BLAKE (hash function)

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.

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 15σ[1] = 14 10 4 8 9 15 13 6 1 12 0 2 11 7 5 3σ[2] = 11 8 12 0 5 2 15 13 10 14 3 6 7 1 9 4σ[3] = 7 9 3 1 13 12 11 14 2 6 5 10 4 0 15 8σ[4] = 9 0 5 7 2 4 10 15 14 1 11 12 6 8 3 13σ[5] = 2 12 6 10 0 11 8 3 4 13 7 5 15 14 1 9σ[6] = 12 5 1 15 14 13 4 10 0 7 6 3 9 2 8 11σ[7] = 13 11 7 14 12 1 3 9 5 0 15 4 8 6 2 10σ[8] = 6 15 14 9 11 3 0 8 12 2 13 7 1 4 10 5σ[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 combines with 2 words of message m[] and two constant words c[]. It is performed 8 times per full round:

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

In the above, r is the round number (0–13), and i 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.

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 ← 0xcbbb9d5dc1059ed8 h₁ ← 0x629a292a367cd507 h₂ ← 0x9159015a3070dd17 h₃ ← 0x152fecd8f70e5939 h₄ ← 0x67332667ffc00b31 h₅ ← 0x8eb44a8768581511 h₆ ← 0xdb0c2e0d64f98fa7 h₇ ← 0x47b5481dbefa4fa4 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 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 (cbBytesRemaining > 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 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 Compress(h, chunk, cBytesCompressed, true) true ⇒ this is the last chunk Result ← first cbHashLen bytes of little endian state vector hEnd 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 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 V_0..7 ← h_0..7 V_8..15 ← IV_0..7 Mix offset 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 m_0..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. S_0..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 h_0..7 ← h_0..7 xor V_0..7 h_0..7 ← h_0..7 xor V_8..15 Result ← hEnd 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: V_a, V_b, V_c, V_d four 8-byte word entries from the work vector V x, y two 8-byte word entries from padded message m Output: V_a, V_b, V_c, V_d the modified versions of V_a, V_b, V_c, V_d V_a ← V_a + V_b + x with input V_d ← (V_d xor V_a) rotateright 32 V_c ← V_c + V_d no input V_b ← (V_b xor V_c) rotateright 24 V_a ← V_a + V_b + y with input V_d ← (V_d xor V_a) rotateright 16 V_c ← V_c + V_d no input V_b ← (V_b xor V_c) rotateright 63 Result ← V_a, V_b, V_c, V_dEnd Algorithm Mix

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.

BLAKE hashes

BLAKE-512("") = A8CFBBD73726062DF0C6864DDA65DEFE58EF0CC52A5625090FA17601E1EECD1B 628E94F396AE402A00ACC9EAB77B4D4C2E852AAAA25A636D80AF3FC7913EF5B8BLAKE-512("The quick brown fox jumps over the lazy dog") = 1F7E26F63B6AD25A0896FD978FD050A1766391D2FD0471A77AFB975E5034B7AD 2D9CCF8DFB47ABBBE656E1B82FBC634BA42CE186E8DC5E1CE09A885D41F43451

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).

BLAKE2 hashes

BLAKE2b-512("") = 786A02F742015903C6C6FD852552D272912F4740E15847618A86E217F71F5419 D25E1031AFEE585313896444934EB04B903A685B1448B755D56F701AFE9BE2CEBLAKE2b-512("The quick brown fox jumps over the lazy dog") = A8ADD4BDDDFD93E4877D2746E62817B116364A1FA7BC148D95090BC7333B3673 F82401CF7AA2E4CB1ECD90296E3F14CB5413F8ED77BE73045B13914CDCD6A918

BLAKE2 uses

GNU Core Utilities implements BLAKE2 in its b2sum 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 BLAKE2 in the Equihash Proof-of-Work.

Bram Cohen's MerkleSet uses BLAKE2s.

FreeBSD's package-management tool pkg uses BLAKE2b.