AES
Advanced Encryption Standard
Advanced Encryption Standard
• Adopted by National Institute of Standards
and Technology (NIST) on May 26, 2002.
• AES is a simple design, a high speed
algorithm, with low memory costs.
• AES is a symmetric block cipher.
– The same key is used to encrypt and decrypt
the message.
– The plain text and the cipher text are the
same size.
AES Block
• AES has a fixed block size of 128 bits called a
state
ABCDEFGHIJKLMNOP
A E I M 41 45 49 4D
(ASCII)
B F J N 42 46 4A 4E
C G K O 43 47 4B 4F
D H L P 44 48 4C 50
AES Key
• AES key is either 128 bits, 192 bits or
256 bits
128 bits (4 words):
11 22 33 44 55 66 77 88 99 00 AA BB CC DD EE FF
11 22 33 44
55 66 77 88
99 00 AA BB
CC DD EE FF
AES Key
or 192 bits (6 words) or 256 bits (8 words)
1122334455667788 1122334455667788
9900AABBCCDDEEFF 9900AABBCCDDEEFF
1122334455667788 1122334455667788
9900AABBCCDDEEFF
11 22 33 44
11 22 33 44
55 66 77 88 55 66 77 88
99 00 AA BB 99 00 AA BB
CC DD EE FF CC DD EE FF
11 22 33 44 11 22 33 44
55 66 77 88 55 66 77 88
99 00 AA BB
CC DD EE FF
Comparisons
Expanded
Key Length Key Length Block Size Number of
(Nk words) (words) (Nb words) Rounds Nr
AES-128 4 44 4 10
AES-192 6 52 4 12
AES-256 8 60 4 14
4 10
Rijndael - 128 4 44 6 12
8 14
4 12
Rijndael - 192 6 52 6 12
8 14
4 14
Rijndael - 256 8 60 6 14
8 14
DES 2* 256 2 16
*
of 64 bits, only 56 are used
Security
• The key security feature is the size of the
key.
Assuming that one could build a machine that
could recover a DES key in a second (i.e., try
255 keys per second), then it would take that
machine approximately 149 thousand-billion
(149 trillion) years to crack a 128-bit AES key.
To put that into perspective, the universe is
believed to be less than 20 billion years old.
• Accepting Moore's Law, doubling
processor speed every 18 months, AES
will be secure for another 109.5 years.
AES Operations
• AES Operates on the binary field GF(28).
– This can be represented as a polynomial b(x)
with binary coefficients b {0,1}:
b7x7 + b6x6 + b5x5 + b4x4 + b3x3 + b2x2 + b1x + b0
• Multiplication in GF(28) consists of
multiplying two polynomials modulo an
irreducible polynomial of degree 8.
– AES uses the following irreducible polynomial
m(x) = x8 + x4 + x3 + x + 1
AES Algorithm
KeyExpansion(byte key[4*Nk], word w[Nb*(Nr+1)],Nk)
Cipher(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 step 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 = state
end
AES Algorithm
KeyExpansion(byte key[4*Nk], word w[Nb*(Nr+1)],Nk)
Cipher(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 step 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 = state
end
AES Algorithm
Key Expansion
– Sample Key:
11223344556677889900AABBCCDDEEFF
• The first 4 (Nk) words are set equal to the key
w[0] 11 22 33 44
w[1] 55 66 77 88
w[2] 99 00 AA BB
w[3] CC DD EE FF
AES Algorithm
Key Expansion
For words 4 through 43
i = Nk // Nk = 4
while (i < Nb*(Nr+1)) { // Nb*(Nr+1)= 4*(10+1)= 44
temp = w[ i – 1 ]
If ( i%Nk == 0 )
rotate word left 1 byte
process each byte through sbox
XOR with RCON[i/Nk-1] // just first byte of w[i]
w[ i ] = w[ i-4 ] XOR temp
i++}
AES Algorithm
Key Expansion
w[0] 11 22 33 44
w[1] 55 66 77 88
w[2] 99 00 AA BB
w[3] CC DD EE FF
i = Nk // Nk = 4 i=4
while (i < Nb*(Nr+1)) { // Nb*(Nr+1)= 4*(10+1)= 44
temp = w[ i - 1 ] temp = w[3] = CC DD EE FF
AES Algorithm
Key Expansion
If ( i%Nk == 0 ) temp = CC DD EE FF
rotate word left 1 bytetemp = DD EE FF CC
process each byte through sbox
temp = sbox[DD] sbox[EE] sbox[FF] sbox[CC]
= C1 28 16 4B
XOR with RCON[i/Nk-1] RCON[0] = 01
temp = (C1 01) 28 16 4B
temp = C0 28 16 4B
rCon – round Constants
Powers of x = 0x02
i 0 1 2 3 4 5 6 7
xi 0x01 0x02 0x04 0x08 0x10 0x20 0x40 0x80
Powers of x = 0x02
i 8 9 A B C D E
xi 0x1b 0x36 0x6c 0xd8 0xab 0x4d 0x9a
• rCon can be implemented with a look-up-table
• 2i in GF(28)
• Removes symmetry and linearity from key expansion.
