BLAKE (hash function)

BLAKE

General
Designers	Jean-Philippe Aumasson, Luca Henzen, Willi Meier, Raphael C.-W. Phan
Successors	BLAKE2
Certification	SHA-3 finalist
Detail
Digest sizes	224, 256, 384 or 512 bits
Structure	HAIFA construction
Rounds	14 or 16
Speed	8.4cpbonCore 2for BLAKE-256; 7.8 cpb for BLAKE-512

BLAKEis acryptographic hash functionbased onDaniel J. Bernstein'sChaChastream cipher,but a permuted copy of the input block,XORedwith round constants, is added before each ChaCha round. LikeSHA-2,there are two variants differing in thewordsize. 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-256andBLAKE-224use 32-bit words and produce digest sizes of 256 bits and 224 bits, respectively, whileBLAKE-512andBLAKE-384use 64-bit words and produce digest sizes of 512 bits and 384 bits, respectively.

TheBLAKE2hash function, based on BLAKE, was announced in 2012. TheBLAKE3hash function, based on BLAKE2, was announced in 2020.

History

BLAKE was submitted to theNIST hash function competitionby 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 toKeccakin 2012, which was selected for theSHA-3algorithm.

Algorithm

LikeSHA-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 ofπ), 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 diagonala b c d,which is combined with 2 words of messagem[]and two constant wordsn[].It is performed 8 times per full round:

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

In the above,ris the round number (0–13), andivaries 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.

"BLAKE reuses the permutation of the ChaCha stream cipher with rotations done in the opposite directions. Some have suspected an advanced optimization, but in fact it originates from a typo in the original BLAKE specifications", Jean-Philippe Aumasson explains in his "Crypto Dictionary".

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.

Example digests

Hash values of an empty string:

BLAKE-224( "" )=
7dc5313b1c04512a174bd6503b89607aecbee0903d40a8a569c94eed
BLAKE-256( "" )=
716f6e863f744b9ac22c97ec7b76ea5f5908bc5b2f67c61510bfc4751384ea7a
BLAKE-384( "" )=
c6cbd89c926ab525c242e6621f2f5fa73aa4afe3d9e24aed727faaadd6af38b620bdb623dd2b4788b1c8086984af8706
BLAKE-512( "" )=
a8cfbbd73726062df0c6864dda65defe58ef0cc52a5625090fa17601e1eecd1b628e94f396ae402a00acc9eab77b4d4c2e852aaaa25a636d80af3fc7913ef5b8

Changing a single bit causes each bit in the output to change with 50% probability, demonstrating anavalanche effect:

BLAKE-512( "The quick brown fox jumps over the lazy dog" )=
1f7e26f63b6ad25a0896fd978fd050a1766391d2fd0471a77afb975e5034b7ad2d9ccf8dfb47abbbe656e1b82fbc634ba42ce186e8dc5e1ce09a885d41f43451
BLAKE-512( "The quick brown fox jumps over the lazy dof")=
a701c2a1f9baabd8b1db6b75aee096900276f0b86dc15d247ecc03937b370324a16a4ffc0c3a85cd63229cfa15c15f4ba6d46ae2e849ed6335e9ff43b764198a

(In this example 266 matching bits out of 512 is about 52% due to the random nature of the avalanche.)

BLAKE2

BLAKE2

General
Designers	Jean-Philippe Aumasson, Samuel Neves,Zooko Wilcox-O'Hearn,Christian Winnerlein
Derived from	BLAKE
Detail
Digest sizes	up to 64 bytes (BLAKE2b); up to 32 bytes (BLAKE2s); arbitrary (BLAKE2X)
Rounds	10 or 12
Speed	3.5cpbonCore i5(Ivy Bridge) for BLAKE2b

BLAKE2is 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,MD5andSHA-1algorithms in applications requiring high performance in software. BLAKE2 was announced on December 21, 2012.Areference implementationis available underCC0,theOpenSSL License,and theApache License 2.0.

BLAKE2b is faster than MD5, SHA-1, SHA-2, and SHA-3, on 64-bit x86-64 and ARM architectures.BLAKE2 provides better security than SHA-2 and similar to that of SHA-3: immunity tolength 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 forBLAKE2b(successor of BLAKE-512), and from 14 to 10 forBLAKE2s(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 onmulti-core processors;BLAKE2bp(4-way parallel) andBLAKE2sp(8-way parallel).

