# BLAKE (hash function)

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Cryptographic Hash Function

BLAKE and BLAKE2 are cryptographic hash functions based on Dan Bernstein's ChaCha stream cipher, but a permuted copy of the input block, XORed with some round constants, is added before each ChaCha round. Like SHA-2, there are two variants differing in the word size. ChaCha operates on a 4×4 array of words. BLAKE repeatedly combines an 8-word hash value with 16 message words, truncating the ChaCha result to obtain the next hash value. BLAKE-256 and BLAKE-224 use 32-bit words and produce digest sizes of 256 bits and 224 bits, respectively, while BLAKE-512 and BLAKE-384 use 64-bit words and produce digest sizes of 512 bits and 384 bits, respectively.

## History

BLAKE was submitted to the NIST hash function competition by Jean-Philippe Aumasson, Luca Henzen, Willi Meier, and Raphael C.-W. Phan. In 2008, there were 51 entries. BLAKE made it to the final round consisting of five candidate but lost to Keccak in 2012, which was selected for the SHA-3 algorithm.

SHA-3 algorithm

## Algorithm

Like SHA-2, BLAKE comes in two variants: one that uses 32-bit words, used for computing hashes up to 256 bits long, and one that uses 64-bit words, used for computing hashes up to 512 bits long. The core block transformation combines 16 words of input with 16 working variables, but only 8 words (256 or 512 bits) are preserved between blocks.

It uses a table of 16 constant words (the leading 512 or 1024 bits of the fractional part of π), and a table of 10 16-element permutations:

```σ[0] = 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
σ[1] = 14 10 4 8 9 15 13 6 1 12 0 2 11 7 5 3
σ[2] = 11 8 12 0 5 2 15 13 10 14 3 6 7 1 9 4
σ[3] = 7 9 3 1 13 12 11 14 2 6 5 10 4 0 15 8
σ[4] = 9 0 5 7 2 4 10 15 14 1 11 12 6 8 3 13
σ[5] = 2 12 6 10 0 11 8 3 4 13 7 5 15 14 1 9
σ[6] = 12 5 1 15 14 13 4 10 0 7 6 3 9 2 8 11
σ[7] = 13 11 7 14 12 1 3 9 5 0 15 4 8 6 2 10
σ[8] = 6 15 14 9 11 3 0 8 12 2 13 7 1 4 10 5
σ[9] = 10 2 8 4 7 6 1 5 15 11 9 14 3 12 13 0
```

The core operation, equivalent to ChaCha's quarter round, operates on a 4-word column or diagonal <code>a b c d</code>, which is combined with 2 words of message <code>m[]</code> and two constant words <code>n[]</code>. It is performed 8 times per full round:

```j ← σ[r%10][2×i] <span style="color:green">// Index computations</span>
k ← σ[r%10][2×i+1]
a ← a + b + (m[j] ⊕ n[k]) <span style="color:green">// Step 1 (with input)</span>
d ← (d ⊕ a) >>> 16
c ← c + d <span style="color:green">// Step 2 (no input)</span>
b ← (b ⊕ c) >>> 12
a ← a + b + (m[k] ⊕ n[j]) <span style="color:green">// Step 3 (with input)</span>
d ← (d ⊕ a) >>> 8
c ← c + d <span style="color:green">// Step 4 (no input)</span>
b ← (b ⊕ c) >>> 7
```

In the above, <code>r</code> is the round number (0–13), and <code>i</code> varies from 0 to 7.

The differences from the ChaCha quarter-round function are:

• The addition of the message words has been added.
• The rotation directions have been reversed.

The 64-bit version (which does not exist in ChaCha) is identical, but the rotation amounts are 32, 25, 16 and 11, respectively, and the number of rounds is increased to 16.

## Tweaks

Throughout the NIST hash function competition, entrants are permitted to "tweak" their algorithms to address issues that are discovered. Changes that have been made to BLAKE are:

• The number of rounds was increased from 10/14 to 14/16. This is to be more conservative about security while still being fast.

## BLAKE2

An improved version of BLAKE called BLAKE2 was announced in December 21, 2012. It was created by Jean-Philippe Aumasson, Samuel Neves, Zooko Wilcox-O'Hearn, and Christian Winnerlein with the goal to replace widely used, but broken MD5 and SHA-1 algorithms. The reference implementation code was released under CC0.