AES Algorithm
Key Expansion
For words 4 through 43
i = Nk // Nk = 4 i=4
while (i < Nb*(Nr+1)) {// Nb*(Nr+1)= 4*(10+1)= 44
temp = W[i-1]
If (i%Nk == 0)
rotate word left 1 byte
process each byte through sbox
XOR with RCON[i] //temp = C0element
just first 28 of16w 4B
w[i] = w[i-4] XOR temp
w[i] = w[i-4] XOR temp
i++}
AES Algorithm
Key Expansion
w[0] 11 22 33 44
w[1] 55 66 77 88
w[2] 99 00 AA BB
w[3] CC DD EE FF
w[4] D1 0A 25 0F
i=4
temp = C0 28 16 4B
w[i] = w[i-4] XOR temp
w[4] = (11 C0) (22 28) (33 16) (44 4B)
w[4] = D1 0A 25 0F
AES Algorithm
Key Expansion
For words 4 through 43
i = Nk // Nk = 4 i=5
while (i < Nb*(Nr+1)) { // Nb*(Nr+1)= 4*(10+1)= 44
temp = w[i-1]
temp = w[4] = D1 0A 25 0F
If (i%Nk == 0)
rotate word left 1 byte
process each byte through sbox
XOR with RCON[i/Nk-1] // just first element of W
w[i] = w[i-4] XOR temp
AES Algorithm
Key Expansion
w[0] 11 22 33 44
w[1] 55 66 77 88
w[2] 99 00 AA BB
w[3] CC DD EE FF
w[4] D1 0A 25 0F
i=5
temp = D1 0A 25 0F
w[i] = w[i-4] XOR temp
w[5] = (55 D1) (66 0A) (77 25) (88 0F)
w[5] = 84 C6 52 87
Beginning Key Expansion for:
11 22 33 44 55 66 77 88 99 00 AA BB CC DD EE FF
i subword rCon w[i-4]XORtemp
w[i]
0 11 22 33 44
1 55 66 77 88
2 99 00 AA BB
3 CC DD EE FF
4 C1 28 16 4B C0 28 16 4B D1 0A 25 0F
5 84 6C 52 87
6 1D 6C F8 3C
7 D1 B1 16 C3
8 C8 47 2E 3E CA 47 2E 3E 1B 4D 0B 31
9 9F 21 59 B6
10 82 4D A1 8A
11 53 FC B7 49
12 B0 A9 3B ED B4 A9 3B ED AF E4 30 DC
13 30 C5 69 6A
14 B2 88 C8 E0
15 E1 74 7F A9
16 92 D2 D3 F8 9A D2 D3 F8 35 36 E3 24
17 05 F3 8A 4E
18 B7 7B 42 AE
19 56 0F 3D 07
20 76 27 C5 B1 66 27 C5 B1 53 11 26 95
21 56 E2 AC DB
22 E1 99 EE 75
23 B7 96 D3 72
24 90 66 40 A9 B0 66 40 A9 E3 77 66 3C
25 B5 95 CA E7
26 54 0C 24 92
27 E3 9A F7 E0
28 B8 68 E1 11 F8 68 E1 11 1B 1F 87 2D
29 AE 8A 4D CA
30 FA 86 69 58
31 19 1C 9E B8
32 9C 0B 6C D4 1C 0B 6C D4 07 14 EB F9
33 A9 9E A6 33
34 53 18 CF 6B
35 4A 04 51 D3
36 F2 D1 66 D6 E9 D1 66 D6 EE C5 8D 2F
37 47 5B 2B 1C
38 14 43 E4 77
39 5E 47 B5 A4
40 A0 D5 49 58 96 D5 49 58 78 10 C4 77
41 3F 4B EF 6B
42 2B 08 0B 1C
43 75 4F BE B8
AES Algorithm
KeyExpansion(byte key[4*Nk], word w[Nb*(Nr+1)],Nk)
Cipher(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 step 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 = state
end
AES Algorithm
KeyExpansion(byte key[4*Nk], word w[Nb*(Nr+1)],Nk)
Cipher(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 step 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 = state
end
AES Algorithm
AddRoundKey
Expanded Key
State
w[0] w[4]
41 45 49 4D 11 22 33 44
42 46 4A 4E 55 66 77 88
43 47 4B 4F 99 00 AA BB
44 48 4C 50 CC DD EE FF
After
AddRoundKey
41 11 45 55 49 99 4D CC 50 10 D0 81
42 22 46 66 4A 00 4E DD 60 20 4A 93
43 33 47 77 4B AA 4F EE 70 30 E1 A1
44 44 48 88 4C BB 50 FF 00 C0 F7 AF
AES Algorithm
KeyExpansion(byte key[4*Nk], word w[Nb*(Nr+1)],Nk)
Cipher(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 step 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 = state
end
AES Algorithm
SubBytes
• SubBytes is the SBOX for AES
• This make AES a non-linear cryptographic system.
