BLAKE (hash function)


BLAKE is a cryptographic hash function based on Dan Bernstein's ChaCha stream cipher, but a permuted copy of the input block, XORed with 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.
The BLAKE2 hash function, based on BLAKE, was announced in 2012. The BLAKE3 hash function, based on BLAKE2, was announced in 2020.

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 candidates but lost to Keccak in 2012, which was selected for the 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 are preserved between blocks.
It uses a table of 16 constant words, and a table of 10 16-element permutations:
σ = 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
σ = 14 10 4 8 9 15 13 6 1 12 0 2 11 7 5 3
σ = 11 8 12 0 5 2 15 13 10 14 3 6 7 1 9 4
σ = 7 9 3 1 13 12 11 14 2 6 5 10 4 0 15 8
σ = 9 0 5 7 2 4 10 15 14 1 11 12 6 8 3 13
σ = 2 12 6 10 0 11 8 3 4 13 7 5 15 14 1 9
σ = 12 5 1 15 14 13 4 10 0 7 6 3 9 2 8 11
σ = 13 11 7 14 12 1 3 9 5 0 15 4 8 6 2 10
σ = 6 15 14 9 11 3 0 8 12 2 13 7 1 4 10 5
σ = 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 a b c d, which is combined with 2 words of message m and two constant words n. It is performed 8 times per full round:
j ← σ // Index computations
k ← σ
a ← a + b + // Step 1
d ← >>> 16
c ← c + d // Step 2
b ← >>> 12
a ← a + b + // Step 3
d ← >>> 8
c ← c + d // Step 4
b ← >>> 7
In the above, r is the round number, and i varies from 0 to 7.
The differences from the ChaCha quarter-round function are:
The 64-bit version 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.

Example digests

Hash values of an empty string:
=
7dc5313b1c04512a174bd6503b89607aecbee0903d40a8a569c94eed
=
716f6e863f744b9ac22c97ec7b76ea5f5908bc5b2f67c61510bfc4751384ea7a
=
c6cbd89c926ab525c242e6621f2f5fa73aa4afe3d9e24aed727faaadd6af38b620bdb623dd2b4788b1c8086984af8706
=
a8cfbbd73726062df0c6864dda65defe58ef0cc52a5625090fa17601e1eecd1b628e94f396ae402a00acc9eab77b4d4c2e852aaaa25a636d80af3fc7913ef5b8
Changing a single bit causes each bit in the output to change with 50% probability, demonstrating an avalanche effect:
=
1f7e26f63b6ad25a0896fd978fd050a1766391d2fd0471a77afb975e5034b7ad2d9ccf8dfb47abbbe656e1b82fbc634ba42ce186e8dc5e1ce09a885d41f43451
=
a701c2a1f9baabd8b1db6b75aee096900276f0b86dc15d247ecc03937b370324a16a4ffc0c3a85cd63229cfa15c15f4ba6d46ae2e849ed6335e9ff43b764198a

BLAKE2

BLAKE2 is a cryptographic hash function based on BLAKE, created by Jean-Philippe Aumasson, Samuel Neves, Zooko Wilcox-O'Hearn, and Christian Winnerlein. The design goal was to replace the widely used, but broken, MD5 and SHA-1 algorithms in applications requiring high performance in software. BLAKE2 was announced on December 21, 2012. A reference implementation is available under CC0, the OpenSSL License, and the Apache Public License 2.0.
BLAKE2b is faster than MD5, SHA-1, SHA-2, and SHA-3, on 64-bit x64 and ARM architectures. BLAKE2 provides security superior to SHA-2 and similar to that of SHA-3: immunity to length extension, indifferentiability from a random oracle, etc.
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, and from 14 to 10 for BLAKE2s.
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 and BLAKE2sp.
BLAKE2X is a family of extensible-output functions. Whereas BLAKE2 is limited to 64-byte digests, BLAKE2X allows for digests of up to 256 GiB. BLAKE2X is itself not an instance of a hash function, and must be based on an actual BLAKE2 instance. An example of a BLAKE2X instance could be BLAKE2Xb16MiB, which would be a BLAKE2X version based on BLAKE2b producing 16,777,216-byte digests.
BLAKE2b and BLAKE2s are specified in RFC 7693. Optional features using the parameter block, are not specified, and thus neither is support for BLAKE2bp, BLAKE2sp, or BLAKE2X.

