Chapter 5 module 3

Advanced EncryptionAdvanced Encryption
Standard (AES)Standard (AES)
Daneshwari I. HattiDaneshwari I. Hatti
1

Advanced Encryption StandardAdvanced Encryption Standard
"It seems very simple.""It seems very simple."
"It is very simple. But if you don't know what"It is very simple. But if you don't know what
the key is it's virtually indecipherable."the key is it's virtually indecipherable."
——Talking to Strange Men,Talking to Strange Men, Ruth RendellRuth Rendell
2

AES OriginsAES Origins
 clear a replacement for DES was neededclear a replacement for DES was needed
have theoretical attacks that can break ithave theoretical attacks that can break it
have demonstrated exhaustive key search attackshave demonstrated exhaustive key search attacks
 can use Triple-DES – but slow, has small blockscan use Triple-DES – but slow, has small blocks
 US NIST issued call for ciphers in 1997US NIST issued call for ciphers in 1997
 15 candidates accepted in Jun 9815 candidates accepted in Jun 98
 5 were shortlisted in Aug-995 were shortlisted in Aug-99
 Rijndael was selected as the AES in Oct-2000Rijndael was selected as the AES in Oct-2000
 issued as FIPS PUB 197 standard in Nov-2001issued as FIPS PUB 197 standard in Nov-2001
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The AES Cipher - RijndaelThe AES Cipher - Rijndael
 designed by Rijmen-Daemen in Belgiumdesigned by Rijmen-Daemen in Belgium
 has 128/192/256 bit keys, 128 bit datahas 128/192/256 bit keys, 128 bit data
 anan iterativeiterative rather thanrather than FeistelFeistel ciphercipher
processesprocesses data as block of 4 columns of 4 bytesdata as block of 4 columns of 4 bytes
operates on entire data block in every roundoperates on entire data block in every round
 designed to have:designed to have:
resistance against known attacksresistance against known attacks
speed and code compactness on many CPUsspeed and code compactness on many CPUs
design simplicitydesign simplicity
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AESAES
EncryptionEncryption
ProcessProcess
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AES StructureAES Structure
 data block ofdata block of 4 columns of 4 bytes is state4 columns of 4 bytes is state
 key is expanded to array of wordskey is expanded to array of words
 has 9/11/13 rounds in which state undergoes:has 9/11/13 rounds in which state undergoes:
byte substitution (1 S-box used on every byte)byte substitution (1 S-box used on every byte)
shift rows (permute bytes between groups/columns)shift rows (permute bytes between groups/columns)
mix columns (subs using matrix multiply of groups)mix columns (subs using matrix multiply of groups)
add round key (XOR state with key material)add round key (XOR state with key material)
view as alternating XOR key & scramble data bytesview as alternating XOR key & scramble data bytes
 initial XOR key material & incomplete last roundinitial XOR key material & incomplete last round
 with fast XOR & table lookup implementationwith fast XOR & table lookup implementation
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Some Comments on AESSome Comments on AES
1.1. anan iterativeiterative rather thanrather than FeistelFeistel ciphercipher
2.2. key expanded into array of 32-bit wordskey expanded into array of 32-bit words
1.1. four words form round key in each roundfour words form round key in each round
3.3. 4 different stages are used as shown4 different stages are used as shown
4.4. has a simple structurehas a simple structure
5.5. onlyonly AddRoundKey uses keyAddRoundKey uses key
6.6. AddRoundKey a form of Vernam cipherAddRoundKey a form of Vernam cipher
7.7. each stage is easily reversibleeach stage is easily reversible
8.8. decryption uses keys in reverse orderdecryption uses keys in reverse order
9.9. decryption does recover plaintextdecryption does recover plaintext
10.10.final round has only 3 stagesfinal round has only 3 stages8