• For every value of b there is a unique value for b’
– It is faster to use a substitution table (and easier).
b'0 x0 1
1 0 0 0 1 1 1 1
b'1 x1 1
1 1 0 0 0 1 1 1
b'2 1 1 1 0 0 0 1 1 x2 0
b'3 = 1 1 1 1 0 0 0 1 x3
+ 0
b'4 1 1 1 1 1 0 0 0 x4 0
0 1 1 1 1 1 0 0 x5
1
b'5
0 0 1 1 1 1 1 0 1
b'6 x6
0 0 0 1 1 1 1 1 0
b'7 x7
x is the inverse value of the byte b
AES Algorithm
SubBytes
Y
0 1 2 3 4 5 6 7 8 9 a b c d e f
0 63 7c 77 7b f2 6b 6f c5 30 1 67 2b fe d7 ab 76
1 ca 82 c9 7d fa 59 47 f0 ad d4 a2 af 9c a4 72 c0
2 b7 fd 93 26 36 3f f7 cc 34 a5 e5 f1 71 d8 31 15
3 4 c7 23 c3 18 96 5 9a 7 12 80 e2 eb 27 b2 75
4 9 83 2c 1a 1b 6e 5a a0 52 3b d6 b3 29 e3 2f 84
5 53 d1 0 ed 20 fc b1 5b 6a cb be 39 4a 4c 58 cf
6 d0 ef aa fb 43 4d 33 85 45 f9 2 7f 50 3c 9f a8
7 51 a3 40 8f 92 9d 38 f5 bc b6 da 21 10 ff f3 d2
X
8 cd 0c 13 ec 5f 97 44 17 c4 a7 7e 3d 64 5d 19 73
9 60 81 4f dc 22 2a 90 88 46 ee b8 14 de 5e 0b db
a e0 32 3a 0a 49 6 24 5c c2 d3 ac 62 91 95 e4 79
b e7 c8 37 6d 8d d5 4e a9 6c 56 f4 ea 65 7a ae 8
c ba 78 25 2e 1c a6 b4 c6 e8 dd 74 1f 4b bd 8b 8a
d 70 3e b5 66 48 3 f6 0e 61 35 57 b9 86 c1 1d 9e
e e1 f8 98 11 69 d9 8e 94 9b 1e 87 e9 ce 55 28 df
f 8c a1 89 0d bf e6 42 68 41 99 2d 0f b0 54 bb 16
AES Algorithm
SubBytes
State
50 10 D0 81 Sbox( 50 ) Sbox( 10 ) Sbox( D0 ) Sbox( 81 )
60 20 4A 93 Sbox( 60 ) Sbox( 20 ) Sbox( 4A ) Sbox( 93 )
70 30 E1 A1 Sbox( 70 ) Sbox( 30 ) Sbox( E1 ) Sbox( A1 )
00 C0 F7 AF Sbox( 00 ) Sbox( C0 ) Sbox( F7 ) Sbox( AF )
53 CA 70 0C
D0 B7 D6 DC
51 04 F8 32
63 BA 68 79
AES Algorithm
KeyExpansion(byte key[4*Nk],word w[Nb*(Nr+1)],Nk)
Cipher(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 step 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 = state
end
AES Algorithm
ShiftRows
• Simple routine which performs a left shift rows 1,
2 and 3 by 1, 2 and 3 bytes respectively
Before Shift Rows After Shift Rows
53 CA 70 0C 53 CA 70 0C
D0 B7 D6 DC B7 D6 DC D0
51 04 F8 32 F8 32 51 04
63 BA 68 79 79 63 BA 68
AES Algorithm
KeyExpansion(byte key[4*Nk], word w[Nb*(Nr+1)],Nk)
Cipher(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 step 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 = state
end
AES Algorithm - MixColumns
• This with shift rows provides diffusion
• The columns are considered polynomials over
GF(28) and multiplied modulo x4+1 with a(x)
where a(x) = {03}x3 + {01}x2 + {01}x + {02}
NOTE: x4+1 is relatively prime to a(x)
a’j (aj*a(x))mod(x4+1)
• This can also be written as matrix multiplication.
