CRYPTONOTE STANDARD 008 Seigen
Category: Main Track Max Jameson
Tuomo Nieminen
Neocortex
Antonio M. Juarez
CryptoNote
March 2013
CryptoNight Hash Function
Abstract
This document is part of the CryptoNote Standards describing a peer
topeer anonymous payment system. It defines the CryptoNote's default
proofofwork hash function, CryptoNight.
Copyright and License Notice
Copyright (c) 2013 CryptoNote. This document is available under the
Creative Commons Attribution 3.0 License (international). To view a
copy of the license visit http://creativecommons.org/licenses/by/3.0/
Table of Contents
1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . 2
2. Definitions . . . . . . . . . . . . . . . . . . . . . . . . . . 2
3. Scratchpad Initialization . . . . . . . . . . . . . . . . . . . 2
4. MemoryHard Loop . . . . . . . . . . . . . . . . . . . . . . . 4
5. Result Calculation . . . . . . . . . . . . . . . . . . . . . . 6
6. References . . . . . . . . . . . . . . . . . . . . . . . . . . 8
Seigen et al. CryptoNight Hash Function [Page 1]
CRYPTONOTE STANDARD 008 March 2013
1. Introduction
CryptoNight is a memoryhard hash function. It is designed to be
inefficiently computable on GPU, FPGA and ASIC architectures. The
CryptoNight algorithm's first step is initializing large scratchpad
with pseudorandom data. The next step is numerous read/write
operations at pseudorandom addresses contained in the scratchpad.
The final step is hashing the entire scratchpad to produce the
resulting value.
2. Definitions
hash function: an efficiently computable function which maps data of
arbitrary size to data of fixed size and behaves similarly to a
random function
scratchpad: a large area of memory used to store intermediate values
during the evaluation of a memoryhard function
3. Scratchpad Initialization
First, the input is hashed using Keccak [KECCAK] with parameters b =
1600 and c = 512. The bytes 0..31 of the Keccak final state are
interpreted as an AES256 key [AES] and expanded to 10 round keys. A
scratchpad of 2097152 bytes (2 MiB) is allocated. The bytes 64..191
are extracted from the Keccak final state and split into 8 blocks of
16 bytes each. Each block is encrypted using the following procedure:
for i = 0..9 do:
block = aes_round(block, round_keys[i])
Where aes_round function performs a round of AES encryption, which
means that SubBytes, ShiftRows and MixColumns steps are performed on
the block, and the result is XORed with the round key. Note that
unlike in the AES encryption algorithm, the first and the last rounds
are not special. The resulting blocks are written into the first 128
bytes of the scratchpad. Then, these blocks are encrypted again in
the same way, and the result is written into the second 128 bytes of
the scratchpad. Each time 128 bytes are written, they represent the
result of the encryption of the previously written 128 bytes. The
process is repeated until the scratchpad is fully initialized.
This diagram illustrates scratchpad initialization:
Seigen et al. CryptoNight Hash Function [Page 2]
CRYPTONOTE STANDARD 008 March 2013
++
Input
++

V
++
 Keccak 
++

V
++
 Final state 
+++++
 Bytes 0..31  Bytes 32..63  Bytes 64..191  Bytes 192..199 
+++++
 
V 
++ V
 Round key 0 ++>++
++    
 .     
 .     AES 
 .     
++    
 Round key 9 ++>++ ++
++       
    +> 
      
    V  
   +>++  
      S 
      
    AES   c 
      
      r 
  +>++  
    a 
  +> 
  .  t 
  .  
  .  c 
  +> 
    h 
  V  
 +>++  p 
    
    a 
  AES   
Seigen et al. CryptoNight Hash Function [Page 3]
CRYPTONOTE STANDARD 008 March 2013
    d 
    
+>++  
  
+> 
 
++
Figure 3: Scratchpad initialization diagram
4. MemoryHard Loop
Prior to the main loop, bytes 0..31 and 32..63 of the Keccak state
are XORed, and the resulting 32 bytes are used to initialize
variables a and b, 16 bytes each. These variables are used in the
main loop. The main loop is iterated 524,288 times. When a 16byte
value needs to be converted into an address in the scratchpad, it is
interpreted as a littleendian integer, and the 21 loworder bits are
used as a byte index. However, the 4 loworder bits of the index are
cleared to ensure the 16byte alignment. The data is read from and
written to the scratchpad in 16byte blocks. Each iteration can be
expressed with the following pseudocode:
scratchpad_address = to_scratchpad_address(a)
scratchpad[scratchpad_address] = aes_round(scratchpad
[scratchpad_address], a)
b, scratchpad[scratchpad_address] = scratchpad[scratchpad_address],
b xor scratchpad[scratchpad_address]
scratchpad_address = to_scratchpad_address(b)
a = 8byte_add(a, 8byte_mul(b, scratchpad[scratchpad_address]))
a, scratchpad[scratchpad_address] = a xor
scratchpad[scratchpad_address], a
Where, the 8byte_add function represents each of the arguments as a
pair of 64bit littleendian values and adds them together,
componentwise, modulo 2^64. The result is converted back into 16
bytes.
The 8byte_mul function, however, uses only the first 8 bytes of each
argument, which are interpreted as unsigned 64bit littleendian
integers and multiplied together. The result is converted into 16
bytes, and finally the two 8byte halves of the result are swapped.
This diagram illustrates the memoryhard loop:
Seigen et al. CryptoNight Hash Function [Page 4]
CRYPTONOTE STANDARD 008 March 2013
++
 Final state 
+++++
 Bytes 0..31  Bytes 32..63  Bytes 64..191  Bytes 192..199 
+++++
 