Substitute BytesSubstitute Bytes
 a simple substitution of each bytea simple substitution of each byte
 uses one table of 16x16 bytes containing auses one table of 16x16 bytes containing a
permutation of all 256 8-bit valuespermutation of all 256 8-bit values
 each byte of state is replaced by byte indexed byeach byte of state is replaced by byte indexed by
row (left 4-bits) & column (right 4-bits)row (left 4-bits) & column (right 4-bits)
eg. byte {95} is replaced by byte in row 9 column 5eg. byte {95} is replaced by byte in row 9 column 5
which has value {2A}which has value {2A}
 S-box constructed using defined transformationS-box constructed using defined transformation
of values in GF(2of values in GF(288
))
 designed to be resistant to all known attacksdesigned to be resistant to all known attacks
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Substitute BytesSubstitute Bytes
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Substitute Bytes ExampleSubstitute Bytes Example
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Shift RowsShift Rows
 a circular byte shift in each eacha circular byte shift in each each
11stst
row is unchangedrow is unchanged
22ndnd
row does 1 byte circular shift to leftrow does 1 byte circular shift to left
3rd row does 2 byte circular shift to left3rd row does 2 byte circular shift to left
4th row does 3 byte circular shift to left4th row does 3 byte circular shift to left
 decrypt inverts using shifts to rightdecrypt inverts using shifts to right
 since state is processed by columns, this stepsince state is processed by columns, this step
permutes bytes between the columnspermutes bytes between the columns
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Mix ColumnsMix Columns
each column is processed separatelyeach column is processed separately
each byte is replaced by a valueeach byte is replaced by a value
dependent on all 4 bytes in the columndependent on all 4 bytes in the column
effectively a matrix multiplication in GF(2effectively a matrix multiplication in GF(288
))
using prime poly m(x) =xusing prime poly m(x) =x88
+x+x44
+x+x33
+x+1+x+1
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Mix Columns ExampleMix Columns Example
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AES ArithmeticAES Arithmetic
uses arithmetic in the finite field GF(2uses arithmetic in the finite field GF(288
))
with irreducible polynomialwith irreducible polynomial
m(x) = xm(x) = x88
+ x+ x44
+ x+ x33
+ x + 1+ x + 1
which iswhich is (100011011)(100011011) oror {11b}{11b}
 e.g.e.g.
{02} • {87} mod {11b} = (1 0000 1110) mod {11b}{02} • {87} mod {11b} = (1 0000 1110) mod {11b}
= (1 0000 1110) xor (1 0001 1011) = (0001 0101)= (1 0000 1110) xor (1 0001 1011) = (0001 0101)
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Mix ColumnsMix Columns
 can express each col as 4 equationscan express each col as 4 equations
to derive each new byte in colto derive each new byte in col
 decryption requires use of inverse matrixdecryption requires use of inverse matrix
with larger coefficients, hence a little harderwith larger coefficients, hence a little harder
 have an alternate characterisationhave an alternate characterisation
each column a 4-term polynomialeach column a 4-term polynomial
with coefficients in GF(2with coefficients in GF(288
))
and polynomials multiplied modulo (xand polynomials multiplied modulo (x44
+1)+1)
coefficients based on linear code withcoefficients based on linear code with
maximal distance between codewordsmaximal distance between codewords
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Add Round KeyAdd Round Key
XOR state with 128-bits of the round keyXOR state with 128-bits of the round key
again processed by column (thoughagain processed by column (though
effectively a series of byte operations)effectively a series of byte operations)
inverse for decryption identicalinverse for decryption identical
since XOR own inverse, with reversed keyssince XOR own inverse, with reversed keys
designed to be as simple as possibledesigned to be as simple as possible
a form of Vernam cipher on expanded keya form of Vernam cipher on expanded key
requires other stages for complexity / securityrequires other stages for complexity / security
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AES Key ExpansionAES Key Expansion
takes 128-bit (16-byte) key and expandstakes 128-bit (16-byte) key and expands
into array of 44/52/60 32-bit wordsinto array of 44/52/60 32-bit words
start by copying key into first 4 wordsstart by copying key into first 4 words
then loop creating words that depend onthen loop creating words that depend on
values in previous & 4 places backvalues in previous & 4 places back
in 3 of 4 cases just XOR these togetherin 3 of 4 cases just XOR these together
11stst
word in 4 has rotate + S-box + XOR roundword in 4 has rotate + S-box + XOR round
constant on previous, before XOR 4constant on previous, before XOR 4thth
backback
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AES Key ExpansionAES Key Expansion
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Key Expansion RationaleKey Expansion Rationale
designed to resist known attacksdesigned to resist known attacks
design criteria includeddesign criteria included
knowing part key insufficient to find many moreknowing part key insufficient to find many more
invertible transformationinvertible transformation
fast on wide range of CPU’sfast on wide range of CPU’s
use round constants to break symmetryuse round constants to break symmetry
diffuse key bits into round keysdiffuse key bits into round keys
enough non-linearity to hinder analysisenough non-linearity to hinder analysis
simplicity of descriptionsimplicity of description
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AESAES
ExampleExample
KeyKey
ExpansionExpansion
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AESAES
ExampleExample
EncryptionEncryption
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AESAES
ExampleExample
AvalancheAvalanche
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AES DecryptionAES Decryption
AES decryption is not identical toAES decryption is not identical to
encryption since steps done in reverseencryption since steps done in reverse
but can define an equivalent inversebut can define an equivalent inverse
cipher with steps as for encryptioncipher with steps as for encryption
but using inverses of each stepbut using inverses of each step
with a different key schedulewith a different key schedule
works since result is unchanged whenworks since result is unchanged when
swap byte substitution & shift rowsswap byte substitution & shift rows
swap mix columns & add (tweaked) roundswap mix columns & add (tweaked) round
keykey
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AES DecryptionAES Decryption
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Implementation AspectsImplementation Aspects
can efficiently implement on 8-bit CPUcan efficiently implement on 8-bit CPU
byte substitution works on bytes using a tablebyte substitution works on bytes using a table
of 256 entriesof 256 entries
shift rows is simple byte shiftshift rows is simple byte shift
add round key works on byte XOR’sadd round key works on byte XOR’s
mix columns requires matrix multiply inmix columns requires matrix multiply in
GF(2GF(288
) which works on byte values, can be) which works on byte values, can be
simplified to use table lookups & byte XOR’ssimplified to use table lookups & byte XOR’s
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Implementation AspectsImplementation Aspects
can efficiently implement on 32-bit CPUcan efficiently implement on 32-bit CPU
redefine steps to use 32-bit wordsredefine steps to use 32-bit words
can precompute 4 tables of 256-wordscan precompute 4 tables of 256-words
then each column in each round can bethen each column in each round can be
computed using 4 table lookups + 4 XORscomputed using 4 table lookups + 4 XORs
at a cost of 4Kb to store tablesat a cost of 4Kb to store tables
designers believe this very efficientdesigners believe this very efficient
implementation was a key factor in itsimplementation was a key factor in its
selection as the AES cipherselection as the AES cipher
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ReferencesReferences
1. William Stallings , “Cryptography and Network Security Principles and Practice”,
Pearson Education Inc., 6th Edition, 2014, ISBN: 978-93-325-1877-3
2. Bruce Schneier, “Applied Cryptography Protocols, Algorithms, and Source code in
C”, Wiley Publications, 2nd Edition, ISBN: 9971-51-348-X
3. Cryptography and Network Security, Behrouz A. Forouzan, TMH, 2007.
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Chapter 5 module 3

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Chapter 5 module 3