Initialization vector

BLAKE2b uses an initialization vector that is the same as the These values are transparently obtained by taking the first 64 bits of the fractional parts of the positive square roots of the first eight prime numbers.
IV0 = 0x6a09e667f3bcc908 //Frac
IV1 = 0xbb67ae8584caa73b //Frac
IV2 = 0x3c6ef372fe94f82b //Frac
IV3 = 0xa54ff53a5f1d36f1 //Frac
IV4 = 0x510e527fade682d1 //Frac
IV5 = 0x9b05688c2b3e6c1f //Frac
IV6 = 0x1f83d9abfb41bd6b //Frac
IV7 = 0x5be0cd19137e2179 //Frac

BLAKE2b algorithm

for the BLAKE2b algorithm. The BLAKE2b algorithm uses 8-byte words, and 128-byte chunks.
Algorithm BLAKE2b
Input:
M Message to be hashed
cbMessageLen: Number, Length of the message in bytes
Key Optional 0..64 byte key
cbKeyLen: Number, Length of optional key in bytes
cbHashLen: Number, Desired hash length in bytes
Output:
Hash Hash of cbHashLen bytes
Initialize State vector h with IV
h0..7 ← IV0..7
Mix key size and desired hash length into h0
h0 ← h0 xor 0x0101kknn
where kk is Key Length
nn is Desired Hash Length
Each time we Compress we record how many bytes have been compressed
cBytesCompressed ← 0
cBytesRemaining ← cbMessageLen
If there was a key supplied
then pad with trailing zeros to make it 128-bytes
and prepend it to the message M
if then
M ← Pad || M
cBytesRemaining ← cBytesRemaining + 128
end if
Compress whole 128-byte chunks of the message, except the last chunk
while 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 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
cBytesCompressed ← cBytesCompressed+cBytesRemaining The actual number of bytes leftover in M
chunk ← Pad If M was empty, then we will still compress a final chunk of zeros
h ← Compress 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 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 Lo 64-bits of UInt128 t
V13 ← V13 xor Hi 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 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 Rounds 10 and 11 use SIGMA and SIGMA respectively
Mix
Mix
Mix
Mix
Mix
Mix
Mix
Mix
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

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 ← rotateright 32
Vc ← Vc + Vd no input
Vb ← rotateright 24
Va ← Va + Vb + y with input
Vd ← rotateright 16
Vc ← Vc + Vd no input
Vb ← rotateright 63
Result ← Va, Vb, Vc, Vd
End Function Mix

Example digests

Hash values of an empty string:
=
1fa1291e65248b37b3433475b2a0dd63d54a11ecc4e3e034e7bc1ef4
=
69217a3079908094e11121d042354a7c1f55b6482ca1a51e1b250dfd1ed0eef9
=
b32811423377f52d7862286ee1a72ee540524380fda1724a6f25d7978c6fd3244a6caf0498812673c5e05ef583825100
=
786a02f742015903c6c6fd852552d272912f4740e15847618a86e217f71f5419d25e1031afee585313896444934eb04b903a685b1448b755d56f701afe9be2ce
Changing a single bit causes each bit in the output to change with 50% probability, demonstrating an avalanche effect:
=
a8add4bdddfd93e4877d2746e62817b116364a1fa7bc148d95090bc7333b3673f82401cf7aa2e4cb1ecd90296e3f14cb5413f8ed77be73045b13914cdcd6a918
=
ab6b007747d8068c02e25a6008db8a77c218d94f3b40d2291a7dc8a62090a744c082ea27af01521a102e42f480a31e9844053f456b4b41e8aa78bbe5c12957bb

Users of BLAKE2

In addition to the reference implementation, the following cryptography libraries provide implementations of BLAKE2:
BLAKE3 is a cryptographic hash function based on Bao and BLAKE2, created by Jack O'Connor, Jean-Philippe Aumasson, Samuel Neves, and Zooko Wilcox-O'Hearn. It was announced on January 9th, 2020 at Real World Crypto.
BLAKE3 is a single algorithm with many desirable features, in contrast to BLAKE and BLAKE2, which are algorithm families with multiple variants. BLAKE3 is a Merkle tree, so it supports a practically unlimited degree of parallelism. The official Rust and C implementations are dual-licensed as public domain and the Apache License.
BLAKE3 is designed to be as fast as possible. The BLAKE3 compression function is closely based on that of BLAKE2s, with the biggest difference being that the number of rounds is reduced from 10 to 7, a change based on the assumption that current cryptography is too conservative. In addition to providing parallelism, the Merkel tree format also allows for verified streaming and incremental updates.