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Effective Software
Implementation of
Advanced Encryption Standard
December 2014
Roman Oliynykov
Professor at
Information T...
Outline
 A few words about myself
 Brief history of AES/Rijndael
 AES properties
 Direct AES implementation and proble...
About myself (I)
 I’m from Ukraine (Eastern part of
Europe),
host country of Euro2012 football
championship
 I live in K...
About myself (II)
 Professor at Information Technologies Security
Department at Kharkov National University of
Radioelect...
Modern and effective solution:
Advanced Encryption Standard (AES)
 result of international public cryptographic competiti...
AES properties
 block length 128 bits only (subset of Rijndael which
supports 128, 192 and 256 bits)
 key length is 128,...
AES parameters: key length,
block size, number of rounds
AES: presentation of processing
bytes as a “cipher state”
AES: main steps
running key schedule procedure:
generation of all round keys
running encryption or decryption
procedure
...
AES: high-level structure
(pseudocode)
AES: high-level structure
(picture for 128 bit key)
AES: SubBytes transformation
AES: ShiftRows
transformation
AES: MixColumns
transformation
AES: AddRoundKey
transformation
AES round key generation (key
expansion)
NB: not all key length (128, 192, 256) must be supported; for many
applications i...
AES round key generation:
RotWord
AES round key generation:
SubBytes
AES round key generation:
round constant application
NB: without Rcon there would be equal blocks in ciphertext if plainte...
AES round key sequence
AES decryption (direct
presentation): reverse operations
in different order
AES/Rijndael design goals
 be extremely fast on 32 bit platforms (+++)
 be compact on hardware implementation with
small...
Direct implementation of AES
round function: SubBytes
16 operations (byte substitution)
Direct implementation of AES
round function: ShiftRows
12 operations (byte permutation)
AES: MixColumns
transformation
60 operations (logical and conditional):

3+ operations for each input byte (48+ total):
•...
Direct implementation of AES
round function

SubBytes: 16 operations (byte substitution)

ShiftRows: 12 operations (byte...
AES effective software
implementation: 32-bit platform
 three different operations can be united
into the single (!) look...
AES effective software
implementation: MixColumns
Matrix multiplication: 7 operations (4 memory look-ups + 3
XORs) instead...
AES round function operations
sequence variants:
Original:

SubBytes

ShiftRows

MixColumns
Equivalent:

ShiftRows

S...
AES effective software implementation:
MixColumns and SubBytes at one
precomputed table
SubBytes and MixColumns: 7 operati...
Fragment of OpenSSL AES source
code (based on Rijndael author's
implementation)
4 tables are needed; size of each table is...
Fragment of OpenSSL AES source
code (based on Rijndael author's
implementation)
ShiftRows is implemented as usual shift an...
AES effective software implementation:
extra memory optimization
Decreasing memory amount: single table (1 kByte instead o...
Main table size for the fastest and
compact optimized 32-bit AES
implementation
 fastest:
 (4 bytes) x (256 different en...
Number of 32-bit operations needed for a
single block encryption at main
transformation (having all round keys)
 ( (4 loo...
AES decryption: high-level
structure (pseudocode)
AES decryption: optimization
 SubBytes() and ShiftRows() transformations
commute, their sequence can be chaged
 The colu...
AES optimized decryption with
changed round keys
Additional details on AES
implementation
 two set of tables for encryption
 main optimized set (MixColumns, ShiftRows an...
Conclusions
 direct AES implementation is very slow (requires
many byte operations and conditions)
 three different roun...
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AES effecitve software implementation

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Slides of my lecture on effective AES implementation in software given at University of Bergen (Norway)

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AES effecitve software implementation

