AES, or Rijndael, Encryption Algorithm

A quick description of the AES (Advanced Encryption Standard) encryption algorithm is provided. This description only covers AES encryption for a single block of 128-bit plaintext with a 128-bit cipher key.

In the same FIPS publication, "Announcing the ADVANCED ENCRYPTION STANDARD (AES)" in 2001, AES decryption algorithms were included for AES-128, AES-196 and AES256.

The AES-128 encryption algorithm is for a single block of 128-bit plaintext with a 128-bit cipher key:

Input: 
   T: 128 bits of plaintext
   K: 128 bits cipher key
   S[]: Substitution box (s-box) of 16x16 well-selected byte values
   KeyExpansion(): Procedure to expand cipher key to round keys
   AddRoundKey(): Add round key procedure
   SubBytes(): Substitution of bytes procedure
   ShiftRows(): Shift rows procedure
   MixColumns(): Mix columns procedure

Output:
   C: 128 bits of ciphertext

Algorithm:
   KeyExpansion(K,k[])           # expanding K to 11 round keys:
                                 # k[0], k[1], k[2], ..., k[10]

   state = T                     # copying plaintext to state
   AddRoundKey(State, k[0])      # adding first round key

   for i = 1 to 9                # loop to repeat 9 rounds
      SubBytes(state)            # performing substitution
      ShiftRows(state)           # performing byte shifting
      MixColumns(state)          # mixing columns in state
      AddRoundKey(state, k[i])   # adding next round key
   end for                       # end of loop

   SubBytes(state)               # performing substitution
   ShiftRows(state)              # performing byte shifting
   AddRoundKey(state, k[10])     # adding last round key

   C = state                     # copying state to ciphertext

As you can see, most operations of the AES encryption algorithm are carried out on the "state" object, which stores the intermediate ciphertext as a 4x4 byte array.

Brief descriptions of procedures and the S-Box used in the AES encryption algorithm are described below.

KeyExpansion() - The KeyExpansion() procedure takes the cipher key, K, as input and generates a key schedule, which is a series of 11 round keys, k[0], k[1], k[2], ..., k[10]. Round constants, S-Box (substitution box), XOR operations, and cyclic shift operations are used in the KeyExpansion() procedure. Details of the KeyExpansion() algorithm are given in next tutorials.

AddRoundKey() - The AddRoundKey() procedure performs the XOR operation of the state and the given round key. The result is stored back to the state as shown below:

AddRoundKey(state,k) {
   state = state XOR k
}

SubBytes() - The SubBytes() procedure performs a lookup operation on the S-Box for each byte in the state. The result is stored back to the state as shown below:

SubBytes(state) {
   for each byte b in state
      h = (b>>4) && 0x0f   # high order 4 bits
      l = b && 0x0f        # low order 4 bits
      b = S[h,l]           # look up in the S-Box
   end for
}
where S[16,16] is (in hexadecimal digits):

   | 0  1  2  3  4  5  6  7  8  9  a  b  c  d  e  f
---|--|--|--|--|--|--|--|--|--|--|--|--|--|--|--|--|
00 |63 7c 77 7b f2 6b 6f c5 30 01 67 2b fe d7 ab 76 
10 |ca 82 c9 7d fa 59 47 f0 ad d4 a2 af 9c a4 72 c0 
20 |b7 fd 93 26 36 3f f7 cc 34 a5 e5 f1 71 d8 31 15 
30 |04 c7 23 c3 18 96 05 9a 07 12 80 e2 eb 27 b2 75 
40 |09 83 2c 1a 1b 6e 5a a0 52 3b d6 b3 29 e3 2f 84 
50 |53 d1 00 ed 20 fc b1 5b 6a cb be 39 4a 4c 58 cf 
60 |d0 ef aa fb 43 4d 33 85 45 f9 02 7f 50 3c 9f a8 
70 |51 a3 40 8f 92 9d 38 f5 bc b6 da 21 10 ff f3 d2 
80 |cd 0c 13 ec 5f 97 44 17 c4 a7 7e 3d 64 5d 19 73 
90 |60 81 4f dc 22 2a 90 88 46 ee b8 14 de 5e 0b db 
a0 |e0 32 3a 0a 49 06 24 5c c2 d3 ac 62 91 95 e4 79 
b0 |e7 c8 37 6d 8d d5 4e a9 6c 56 f4 ea 65 7a ae 08 
c0 |ba 78 25 2e 1c a6 b4 c6 e8 dd 74 1f 4b bd 8b 8a 
d0 |70 3e b5 66 48 03 f6 0e 61 35 57 b9 86 c1 1d 9e 
e0 |e1 f8 98 11 69 d9 8e 94 9b 1e 87 e9 ce 55 28 df 
f0 |8c a1 89 0d bf e6 42 68 41 99 2d 0f b0 54 bb 16 

ShiftRows() - The SubBytes() procedure performs a cyclic left shift operation on each row of bytes in the state. The result is stored back to the state as shown below. The S-Box is presented at the end of the section.

ShiftRows(state) {
   Row[0..3] = state               # copying state to rows
   Row[1] = LeftRotate(Row[1],1)   # left rotating by 1 byte
   Row[2] = LeftRotate(Row[2],2)   # left rotating by 2 bytes
   Row[3] = LeftRotate(Row[3],3)   # left rotating by 3 bytes
   state = Row[0..3]               # copying rows to state
}

MixColumns() - The MixColumns() procedure performs a matrix multiplication of the state with a static matrix. Details of the MixColumns() algorithm are given in next tutorials.

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