a ’0 02 03 01 01 a0
a ’1 01 02 03 01 a1
=
a ’2 01 01 02 03 a2
a ’3 03 01 01 02 a3
AES Algorithm - MixColumns
a ’0 02 03 01 01 a0 a’0a’=0 =2a2a
0 0 3a
+ 3a
1 1a+
2 aa
2 3+ a3
a ’1 01 02 03 01 a1 a’1a’=1 =a0a0 2a
+ 2a
1 13a
+23a
a2 3+ a3
=
a ’2 01 01 02 03 a2 a’2a’=2 =a0a0 a+1 a 12a
+22a
3a
2 +3 3a3
a ’3 03 01 01 02 a3 a’3a’=3 =3a3a
0 0 a
+1 a 1a+
2 a2a
2 +3 2a3
Addition is easy in GF(28) : Addition is just the XOR operation
Multiplication by 1 is easy in GF(28) : Multiplication by one is the identity
Multiplication by 2 in GF(28) takes some work:
. If multiplying by a value < 0x80 just shift all the bits
left by 1 . If multiplying by a value ≥ 0x80 shift
left by 1 and XOR with 0x1b . This prevents overflow
and keeps the values within range
To Multiply by 3 in GF(28) : a * 0x03 = a * (0x02 + 0x01) = (a * 0x02) (a * 0x01)
AES Algorithm
KeyExpansion(byte key[4*Nk], word w[Nb* (Nr+1)],Nk)
Cipher(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 step 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 = state
end
Sample Conversions
Input String Key Output String (HEX)
ABCDEFGHIJKLMNOP 11223344556677889900AABBCCDDEEFF BC4784A37D6F46452656B993D53393F5
ABCDEFGHIJKLMNOP 01223344556677889900AABBCCDDEEFF 855866490543FDF6504FC84088FEDCA0
ABCDEFFHIJKLMNOP 11223344556677889900AABBCCDDEEFF 372CCA446C0D391C4381392344630EE1
Input String(HEX) Key Output String (HEX)
00000000000000000000000000000000 00000000000000000000000000000000 66E94BD4EF8A2C3B884CFA59CA342B2E
00000000000000000000000000000000 00000000000000000000000000000001 0545AAD56DA2A97C3663D1432A3D1C84
00000000000000000000000000000001 00000000000000000000000000000001 A17E9F69E4F25A8B8620B4AF78EEFD6F
AES Algorithm
Encryption Decryption
PlainText Cipher Text
RoundKey AddRoundKey 1st Round RoundKey* AddRoundKey 1st Round
SubBytes InvShiftRows
ShiftRows Repeat InvSubBytes Repeat
Nr -1 Nr -1
MixColumns RoundKey* AddRoundKey
Round Round
RoundKey AddRoundKey InvMixColumns
SubBytes InvShiftRows
Last Last
ShiftRows InvSubBytes
Round Round
RoundKey AddRoundKey RoundKey* AddRoundKey
CipherText Plain Text
*
RoundKey Added in reverse order
Larger Plain Texts
• How to avoid frequency analysis?
Cipher Block Chaining
Padding
• If plaintext messages are not divisible by
16 bytes. Padding may be a solution.
• An easy method is to add a single 1 bit at
the end of the message followed by
enough 0’s to fill the block.
– If the block is filled, encode one more block
with a 1 followed by 0’s.
Attacks on AES
• Differential Cryptanalysis – Study of how
differences in input affect differences in
output.
– Greatly reduced due to high number of rounds.
• Linear Cryptanalysis – Study of correlations
between input and output.
– SBOX & Mix Columns are designed to frustrate
Linear Analysis
Attacks on AES
• Side Channel Attacks – Attacks based on
studying and measuring the actual
implementation of the code.
