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Encrypt It

Keep Your Data Secure with the New Advanced Encryption

Standard

James McCaffrey

This article assumes you're familiar with C# and bit manipulation

Level of Difficulty 1 2 3

Download the code for this article: AES.exe

(143KB)

SUMMARY The Advanced Encryption Standard (AES) is a National Institute of Standards and Technology

specification for the encryption of electronic data. It is expected to become the accepted means of encrypting

digital information, including financial, telecommunications, and government data. This article presents an overview

of AES and explains the algorithms it uses. Included is a complete C# implementation and examples of

encrypting .NET data. After reading this article you will be able to encrypt data using AES, test AES-based software,

and use AES encryption in your systems.

he National Institute of Standards and Technology (NIST) established the new Advanced Encryption

Standard (AES) specification on May 26, 2002. In this article I will provide a working implementation of

AES written in C#, and a complete explanation of exactly what AES is and how the code works. I'll show

you how to encrypt data using AES and extend the code given here to develop a commercial-quality AES

class. I'll also explain how and why to incorporate AES encryption into your software systems, and how to

test AES-based software.

Note that the code presented in this article and any other implementation based on this article is subject to

applicable Federal cryptographic module export controls (see Commercial Encryption Export Controls

for the exact

regulations).

AES is a new cryptographic algorithm that can be used to protect electronic data. Specifically, AES is an iterative,

symmetric-key block cipher that can use keys of 128, 192, and 256 bits, and encrypts and decrypts data in blocks

of 128 bits (16 bytes). Unlike public-key ciphers, which use a pair of keys, symmetric-key ciphers use the same ke

to encrypt and decrypt data. Encrypted data returned by block ciphers have the same number of bits that the input

data had. Iterative ciphers use a loop structure that repeatedly performs permutations and substitutions of the

input data. Figure 1 shows AES in action encrypting and then decrypting a 16-byte block of data using a 192-bit

key.

Figure 1 Some Data

AES is the successor to the older Data Encryption Standard (DES). DES was approved as a Federal standard in

1977 and remained viable until 1998 when a combination of advances in hardware, software, and cryptanalysis

theory allowed a DES-encrypted message to be decrypted in 56 hours. Since that time numerous other successful

attacks on DES-encrypted data have been made and DES is now considered past its useful lifetime.

In late 1999, the Rijndael (pronounced "rain doll") algorithm, created by researchers Joan Daemen and Vincent

Rijmen, was selected by the NIST as the proposal that best met the design criteria of security, implementation

efficiency, versatility, and simplicity. Although the terms AES and Rijndael are sometimes used interchangeably,

they are distinct. AES is widely expected to become the de facto standard for encrypting all forms of electronic data

including data used in commercial applications such as banking and financial transactions, telecommunications, and

private and Federal information.

Overview of the AES Algorithm

The AES algorithm is based on permutations and substitutions. Permutations are rearrangements of data, and

substitutions replace one unit of data with another. AES performs permutations and substitutions using several

different techniques. To illustrate these techniques, let's walk through a concrete example of AES encryption using

the data shown in Figure 1.

The following is the 128-bit value that you will encrypt with the indexes array:

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00 11 22 33 44 55 66 77 88 99 aa bb cc dd ee ff

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

The 192-bit key value is:

00 01 02 03 04 05 06 07 08 09 0a 0b 0c 0d 0e 0f 10 11 12 13 14 15 16 17

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23

Figure 2 Sbox

When the AES constructor is called, two tables that will be used by the encryption method are initialized. The first

table is a substitution box named Sbox. It is a 16 × 16 matrix. The first five rows and columns of Sbox are shown

in Figure 2. Behind the scenes, the encryption routine takes the key array and uses it to generate a "key schedule"

table named w[], shown in Figure 3.

Figure 3 Key Sched.

The first Nk (6) rows of w[] are seeded with the original key value (0x00 through 0x17) and the remaining rows

are generated from the seed key. The variable Nk represents the size of the seed key in 32-bit words. You'll see

exactly how w[] is generated later when I examine the AES implementation. The point is that there are now many

keys to use instead of just one. These new keys are called the round keys to distinguish them from the original

seed key.

Figure 4 State

The AES encryption routine begins by copying the 16-byte input array into a 4×4 byte matrix named State (see

Figure 4). The AES encryption algorithm is named Cipher and operates on State[] and can be described in

pseudocode (see Figure 5

The encryption algorithm performs a preliminary processing step that's called AddRoundKey in the specification.

AddRoundKey performs a byte-by-byte XOR operation on the State matrix using the first four rows of the key

schedule, and XORs input State[r,c] with round keys table w[c,r].