BLAKE2 removes addition of constants to message words from BLAKE round function, changes two rotation constants, simplifies padding, adds parameter block that is XOR'ed with initialization vectors, and reduces the number of rounds from 16 to 12 for BLAKE2b (successor of BLAKE-512), and from 14 to 10 for BLAKE2s (successor of BLAKE-256).

BLAKE2 supports keying, salting, personalization, and hash tree modes, and can output digests from 1 up to 64 bytes for BLAKE2b or up to 32 bytes for BLAKE2s. There are also parallel versions designed for increased performance on multi-core processors; BLAKE2bp (4-way parallel) and BLAKE2sp (8-way parallel).

There is an "Extendable-Output Function" (XOF) variant of BLAKE2 called "BLAKE2X", which is able to output a very large number of random bits (instead of just 256 or 512).

### Initialization vector

Blake2b uses an initialization vector that is the same as the IV used by SHA-512. These values are obtained by taking the first 64 bits of the fractional parts of the square roots of the first eight prime numbers.

IV0 = 0x6A09E667F3BCC908 //Frac(Sqrt(2)) IV1 = 0xBB67AE8584CAA73B //Frac(Sqrt(3)) IV2 = 0x3C6EF372FE94F82B //Frac(Sqrt(5)) IV3 = 0xA54FF53A5F1D36F1 //Frac(Sqrt(7)) IV4 = 0x510E527FADE682D1 //Frac(Sqrt(11)) IV5 = 0x9B05688C2B3E6C1F //Frac(Sqrt(13)) IV6 = 0x1F83D9ABFB41BD6B //Frac(Sqrt(17)) IV7 = 0x5BE0CD19137E2179 //Frac(Sqrt(19))

### Blake2b algorithm

Pseudocode for the BLAKE2b algorithm. The BLAKE2b algorithm uses 8-byte (UInt64) words, and 128-byte chunks.

```Algorithm BLAKE2b
Input:
M                               Message to be hashed
cbMessageLen: Number, (0..2128)  Length of the message in bytes
Key                             Optional 0..64 byte key
cbKeyLen: Number, (0..64)       Length of optional key in bytes
cbHashLen: Number, (1..64)      Desired hash length in bytes
Output:
Hash                            Hash of cbHashLen bytes
Initialize State vector h with IV
h0..7 ← IV0..7
Mix key size (cbKeyLen) and desired hash length (cbHashLen) into h0
h0 ← h0 xor 0x0101kknn
where kk is Key Length (in bytes)
nn is Desired Hash Length (in bytes)
Each time we Compress we record how many bytes have been compressed
cBytesCompressed ← 0
cBytesRemaining  ← cbMessageLen
If there was a key supplied (i.e. cbKeyLen > 0)
then pad with trailing zeros to make it 128-bytes (i.e. 16 words)
and prepend it to the message M
if (cbKeyLen > 0) then
M ← Pad(Key, 128) || M
cBytesRemaining ← cBytesRemaining + 128
end if
Compress whole 128-byte chunks of the message, except the last chunk
while (cBytesRemaining > 128) do
chunk ← get next 128 bytes of message M
cBytesCompressed ← cBytesCompressed + 128  increase count of bytes that have been compressed
cBytesRemaining  ← cBytesRemaining  - 128  decrease count of bytes in M remaining to be processed
h ← Compress(h, chunk, cBytesCompressed, false)  false ⇒ this is not the last chunk
end while
Compress the final bytes from M
chunk ← get next 128 bytes of message M  We will get cBytesRemaining bytes (i.e. 0..128 bytes)
cBytesCompressed ← cBytesCompressed+cBytesRemaining  The actual number of bytes leftover in M
chunk ← Pad(chunk, 128)  If M was empty, then we will still compress a final chunk of zeros
h ← Compress(h, chunk, cBytesCompressed, true)  true ⇒ this is the last chunk
Result ← first cbHashLen bytes of little endian state vector h
End Algorithm BLAKE2b
```