 ++ 
+> XOR <+
++
 
++ ++
 
V V
++ ++
 a   b 
++ ++
 
 REPEAT 524288 TIMES 
  address ++
+> 
 ++  read  
+> AES < 
 ++ V  
  ++  S 
 +> XOR   
  ++ write  c 
   +> 
  ++ address  r 
 +> 
  ++ read  a 
 +> 8byte_mul <+ 
  ++   t 
     
  V   c 
  ++   
+> 8byte_add    h 
 ++   
   write  p 
 +> 
    a 
 V   
 ++   d 
  XOR <+  
 ++  
++   
++  
  ++
 END REPEAT 
Seigen et al. CryptoNight Hash Function [Page 5]
CRYPTONOTE STANDARD 008 March 2013
 
Figure 4: Memoryhard loop diagram
5. Result Calculation
After the memoryhard part, bytes 32..63 from the Keccak state are
expanded into 10 AES round keys in the same manner as in the first
part.
Bytes 64..191 are extracted from the Keccak state and XORed with the
first 128 bytes of the scratchpad. Then the result is encrypted in
the same manner as in the first part, but using the new keys. The
result is XORed with the second 128 bytes from the scratchpad,
encrypted again, and so on.
After XORing with the last 128 bytes of the scratchpad, the result is
encrypted the last time, and then the bytes 64..191 in the Keccak
state are replaced with the result. Then, the Keccak state is passed
through Keccakf (the Keccak permutation) with b = 1600.
Then, the 2 loworder bits of the first byte of the state are used to
select a hash function: 0=BLAKE256 [BLAKE], 1=Groestl256 [GROESTL],
2=JH256 [JH], and 3=Skein256 [SKEIN]. The chosen hash function is
then applied to the Keccak state, and the resulting hash is the
output of CryptoNight.
The diagram below illustrates the result calculation:
Seigen et al. CryptoNight Hash Function [Page 6]
CRYPTONOTE STANDARD 008 March 2013
++
 Final state 
+++++
 Bytes 0..31  Bytes 32..63  Bytes 64..191  Bytes 192..199 
+++++
   
 ++  
 V   
++   
 Round key 0 ++  
++     
 .      
 .      
 .      
++     
++  Round key 9 ++  V 
  ++      ++ 
 > XOR  
        ++ 
 S         
        V 
 c       +>++ 
         
 r         
        AES  
 a         
         
 t      +>++ 
       
 c      V 
      ++ 
 h > XOR  
      ++ 
 p       
      . 
 a      . 
      . 
 d       
      V 
      ++ 
 > XOR  
      ++ 
++      
    V 
   +>++ 
     
     
    AES  
Seigen et al. CryptoNight Hash Function [Page 7]
CRYPTONOTE STANDARD 008 March 2013
     
     
  +>++ 
   
V V V V
+++++
 Bytes 0..31  Bytes 32..63  Bytes 64..191  Bytes 192..199 
+++++
 Modified state 
++

V
++
 Keccakf 
++
 
++ 
 
V V
++ ++
 Select hash > Chosen hash 
++ ++

V
++
 Final result 
++
Figure 5: Result calculation diagram
Hash examples:
Empty string:
eb14e8a833fac6fe9a43b57b336789c46ffe93f2868452240720607b14387e11.
"This is a test":
a084f01d1437a09c6985401b60d43554ae105802c5f5d8a9b3253649c0be6605.
6. References
[AES] "Announcing the ADVANCED ENCRYPTION STANDARD", FIPS 197, 2001.
[BLAKE] Aumasson, J.P., Henzen, L., Meier, W., and R. C.W. Phan,
"SHA3 proposal BLAKE", 2010.
[GROESTL] Gauravaram, P., Knudsen, L., Matusiewicz, K., Mendel, F.,
Seigen et al. CryptoNight Hash Function [Page 8]
CRYPTONOTE STANDARD 008 March 2013
Rechberger, C., Schlaffer, M., and S. Thomsen, "Groestl  a SHA3
candidate", 2011.
[JH] Wu, H., "The Hash Function JH", 2011.
[KECCAK] Bertoni, G., Daemen, J., Peeters, M., and G. Van Assche,
"The Keccak reference", 2011.
[SKEIN] Ferguson, N., Lucks, S., Schneier, B., Whiting, D., Bellare,
M., Kohno, T., Callas, J., and J. Walker, "The Skein Hash Function
Family", 2008.
Seigen et al. CryptoNight Hash Function [Page 9]