Advanced Encryption Standard
Topics
Origin of AES
Basic AES
Inside Algorithm
Final Notes
Origin of AES
A replacement for DES was needed
Key size is too small
Can use Triple-DES but slow, small block
US NIST issued call for ciphers in 1997
15 candidates accepted in Jun 98
5 were shortlisted in Aug 99
AES Competition Requirements
Private key symmetric block cipher
128-bit data, 128/192/256-bit keys
Stronger & faster than Triple-DES
Provide full specification & design details
Both C & Java implementations
AES Evaluation Criteria
initial criteria:
security effort for practical cryptanalysis
cost in terms of computational efficiency
algorithm & implementation characteristics
final criteria
general security
ease of software & hardware implementation
implementation attacks
flexibility (in en/decrypt, keying, other factors)
AES Shortlist
After testing and evaluation, shortlist in Aug-99
MARS (IBM) - complex, fast, high security margin
RC6 (USA) - v. simple, v. fast, low security margin
Rijndael (Belgium) - clean, fast, good security margin
Serpent (Euro) - slow, clean, v. high security margin
Twofish (USA) - complex, v. fast, high security margin
Found contrast between algorithms with
few complex rounds versus many simple rounds
Refined versions of existing ciphers versus new
proposals
Rijndae: pronounce Rain-Dahl
The AES Cipher - Rijndael
Rijndael was selected as the AES in Oct-2000
An iterative rather than Feistel cipher
Designed by Vincent Rijmen and Joan Daemen in
Belgium
Issued as FIPS PUB 197 standard in Nov-2001
processes data as block of 4 columns of 4 bytes (128
bits)
operates on entire data block in every round
V. Rijmen
Rijndael design:
simplicity
has 128/192/256 bit keys, 128 bits data
resistant against known attacks
speed and code compactness on many CPUs
J. Daemen
Topics
Origin of AES
Basic AES
Inside Algorithm
Final Notes
AES Conceptual Scheme
Plaintext (128 bits)
AES
Key (128-256 bits)
Ciphertext (128 bits)
Multiple rounds
Rounds are (almost) identical
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First and last round are a little different
Overall Structure
High Level Description
No MixColumns
128-bit values
Data block viewed as 4-by-4 table of bytes
Represented as 4 by 4 matrix of 8-bit bytes.
Key is expanded to array of 32 bits words
1 byte
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Data Unit
Unit Transformation
Changing Plaintext to State
Topics
Origin of AES
Basic AES
Inside Algorithm
Final Notes
AES encryption round
current state
Byte
substitution
AES
S-box
Shift rows
Mix
columns
key
Key
schedule
round key
++
new state
Details of Each Round
SubBytes: Byte Substitution
A simple substitution of each byte
provide a confusion
Uses one S-box of 16x16 bytes containing a permutation of
all 256 8-bit values
Each byte of state is replaced by byte indexed by row (left
4-bits) & column (right 4-bits)
eg. byte {95} is replaced by byte in row 9 column 5
which has value {2A}
S-box constructed using defined transformation of values in
Galois Field- GF(28)
Galois : pronounce Gal-Wa
SubBytes and InvSubBytes
SubBytes Operation
The SubBytes operation involves 16 independent
byte-to-byte transformations. Interpret the byte as two
S1,1 = xy16
hexadecimal digits xy
SW implementation, use
row (x) and column (y) as
lookup pointer
xy16
SubBytes Table
Implement by Table Lookup
InvSubBytes Table
Sample SubByte Transformation
The SubBytes and InvSubBytes
transformations are inverses of each other.
ShiftRows
Shifting, which permutes the bytes.
A circular byte shift in each each
1st row is unchanged
2nd row does 1 byte circular shift to left
3rd row does 2 byte circular shift to left
4th row does 3 byte circular shift to left
In the encryption, the transformation
is called ShiftRows
In the decryption, the transformation
is called InvShiftRows and the shifting
is to the right
ShiftRows Scheme
ShiftRows and InvShiftRows
MixColumns
ShiftRows and MixColumns provide diffusion to
the cipher
Each column is processed separately
Each byte is replaced by a value dependent
on all 4 bytes in the column
Effectively a matrix multiplication in GF(28)
using prime poly m(x) =x8+x4+x3+x+1
MixColumns Scheme
The MixColumns transformation operates at the column level; it
transforms each column of the state to a new column.
MixColumn and InvMixColumn
AddRoundKey
XOR state with 128-bits of the round key
AddRoundKey proceeds one column at a time.
Inverse for decryption identical
adds a round key word with each state column
matrix
the operation is matrix addition
since XOR own inverse, with reversed keys
Designed to be as simple as possible
AddRoundKey Scheme
AES Round
AES Key Scheduling
takes 128-bits (16-bytes) key and expands
into array of 44 32-bit words
Key Expansion Scheme
Key Expansion submodule
RotWord performs a one byte circular left shift on
a word For example:
RotWord[b0,b1,b2,b3] = [b1,b2,b3,b0]
SubWord performs a byte substitution on each
byte of input word using the S-box
SubWord(RotWord(temp)) is XORed with
RCon[j] the round constant
Round Constant (RCon)
RCON is a word in which the three rightmost bytes are zero
It is different for each round and defined as:
RCon[j] = (RCon[j],0,0,0)
where RCon[1] =1 , RCon[j] = 2 * RCon[j-1]
Multiplication is defined over GF(2^8) but can be implement
in Table Lookup
Key Expansion Example (1st Round)
Example of expansion of a 128-bit cipher key
Cipher key = 2b7e151628aed2a6abf7158809cf4f3c
w0=2b7e1516 w1=28aed2a6 w2=abf71588 w3=09cf4f3c
Topics
Origin of AES
Basic AES
Inside Algorithm
Final Notes
AES Security
AES was designed after DES.
Most of the known attacks on DES were already
tested on AES.
Brute-Force Attack
Statistical Attacks
AES is definitely more secure than DES due to the
larger-size key.
Numerous tests have failed to do statistical analysis of
the ciphertext
Differential and Linear Attacks
There are no differential and linear attacks on AES as
yet.
Implementation Aspects
The algorithms used in AES are so simple
that they can be easily implemented using
cheap processors and a minimum amount
of memory.
Very efficient
Implementation was a key factor in its
selection as the AES cipher
Other Block Ciphers
Blowfish (Schneier, open)
Twofish (Schneier et al., open)
IDEA (patented)
Skipjack (NSA, Clipper)
...
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