#### Compress

The Compress function takes a full 128-byte chunk of the input message and mixes it into the ongoing state array:

```Function Compress
Input:
h                      Persistent state vector
chunk                  128-byte (16 double word) chunk of message to compress
t: Number, 0..2128     Count of bytes that have been fed into the Compression
IsLastBlock: Boolean   Indicates if this is the final round of compression
Output:
h                      Updated persistent state vector
Setup local work vector V
V0..7 ← h0..7   First eight items are copied from persistent state vector h
V8..15 ← IV0..7 Remaining eight items are initialized from the IV
Mix the 128-bit counter t into V12:V13
V12 ← V12 xor Lo(t)    Lo 64-bits of UInt128 t
V13 ← V13 xor Hi(t)    Hi 64-bits of UInt128 t
If this is the last block then invert all the bits in V14
if IsLastBlock then
V14 ← V14 xor 0xFFFFFFFFFFFFFFFF
Treat each 128-byte message chunk as sixteen 8-byte (64-bit) words m
m0..15 ← chunk
Twelve rounds of cryptographic message mixing
for i from 0 to 11 do
Select message mixing schedule for this round.
BLAKE2b uses 12 rounds, while SIGMA has only 10 entries.
S0..15 ← SIGMA[i mod 10]   Rounds 10 and 11 use SIGMA[0] and SIGMA[1] respectively

Mix(V0, V4, V8,  V12, m[S0], m[S1])
Mix(V1, V5, V9,  V13, m[S2], m[S3])
Mix(V2, V6, V10, V14, m[S4], m[S5])
Mix(V3, V7, V11, V15, m[S6], m[S7])
Mix(V0, V5, V10, V15, m[S8],  m[S9])
Mix(V1, V6, V11, V12, m[S10], m[S11])
Mix(V2, V7, V8,  V13, m[S12], m[S13])
Mix(V3, V4, V9,  V14, m[S14], m[S15])
end for
Mix the upper and lower halves of V into ongoing state vector h
h0..7 ← h0..7 xor V0..7
h0..7 ← h0..7 xor V8..15
Result ← h
End Function Compress
Result ← h
<span style="color: #004DBB;">End Function</span> Compress
```

#### Mix

The Mix function is called by the Compress function, and mixes two 8-byte words from the message into the hash state. In most implementations this function would be written inline, or as an inlined function. Function Mix

```  Inputs:
Va, Vb, Vc, Vd       four 8-byte word entries from the work vector V
x, y                two 8-byte word entries from padded message m
Output:
Va, Vb, Vc, Vd       the modified versions of Va, Vb, Vc, Vd
Va ← Va + Vb + x          with input
Vd ← (Vd xor Va) rotateright 32
Vc ← Vc + Vd              no input
Vb ← (Vb xor Vc) rotateright 24
Va ← Va + Vb + y          with input
Vd ← (Vd xor Va) rotateright 16
Vc ← Vc + Vd              no input
Vb ← (Vb xor Vc) rotateright 63
Result ← Va, Vb, Vc, Vd
End Algorithm Mix
```

### BLAKE2 hashes

```BLAKE2b-512("")
= 786A02F742015903C6C6FD852552D272912F4740E15847618A86E217F71F5419
D25E1031AFEE585313896444934EB04B903A685B1448B755D56F701AFE9BE2CE
```
```BLAKE2b-512("The quick brown fox jumps over the lazy dog")
F82401CF7AA2E4CB1ECD90296E3F14CB5413F8ED77BE73045B13914CDCD6A918
```

### BLAKE2 uses

GNU Core Utilities implements BLAKE2 in its BLAKE2 command.

Argon2, the winner of the Password Hashing Competition uses BLAKE2.

Noise (crypto protocol), which is now used in WhatsApp includes BLAKE2 as an option.

RAR file archive format version 5 supports an optional 256-bit BLAKE2sp file checksum instead of the default 32-bit CRC32. It was implemented in WinRAR v5+.

NeoScrypt, a password based key derivation function, employs BLAKE2s within its FastKDF component.

librsync uses BLAKE2.

Chef's Habitat deployment system uses BLAKE2 for package signing.

Several crypto libraries, including OpenSSL, Crypto++, libsodium, [Botan, and Bouncy Castle include BLAKE2.

Zcash, a cryptocurrency, uses BLAKE2b in the Equihash Proof-of-Work and as a key derivation function.

Bram Cohen's MerkleSet uses BLAKE2s.

FreeBSD's package-management tool pkg uses BLAKE2b.