BLAKE2Xis a family ofextendable-output functions(XOFs). 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 beBLAKE2Xb16MiB,which would be a BLAKE2X version based on BLAKE2b producing 16,777,216-byte digests (or exactly 16MiB,hence the name of such an instance).

BLAKE2b and BLAKE2s are specified in RFC 7693. Optional features using the parameter block (salting, personalized hashes, tree hashing, et cetera), 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 IV used by SHA-512. These values aretransparently obtainedby taking the first 64 bits of the fractional parts of the positive 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

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

AlgorithmBLAKE2b
Input:
MMessage to be hashed
cbMessageLen: Number, (0..2128)Length of the message in bytes
KeyOptional 0..64 byte key
cbKeyLen: Number, (0..64)Length of optional key in bytes
cbHashLen: Number, (1..64)Desired hash length in bytes
Output:
HashHash of cbHashLen bytes

Initialize State vectorhwithIV
h0..7← IV0..7

Mix key size (cbKeyLen) and desired hash length (cbHashLen) into h0
h0← h0xor 0x0101kknn
wherekkis Key Length (in bytes)
nnis 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 messageM
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 messageM
cBytesCompressed ← cBytesCompressed + 128increase count of bytes that have been compressed
cBytesRemaining ← cBytesRemaining - 128decrease count of bytes inMremaining to be processed

h ← Compress(h, chunk, cBytesCompressed, false)false ⇒ this is not the last chunk
end while

Compress the final bytes fromM
chunk ← get next 128 bytes of messageMWe will get cBytesRemaining bytes (i.e. 0..128 bytes)
cBytesCompressed ← cBytesCompressed+cBytesRemainingThe actual number of bytes leftover inM
chunk ← Pad(chunk, 128)IfMwas 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 AlgorithmBLAKE2b

Compress

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

FunctionCompress
Input:
hPersistent state vector
chunk128-byte (16 double word) chunk of message to compress
t: Number, 0..2128Count of bytes that have been fed into the Compression
IsLastBlock: BooleanIndicates if this is the final round of compression
Output:
hUpdated persistent state vector

Setup local work vector V
V0..7← h0..7First eight items are copied from persistent state vectorh
V8..15← IV0..7Remaining eight items are initialized from theIV

Mix the 128-bit countertinto V12:V13
V12← V12xorLo(t)Lo 64-bits of UInt128t
V13← V13xorHi(t)Hi 64-bits of UInt128t

If this is the last block then invert all the bits in V14
ifIsLastBlockthen
V14← V14xor0xFFFFFFFFFFFFFFFF

Treat each 128-byte messagechunkas sixteen 8-byte (64-bit) wordsm
m0..15← chunk

Twelve rounds of cryptographic message mi xing
forifrom0to11do
Select message mi xing schedule for this round.
BLAKE2b uses 12 rounds, while SIGMA has only 10 entries.
S0..15← SIGMA[imod10]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..7xorV0..7
h0..7← h0..7xorV8..15

Result← h
End FunctionCompress

Mix

TheMixfunction is called by theCompressfunction, 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.

FunctionMix
Inputs:
Va,Vb,Vc,Vdfour 8-byte word entries from the work vector V
x, ytwo 8-byte word entries from padded message m
Output:
Va,Vb,Vc,Vdthe modified versions of Va,Vb,Vc,Vd

Va← Va+ Vb+ xwith input
Vd← (VdxorVa)rotateright32

Vc← Vc+ Vdno input
Vb← (VbxorVc)rotateright24

Va← Va+ Vb+ ywith input
Vd← (VdxorVa)rotateright16

Vc← Vc+ Vdno input
Vb← (VbxorVc)rotateright63

Result← Va,Vb,Vc,Vd

End FunctionMix

Example digests

Hash values of an empty string:

BLAKE2s-224( "" )=
1fa1291e65248b37b3433475b2a0dd63d54a11ecc4e3e034e7bc1ef4
BLAKE2s-256( "" )=
69217a3079908094e11121d042354a7c1f55b6482ca1a51e1b250dfd1ed0eef9
BLAKE2b-384( "" )=
b32811423377f52d7862286ee1a72ee540524380fda1724a6f25d7978c6fd3244a6caf0498812673c5e05ef583825100
BLAKE2b-512( "" )=
786a02f742015903c6c6fd852552d272912f4740e15847618a86e217f71f5419d25e1031afee585313896444934eb04b903a685b1448b755d56f701afe9be2ce

