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)" in 2001.

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

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

Last update: 2015.

Table of Contents

 About This Book

 Cryptography Terminology

 Cryptography Basic Concepts

Introduction to AES (Advanced Encryption Standard)

 What Is AES (Advanced Encryption Standard)?

 AES, or Rijndael, Encryption Algorithm

 AES Key Schedule Algorithm

 AES Key Schedule Example

 AES MixColumns() Procedure Algorithm

 Example Vector of AES Encryption

 AES Standard Decryption Algorithm

AES Equivalent Decryption Algorithm

 Introduction to DES Algorithm

 DES Algorithm - Illustrated with Java Programs

 DES Algorithm Java Implementation

 DES Algorithm - Java Implementation in JDK JCE

 DES Encryption Operation Modes

 DES in Stream Cipher Modes

 PHP Implementation of DES - mcrypt

 Blowfish - 8-Byte Block Cipher

 Secret Key Generation and Management

 Cipher - Secret Key Encryption and Decryption

 Introduction of RSA Algorithm

 RSA Implementation using java.math.BigInteger Class

 Introduction of DSA (Digital Signature Algorithm)

 Java Default Implementation of DSA

 Private key and Public Key Pair Generation

 PKCS#8/X.509 Private/Public Encoding Standards

 Cipher - Public Key Encryption and Decryption

 MD5 Mesasge Digest Algorithm

 SHA1 Mesasge Digest Algorithm

 OpenSSL Introduction and Installation

 OpenSSL Generating and Managing RSA Keys

 OpenSSL Managing Certificates

 OpenSSL Generating and Signing CSR

 OpenSSL Validating Certificate Path

 "keytool" and "keystore" from JDK

 "OpenSSL" Signing CSR Generated by "keytool"

 Migrating Keys from "keystore" to "OpenSSL" Key Files

 Certificate X.509 Standard and DER/PEM Formats

 Migrating Keys from "OpenSSL" Key Files to "keystore"

 Using Certificates in IE (Internet Explorer)

 Using Certificates in Firefox

 Using Certificates in Google Chrome

 Outdated Tutorials

 References

 PDF Printing Version