  1. 1. Effective Software Implementation of Advanced Encryption Standard December 2014 Roman Oliynykov Professor at Information Technologies Security Department Kharkov National University of Radioelectronics Head of Scientific Research Department JSC “Institute of Information Technologies” Ukraine Visiting professor at Samsung Advanced Technology Training Institute Korea ROliynykov@gmail.com
  2. 2. Outline  A few words about myself  Brief history of AES/Rijndael  AES properties  Direct AES implementation and problems with it  Methods for effective encryption implementation (proposed by Rijndael authors in their submission to AES competition)  Decryption optimization  Conclusions
  3. 3. About myself (I)  I’m from Ukraine (Eastern part of Europe), host country of Euro2012 football championship  I live in Kharkov (the second biggest city in the country, population is 1.5 million people), Eastern Ukraine (near Russia), former capital of the Soviet Ukraine (1918-1934) three Nobel prize winners worked at Kharkov University
  4. 4. About myself (II)  Professor at Information Technologies Security Department at Kharkov National University of Radioelectronics  courses on computer networks and operation system security, special mathematics for cryptographic applications  Head of Scientific Research Department at JSC “Institute of Information Technologies”  Scientific interests: symmetric cryptographic primitives synthesis and cryptanalysis  Visiting professor at Samsung Advanced Technology Training Institute  courses on computer networks and operation system security, software security, effective application and implementation of symmetric cryptography
  5. 5. Modern and effective solution: Advanced Encryption Standard (AES)  result of international public cryptographic competition (1997-2000)  had been chosen among 15 candidate ciphers (developed in the US, Belgium, Denmark, Germany, Israel, Japan, Switzerland, Armenia, etc.)  original name is Rijndael (developed by researchers from Belgium)  votes on 3rd AES conference had been given to this cipher, but the rest Twofish (US), MARS (US, IBM), E2 (Japan, Camellia predecessor), Serpent (Israel) are also remain strong  the most researched block cipher all over the world (2014, open publications)  basis for development of many other symmetric primitives
  6. 6. AES properties  block length 128 bits only (subset of Rijndael which supports 128, 192 and 256 bits)  key length is 128, 192 and 256 bits  uses Substitution-Permutation Network (SPN)  number of rounds (10,12,14) depends on key length  quite transparent design, algebraic structure (theoretically may be vulnerable to algebraic analysis)  quite effective in software (32-bit platforms) and hardware implementation
  7. 7. AES parameters: key length, block size, number of rounds
  8. 8. AES: presentation of processing bytes as a “cipher state”
  9. 9. AES: main steps running key schedule procedure: generation of all round keys running encryption or decryption procedure  or, for compact hardware implementation, sequential operations:  generation of the current round key  one encryption round
  10. 10. AES: high-level structure (pseudocode)
  11. 11. AES: high-level structure (picture for 128 bit key)
  12. 12. AES: SubBytes transformation
  13. 13. AES: ShiftRows transformation
  14. 14. AES: MixColumns transformation
  15. 15. AES: AddRoundKey transformation
  16. 16. AES round key generation (key expansion) NB: not all key length (128, 192, 256) must be supported; for many applications it’s enough to have the single key length
  17. 17. AES round key generation: RotWord
  18. 18. AES round key generation: SubBytes
  19. 19. AES round key generation: round constant application NB: without Rcon there would be equal blocks in ciphertext if plaintext and keys have equal blocks (1, 2 or 4 bytes repeats in plaintext and key)
  20. 20. AES round key sequence
  21. 21. AES decryption (direct presentation): reverse operations in different order
  22. 22. AES/Rijndael design goals  be extremely fast on 32 bit platforms (+++)  be compact on hardware implementation with small number of gates (++)  possibility to implement cipher on 8-bit smart- card processors actual for 1990th (++)  cryptographic strength (+)
  23. 23. Direct implementation of AES round function: SubBytes 16 operations (byte substitution)
  24. 24. Direct implementation of AES round function: ShiftRows 12 operations (byte permutation)