Changing a single bit causes each bit in the output to change with 50% probability, demonstrating anavalanche effect:

BLAKE2b-512( "The quick brown fox jumps over the lazy dog" )=
a8add4bdddfd93e4877d2746e62817b116364a1fa7bc148d95090bc7333b3673f82401cf7aa2e4cb1ecd90296e3f14cb5413f8ed77be73045b13914cdcd6a918
BLAKE2b-512( "The quick brown fox jumps over the lazy dof")=
ab6b007747d8068c02e25a6008db8a77c218d94f3b40d2291a7dc8a62090a744c082ea27af01521a102e42f480a31e9844053f456b4b41e8aa78bbe5c12957bb

Users of BLAKE2

• Argon2,the winner of thePassword Hashing Competition,uses BLAKE2b
• Chef's Habitat deployment system uses BLAKE2b for package signing
• FreeBSD Portspackage management tool uses BLAKE2b
• GNU Core Utilitiesimplements BLAKE2b in its b2sum command
• IPFSallows use of BLAKE2b for tree hashing
• librsyncuses BLAKE2b
• Noise (cryptographic protocol),which is used inWhatsAppincludes BLAKE2 as an option.
• RARarchive format version 5 supports an optional 256-bit BLAKE2sp file checksum instead of the default 32-bitCRC32;it was implemented inWinRARv5+
• 7-Zip(in order to support the RAR archive format version 5) can generate the BLAKE2sp signature for each file in the Explorer shell via "CRC SHA" context menu, and choosing '*'
• rmlintuses BLAKE2b for duplicate file detection
• WireGuarduses BLAKE2s for hashing
• Zcash,a cryptocurrency, uses BLAKE2b in theEquihashproof of work,and as akey derivation function
• NANO,a cryptocurrency, uses BLAKE2b in the proof of work, for hashing digital signatures and as akey derivation function
• Polkadot,a multi-chain blockchain uses BLAKE2b as its hashing algorithm.
• Kadena (cryptocurrency),a scalable proof of work blockchain that uses Blake2s_256 as its hashing algorithm.
• PCI Vault,uses BLAKE2b as its hashing algorithm for the purpose of PCI compliant PCD tokenization.
• Ergo,a cryptocurrency, uses BLAKE2b256 as a subroutine of its hashing algorithm called Autolykos.
• Linux kernel,version 5.17 replaced SHA-1 with BLAKE2s for hashing theentropy poolin therandom number generator.
• Open Network for Digital Commerce,a Government of India initiative, uses BLAKE-512 to sign API requests.
• checksum,a Windows file hashing program has Blake2s as one of its algorithms

Implementations

In addition to the reference implementation,the following cryptography libraries provide implementations of BLAKE2:

• Botan
• Bouncy Castle
• Crypto++
• Libgcrypt
• libsodium
• OpenSSL
• wolfSSL

BLAKE3

BLAKE3

General
Designers	Jack O'Connor, Samuel Neves, Jean-Philippe Aumasson,Zooko Wilcox-O'Hearn
First published	January 9, 2020(2020-01-09)
Derived from	Bao,BLAKE2
Detail
Digest sizes	256 bits, arbitrarily extensible
Structure	Merkle tree
Rounds	7
Speed	0.49cpbon Cascade Lake-SP with AVX-512

BLAKE3is a cryptographic hash function based on Bao and BLAKE2, created by Jack O'Connor, Jean-Philippe Aumasson, Samuel Neves, andZooko Wilcox-O'Hearn.It was announced on January 9, 2020, atReal World Crypto.

BLAKE3 is a single algorithm with many desirable features (parallelism,XOF,KDF,PRFandMAC), in contrast to BLAKE and BLAKE2, which are algorithm families with multiple variants. BLAKE3 has abinary treestructure, so it supports a practically unlimited degree of parallelism (both SIMD and multithreading) given long enough input. The officialRustandCimplementationsaredual-licensedas public domain (CC0) and theApache License.

BLAKE3 is designed to be as fast as possible. It is consistently a few times faster than BLAKE2. 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 Merkle tree format also allows for verified streaming (on-the-fly verifying) and incremental updates.

External links

• The BLAKE web site
• The BLAKE2 web site
• The BLAKE3 web site