The Advanced Encryption Standard (AES) Simplified.

The Advanced Encryption Standard (AES) Simplified

Cryptosystems and Secrecy

With cryptosystems, we desire perfect secrecy: the probability that the contents of some intercepted data corresponds to some plaintext message is unaltered by knowledge of the ciphertext for that message.

Measuring the strength for cryptosystem by what is known as its work factor:

the amount of time needed to decipher a message without knowledge of the key. A cryptosystem is considered secure when its workfactor is exponential in the length of the key: 2.

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Cryptosystem Design

General goals for designing secure encryption algorithms: Confusion

Diffusion

A good encryption algorithm would satisfy the following two criteria:

No output bit should be a linear function of the input bits. In other words, the algorithm must induce non-linearity. This ensures confusion.

Avalanche Criteria: the probability of changing a given bit in the output is ½ when any subset of the input bits are complemented

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Advanced Encryption Standard (AES)

the US "standard" secret key cryptosystem, replacing DES (Data Encryption Standard, adopted in 1977)

AES is the result of a three year competition. This competition was announced in September 1997 and had entries from 12 different countries

The one submission that eventually won was called "Rijndael" and was invented by two Belgians, Joan Daemen and Vincent Rijmen.

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A Brief History of DES

In 1974, IBM proposed "Lucifer", an encryption algorithm that uses 64-bit keys. Two years later, NBS (in consultation with NSA) made a modified version of that algorithm into a standard.

DES takes in 64 bits of data, employs a 56-bit key, and executes 16 cycles of substitution and permutation before outputting 64 bits of encrypted data.

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A Brief History of DES

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A Brief History of DES

In the summer of 1998, the Electronic Frontier Foundation (EFF) built a DES cracker machine at a cost of $250,000 It had 1536 chips, worked at a rate of 88 billion keys per second, and was able to break a DES encrypted message in 56 hours One year later, with the cracker working in tandem with 100,000 PCs over the Internet, a DES encrypted message was cracked in only 22 hours. One common way to make DES more secure today is to encrypt three times using DES.

triple-DES (3DES). 3DES is extremely slow, so a better algorithm was needed.

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Requirements for AES

AES had to be a private key algorithm. It had to use a shared secret key.

It had to support the following key sizes: 128 bits ( = 3.4 x 10 keys, equivalent to 2560-bit RSA)

192 bits ( = 6.2 x 10 keys)

256 bits ( = 1.1 x 10 keys)

DES uses only 56-bit keys, giving a key space of 7.2 x 10 keys

If you were able to search half the DES key space in 1 second, then on average, it would take 149 trillion years to crack a 128-bit AES key.

38

57

77

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Requirements for AES

It had to satisfy certain engineering criteria:performance, efficiency, implementability, and flexibility.

Rijndael can be implemented easily in both hardware and software,

has realizations that require little memory (so the algorithm can be used in smartcards).

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Requirements for AESIt had to be a block cipher

an encryption algorithm structured in terms of an internal function and runs that function repeatedly on the input.

Each iteration is called a round;

AES uses 10 rounds.

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Requirements for AES

AES is also an instance of a Feistel cipher, a special case of a block cipher.

The input to such a cipher consists of 2t bits.

The input is first divided into 2 parts:

L and R

The cipher then proceeds in rounds.

In the i-th round, Li := Ri-1

Ri := Li-1 XOR f(Ri-1, ki),

where f is some function, and k is some number derived from the key, to be used in round i.

0 0

i

i

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The AES Cipher

Block length is limited to 128 bit

The key size can be independently specified to 128, 192 or 256 bits

Key size (words/bytes/bits) 4/16/128 6/24/192 8/32/256

Number of rounds 10 12 14

Expanded key size (words/byte) 44/176 52/208 60/240

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The AES CipherKey received as input array of 4 rows and Nk columnsNk = 4,6, or 8, parameter which depends key sizeInput key is expanded into an array of 44/52/60 words of 32 bits each

4 different words serve as a key for each round

k0 k4 k8 k12

k1

k2

k3

k5

k6

k7

k9

k10

k11

k13

k14

k15

w0 w1 w2 …… w42 w43

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The AES Cipher

Single 128 bit block as input

Copied to a State array with Nb columns (Nb=4)

in0 in4 in8 in12

in1

in2

in3

in5

in6

in7

in9

in10

in11

in13

in14

in15

S00 S01 S02 S03

S10

S20

S30

S11

S21

S31

S12

S22

S32

S13

S23

S33

o0 o4 o8 o12

o1

o2

o3

o5

o6

o7

o9

o10

o11

o13

o14

o15

Input State array Output

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The AES Cipher

Number of rounds, Nr, depends on key size

Each round is a repetition of functions that perform a transformation over State array

Consists of 4 main functions: one permutation and three substitutions

Substitute bytes, Shift rows, Mix columns, Add round key

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The AES Cipher

AddRoundKey() – round key is added to the State using XOR operationMixColumns() – takes all the columns of the State and mixes their data, independently of one another, making use of arithmetic over GF(2^8)ShiftRows() – processes the State by cyclically shifting the last three rows of the State by different offsetsSubBytes() – uses S-box to perform a byte-by-byte substitution of State

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The AES CipherAdd round key

Substitute bytes

Shift rows

Mix columns

Add Round key

Substitute bytes

Shift rows

Mix columns

Add round key

Substitute bytes

Shift rows

Add round key

plaintext

Cipher text

keyW[4,7] W[36,39

]W[40,43]

Round 1

Round 9

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The AES CipherCipher(byte in[4*Nb], byte out[4*Nb], word w[Nb*(Nr+1)])Begin byte state[4,Nb] state = in AddRoundKey(state, w[0, Nb-1])

for round=1 to Nr-1 SubBytes(state) ShiftRows(state) MixColumns(state) AddRoundKey(state, w[round*Nb, round+1)*Nb-1]) end for

SubBytes(state) ShiftRows(state) AddRoundKey(state, w[Nr*Nb, (Nr+1)*Nb-1)

Out = stateend

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The AES Cipher

Only Add round key makes use of the key

Other three functions are used for diffusion and confusion

Final round consists of only three stages

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The AES Inverse CipherAdd round key

Inv. Shift rows

Inv. Sub bytes

Add round key

Inv. Mix Columns

Inv. Shift rows

Inv. Sub bytes

Add round key

Inv. Mix columns

Inv. Shift rows

Inv. Sub bytes

Add round key

ciphertext

plaintext

keyW[36,39]

W[4,7] W[0,3]R

ound 1

Round 9

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The AES Inverse CipherInvCipher(byte in[4*Nb], byte out[4*Nb], word w[Nb*(Nr+1)])Begin byte state[4,Nb] state = in AddRoundKey(state, w[Nr*Nb, (Nr+1)*Nb-1)

for round=1 to Nr-1 InvShiftRows(state) InvSubBytes(state) AddRoundKey(state, w[round*Nb, round+1)*Nb-1]) InvMixColumns(state) end for

InvShiftRows(state) InvSubBytes(state) AddRoundKey(state, w[0, Nb-1])

Out = stateend

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The AES Inverse Cipher

Decryption algorithm uses the expanded key in reverse orderAll functions are easily reversible and their inverse form is used in decryptionDecryption algorithm is not identical to the encryption algorithmAgain, final round consists of only three stages

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