– For some implementations of AES the key has
been obtained in under 100 minutes.
• Computer running AES was 850MHz, Pentium III
running FreeBSD 4.8
Types of Side Channel Attacks
• Timing Attacks – Watches movement of
data in and out of the CPU or memory.
– It is difficult to retrieve an array element in a
time that is not dependent on the index value.
• Power Attacks – Watches power
consumption by CPU or memory.
– Changing one bit requires considerably less
power than changing all bits in a byte.
Attack Precautions
• Avoid use of arrays. Compute values in
SBOX and rCon.
• Design algorithms and devices to work
with constant time intervals. (independent
of key and plaintext.)
– Hidden CPU timing data is a threat.
• Use same memory throughout, Cache is
faster than DRAM
• Compute Key Expansion on the fly.
• Utilize pipelining to stabilize CPU power
consumption.
Joan Daemen & Vincent Rijmen’s
AES Selling Points
• Extremely fast compared to other block
ciphers. (tradeoff between size and speed)
• The round transformation is parallel by
design. Important in dedicated hardware.
• Amenable to pipelining
• The cipher does not use arithmetic
operations so has no bias towards big or
little endian architectures.
Joan Daemen & Vincent Rijmen’s
AES Selling Points
• Fully Self-supporting. Does not use
Sboxes of other ciphers, bits from Rand
tables, digits of or any other such jokes.
• Is not based on obscure or not well
understood processes
• The tight cipher design does not leave
enough room to hide a trap door.
Joan Daemen & Vincent Rijmen’s
AES Limitations
• The inverse cipher is less suited to smart
cards, as it takes more codes and cycles.
• The cipher and inverse cipher make use of
different codes and/or tables.
• In hardware, The inverse cipher can only
partially re-use circuitry which implements
the cipher.
References
About AES
AES Proposal : Rijndael
Joan Daemen, Vincent Rijmen,
2nd version of document to NIST
Polynomials in the Nations Service: Using Algebra to Design the
Advanced Encryption Standard Susan Landau
The Mathmatical Association of America,
Monthly 111 Feb 2004 Page(s):89-117
Selecting the Advanced Encryption Standard Burr, W.E.;
Security & Privacy Magazine, IEEE
Volume 1, Issue 2, Mar-Apr 2003 Page(s):43 - 52
Title: Introduction to Cryptography
Author: Johannes A Buchman
Publisher: Springer; 2 edition (July 13, 2004)
References
Security and Attacking AES
Power-analysis attack on an ASIC AES implementation
Ors, S.B.; Gurkaynak, F.; Oswald, E.; Preneel, B.;Information Technology:
Coding and Computing, 2004. Proceedings. ITCC 2004. International
Conference onVolume 2, 2004 Page(s):546 - 552 Vol.2
Algebraic attacks on cipher systems
Penzhorn, W.T.;
AFRICON, 2004. 7th AFRICON Conference in Africa
Volume 2, 2004 Page(s):969 - 974 Vol.2
Cache-Timing attacks on AES Daniel J Bernstein
Preliminary version of report to National Science Foundation, grant CCR-
9983950
References
Applications / Implementations: AES
A high throughput low cost AES processor
Chih-Pin Su; Tsung-Fu Lin; Chih-Tsiun Huang; Cheng-Wen Wu;
Communications Magazine, IEEE
Volume 41, Issue 12, Dec. 2003 Page(s):86 - 91
An efficient FPGA implementation of advanced encryption standard
algorithm
Shuenn-Shyang Wang; Wan-Sheng Ni;
Circuits and Systems, 2004. ISCAS '04.
Volume 2, 23-26 May 2004 Page(s):II - 597-600 Vol.2
High-speed VLSI architectures for the AES algorithm
Xinmiao Zhang; Parhi, K.K.;
Very Large Scale Integration (VLSI) Systems
Volume 12, Issue 9, Sept. 2004 Page(s):957 – 967
Fast implementation of AES cryptographic algorithms in smart cards
Chi-Feng Lu; Yan-Shun Kao; Hsia-Ling Chiang; Chung-Huang Yang;
Security Technology, 2003.
14-16 Oct. 2003 Page(s):573 - 579
References
Applications / Implementations : AES
A new VLSI implementation of the AES algorithm
Liang Deng; Hongyi Chen;
Communications, Circuits and Systems and West Sino Expositions, IEEE
2002 International Conference on
Volume 2, 29 June-1 July 2002 Page(s):1500 - 1504 vol.2
