp variable
      if (i mod 4 = 0)
         temp = SubWord(RotWord(temp)) 
         temp = temp XOR Rcon[i/4]
      end if
      w[i] = w[i-4] XOR temp
   end for
   
   for i = 0 to 10      # building 11 round keys as 4x4 byte arrays
      ik[i] = w[4*i..4*i+3]
   end for

   for r = 1 to 9       # extra step for the inverse round keys 
      InvMixColumns(ik[r])
   end for