  25. 25. AES: MixColumns transformation 60 operations (logical and conditional):  3+ operations for each input byte (48+ total): • shift and conditional XOR (mult by 02) • XOR (mult by 03)  3 XORs for each row (12 total)
  26. 26. Direct implementation of AES round function  SubBytes: 16 operations (byte substitution)  ShiftRows: 12 operations (byte permutation)  MixColumns: 60 or even more operations (conditions will prevent effective pipelining)  AddRoundKey: 16 operations (logical) TOTAL: more than 102 operations per round
  27. 27. AES effective software implementation: 32-bit platform  three different operations can be united into the single (!) look-up table access:  SubBytes (non-linear)  ShiftRows (linear)  MixColumns (linear)  cipher consists of look-up table accesses and round key additions
  28. 28. AES effective software implementation: MixColumns Matrix multiplication: 7 operations (4 memory look-ups + 3 XORs) instead of 60:  32-bit XOR of 4 columns  each column depends on one input byte only  all 4 bytes in each column are precomputed and stored in advance
  29. 29. AES round function operations sequence variants: Original:  SubBytes  ShiftRows  MixColumns Equivalent:  ShiftRows  SubBytes  MixColumns
  30. 30. AES effective software implementation: MixColumns and SubBytes at one precomputed table SubBytes and MixColumns: 7 operations (4 memory look-ups + 3 XORs) total:  32-bit XOR of 4 columns  each column depends on one input byte only (already sent throw S-box)  all 4 bytes in each column are precomputed and stored in advance
  31. 31. Fragment of OpenSSL AES source code (based on Rijndael author's implementation) 4 tables are needed; size of each table is 256 * 4 = 1 kByte
  32. 32. Fragment of OpenSSL AES source code (based on Rijndael author's implementation) ShiftRows is implemented as usual shift and mask of 32-bit register; SubBytes and MixColumns are implemented as memory lookups (8 bit → 32 bit)
  33. 33. AES effective software implementation: extra memory optimization Decreasing memory amount: single table (1 kByte instead of 4 tables of 1 kB each)
  34. 34. Main table size for the fastest and compact optimized 32-bit AES implementation  fastest:  (4 bytes) x (256 different entries to S-box) x x (4 different positions for ShiftRow) == 4 kbytes  compact optimized:  (4 bytes) x (256 different entries to S-box) == == 1 kbyte  three additional operations in C ( << , >>, | or ^) are needed besides a table look-up NB: for reaching highest performance precomputed tables and processing data must fit into L1 processor cache (32-64kBytes for modern processors)
  35. 35. Number of 32-bit operations needed for a single block encryption at main transformation (having all round keys)  ( (4 look-up) + (3 xors) ) * (4 columns) == == 28 operations / round  4 xors with round keys == == 4 operations / round  (28 + 4) * (9 rounds) == 288 operations for high strength encryption of 9 rounds (!)  (16 operations on SubBytes) + (24 operations on ShiftRows) + (4 xors with round keys) == == 44 operations at last round
  36. 36. AES decryption: high-level structure (pseudocode)
  37. 37. AES decryption: optimization  SubBytes() and ShiftRows() transformations commute, their sequence can be chaged  The column mixing operations - MixColumns() and InvMixColumns() – are linear with respect to the column input, which means InvMixColumns(state xor Round Key) == InvMixColumns(state) xor InvMixColumns(Round Key)
  38. 38. AES optimized decryption with changed round keys
  39. 39. Additional details on AES implementation  two set of tables for encryption  main optimized set (MixColumns, ShiftRows and SubBytes)  separate S-box array for the last round  two set of tables for decryption (complexity is the same as for encryption)  main optimized set (InvMixColumns, InvShiftRows and InvSubBytes)  separate reverse S-box array for the last round NB: ECB decryption is not needed for the most block cipher modes of operation
  40. 40. Conclusions  direct AES implementation is very slow (requires many byte operations and conditions)  three different round function operations can be united into the single look-up table access  with effective implementation AES consists of look- up table accesses and round key additions  the fastest version AES requires 4 kB of memory for tables, fast but compact requires 1 kB  fast AES decryption operation has the same speed as encryption and uses changed order of round function operations with modified round keys

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