For example, if the first row of the State matrix holds the bytes { 00, 44, 88, cc }, and the first column of the key

schedule is { 00, 04, 08, 0c }, then the new value of State[0,2] is the result of XORing State[0,2] (0x88) with w

[2,0] (0x08), or 0x80:

1 0 0 0 1 0 0 0

0 0 0 0 1 0 0 0 XOR

1 0 0 0 0 0 0 0

The main loop of the AES encryption algorithm performs four different operations on the State matrix, called

SubBytes, ShiftRows, MixColumns, and AddRoundKey in the specification. The AddRoundKey operation is the same

as the preliminary AddRoundKey except that each time AddRoundKey is called, the next four rows of the key

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schedule are used. The SubBytes routine is a substitution operation that takes each byte in the State matrix and

substitutes a new byte determined by the Sbox table. For example, if the value of State[0,1] is 0x40 and you want

to find its substitute, you take the value at State[0,1] (0x40) and let x equal the left digit (4) and y equal the right

digit (0). Then you use x and y as indexes into the Sbox table to find the substitution value, as shown in Figure 2.

ShiftRows is a permutation operation that rotates bytes in the State matrix to the left. Figure 6 shows how

ShiftRows works on State[]. Row 0 of State is rotated 0 positions to the left, row 1 is rotated 1 position left, row 2

is rotated 2 positions left, and row 3 is rotated 3 positions left.

Figure 6 Running ShiftRows on State

The MixColumns operation is a substitution operation that is the trickiest part of the AES algorithm to understand.

It replaces each byte with the result of mathematical field additions and multiplications of values in the byte's

column. I will explain the details of special field addition and multiplication in the next section.

Suppose the value at State[0,1] is 0x09, and the other values in column 1 are 0x60, 0xe1, and 0x04; then the

new value for State[0,1] is shown in the following:

State[0,1] = (State[0,1] * 0x01) +

(State[1,1] * 0x02) +

(State[2,1] * 0x03) +

(State[3,1] * 0x01)

= (0x09 * 0x01) + (0x60 * 0x02) + (0xe1 * 0x03) +

(0x04 * 0x01)

= 0x57

The addition and multiplication are special mathematical field operations, not the usual addition and multiplication

on integers.

The four operations SubBytes, ShiftRows, MixColumns, and AddRoundKey are called inside a loop that executes N

times—the number of rounds for a given key size, less 1. The number of rounds that the encryption algorithm uses

is either 10, 12, or 14 and depends on whether the seed key size is 128, 192, or 256 bits. In this example, because

Nr equals 12, the four operations are called 11 times. After this iteration completes, the encryption algorithm

finishes by calling SubBytes, ShiftRows, and AddRoundKey before copying the State matrix to the output

parameter.

In summary, there are four operations that are at the heart of the AES encryption algorithm. AddRoundKey

substitutes groups of 4 bytes using round keys generated from the seed key value. SubBytes substitutes individual

bytes using a substitution table. ShiftRows permutes groups of 4 bytes by rotating 4-byte rows. MixColumns

substitutes bytes using a combination of both field addition and multiplication.

Field Addition and Multiplication in GF(28)

As you've seen, the AES encryption algorithm uses fairly straightforward techniques for substitution and

permutation, except for the MixColumns routine. The MixColumns routine uses special addition and multiplication.

The addition and multiplication used by AES are based on mathematical field theory. In particular, AES is based on

a field called GF(28).

The GF(28) field consists of a set of 256 values from 0x00 to 0xff, plus addition and multiplication, hence the

(28). GF stands for Galois Field, named after the mathematician who founded field theory. One of the

characteristics of GF(28) is that the result of an addition or multiplication operation must be in the set {0x00 ...

0xff}. Although the theory of fields is rather deep, the net result for GF(28) addition is simple: GF(28) addition is

just the XOR operation.

Multiplication in GF(28) is trickier, however. As you'll see later in the C# implementation, the AES encryption and

decryption routines need to know how to multiply by only the seven constants 0x01, 0x02, 0x03, 0x09, 0x0b,

0x0d, and 0x0e. So instead of explaining GF(28) multiplication theory in general, I will explain it just for these

seven specific cases.

Multiplication by 0x01 in GF(28) is special; it corresponds to multiplication by 1 in normal arithmetic and works

the same way—any value times 0x01 equals itself.

Now let's look at multiplication by 0x02. As in the case of addition, the theory is deep, but the net result is fairly

simple. If the value being multiplied is less than 0x80, then the result of multiplication is just the value left-shifted

1 bit position. If the value being multiplied is greater than or equal to 0x80, then the result of multiplication is the

value left-shifted 1 bit position XORed with the value 0x1b. This prevents "field overflow" and keeps the product of

the multiplication in range.

Once you've established addition and multiplication by 0x02 in GF(28), you can use them to define multiplication

by any constant. To multiply by 0x03 in GF(28), you can decompose 0x03 as powers of 2 and additions. To multipl

an arbitrary byte b by 0x03, observe that 0x03 = 0x02 + 0x01. Thus:

b * 0x03 = b * (0x02 + 0x01)

= (b * 0x02) + (b * 0x01)

This can be done because you know how to multiply by 0x02 and 0x01 and how to perform addition. Similarly, to

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剩余13页未读，继续阅读

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内容反馈

草吃兔

2012-11-30

果然经典，不过貌似不能用作毕设翻译啊，文章真心不错
shankugan

2013-03-11

为什么不能用来毕设翻译？不能因为别人翻译过你就不去翻译了嘛…经典的东西，赞！

xlong1

粉丝: 2
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