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Cryptographic hash function

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 | 8.4 cpb on Core 2 for BLAKE-256; 7.8 cpb for BLAKE-512 |

**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.

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.

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 `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[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, `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.

"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".^{[1]}

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.

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.

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 an avalanche 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

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 | 3.5 cpb on Core i5 (Ivy Bridge) for BLAKE2b^{[2]} |

**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.^{[3]} A reference implementation is available under CC0, the OpenSSL License, and the Apache Public License 2.0.^{[4]}^{[5]}

BLAKE2b is faster than MD5, SHA-1, SHA-2, and SHA-3, on 64-bit x86-64 and ARM architectures.^{[4]} BLAKE2 provides better security than SHA-2 and similar to that of SHA-3: immunity to length extension, indifferentiability from a random oracle, etc.^{[6]}

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).

**BLAKE2X** is a family of extensible-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 be **BLAKE2Xb16MiB**, which would be a BLAKE2X version based on BLAKE2b producing 16,777,216-byte digests (or exactly 16 MiB, hence the name of such an instance).^{[7]}

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.^{[8]}

BLAKE2sp is the BLAKE2 version used by 7zip file compressor signature in context menu "CRC SHA"

BLAKE2b uses an initialization vector that is the same as the IV used by SHA-512. 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.

IV_{0}= 0x6a09e667f3bcc908 // Frac(sqrt(2)) IV_{1}= 0xbb67ae8584caa73b // Frac(sqrt(3)) IV_{2}= 0x3c6ef372fe94f82b // Frac(sqrt(5)) IV_{3}= 0xa54ff53a5f1d36f1 // Frac(sqrt(7)) IV_{4}= 0x510e527fade682d1 // Frac(sqrt(11)) IV_{5}= 0x9b05688c2b3e6c1f // Frac(sqrt(13)) IV_{6}= 0x1f83d9abfb41bd6b // Frac(sqrt(17)) IV_{7}= 0x5be0cd19137e2179 // Frac(sqrt(19))

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

AlgorithmBLAKE2bInput:MMessage to be hashedcbMessageLen: Number, (0..2^{128})Length of the message in bytesKeyOptional 0..64 byte keycbKeyLen: Number, (0..64)Length of optional key in bytescbHashLen: Number, (1..64)Desired hash length in bytesOutput:HashHash of cbHashLen bytesInitialize State vectorhhwithIV_{0..7}← IV_{0..7}Mix key size (cbKeyLen) and desired hash length (cbHashLen) into hh_{0}_{0}← h_{0}xor 0x0101kknnwherekkis Key Length (in bytes)nnis Desired Hash Length (in bytes)Each time we Compress we record how many bytes have been compressedcBytesCompressed ← 0 cBytesRemaining ← cbMessageLenIf 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 messageMif(cbKeyLen > 0)thenM ← Pad(Key, 128) || M cBytesRemaining ← cBytesRemaining + 128end ifCompress whole 128-byte chunks of the message, except the last chunkwhile(cBytesRemaining > 128)dochunk ← get next 128 bytes of messageMcBytesCompressed ← cBytesCompressed + 128increase count of bytes that have been compressedcBytesRemaining ← cBytesRemaining - 128decrease count of bytes inh ← Compress(h, chunk, cBytesCompressed, false)Mremaining to be processedfalse ⇒ this is not the last chunkend whileCompress the final bytes fromchunk ← get next 128 bytes of messageMMWe will get cBytesRemaining bytes (i.e. 0..128 bytes)cBytesCompressed ← cBytesCompressed+cBytesRemainingThe actual number of bytes leftover inchunk ← Pad(chunk, 128)MIfh ← Compress(h, chunk, cBytesCompressed, true)Mwas empty, then we will still compress a final chunk of zerostrue ⇒ this is the last chunkResult← first cbHashLen bytes of little endian state vector hEnd AlgorithmBLAKE2b

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

FunctionCompressInput:hPersistent state vectorchunk128-byte (16 double word) chunk of message to compresst: Number, 0..2^{128}Count of bytes that have been fed into the CompressionIsLastBlock: BooleanIndicates if this is the final round of compressionOutput:hUpdated persistent state vectorSetup local work vector VV_{0..7}← h_{0..7}First eight items are copied from persistent state vectorVh_{8..15}← IV_{0..7}Remaining eight items are initialized from theIVMix the 128-bit countertinto V_{12}:V_{13}V_{12}← V_{12}xorLo(t)Lo 64-bits of UInt128Vt_{13}← V_{13}xorHi(t)Hi 64-bits of UInt128tIf this is the last block then invert all the bits in V_{14}ifIsLastBlockthenV_{14}← V_{14}xor0xFFFFFFFFFFFFFFFFTreat each 128-byte messagemchunkas sixteen 8-byte (64-bit) wordsm_{0..15}← chunkTwelve rounds of cryptographic message mixingforifrom0to11doSelect message mixing schedule for this round.BLAKE2b uses 12 rounds, while SIGMA has only 10 entries.S_{0..15}← SIGMA[imod10]Rounds 10 and 11 use SIGMA[0] and SIGMA[1] respectivelyMix(V_{0}, V_{4}, V_{8}, V_{12}, m[S_{0}], m[S_{1}]) Mix(V_{1}, V_{5}, V_{9}, V_{13}, m[S_{2}], m[S_{3}]) Mix(V_{2}, V_{6}, V_{10}, V_{14}, m[S_{4}], m[S_{5}]) Mix(V_{3}, V_{7}, V_{11}, V_{15}, m[S_{6}], m[S_{7}]) Mix(V_{0}, V_{5}, V_{10}, V_{15}, m[S_{8}], m[S_{9}]) Mix(V_{1}, V_{6}, V_{11}, V_{12}, m[S_{10}], m[S_{11}]) Mix(V_{2}, V_{7}, V_{8}, V_{13}, m[S_{12}], m[S_{13}]) Mix(V_{3}, V_{4}, V_{9}, V_{14}, m[S_{14}], m[S_{15}])end forMix the upper and lower halves of V into ongoing state vector hh_{0..7}← h_{0..7}xorV_{0..7}h_{0..7}← h_{0..7}xorV_{8..15}Result← hEnd FunctionCompress

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.

FunctionMixInputs:V_{a}, V_{b}, V_{c}, V_{d}four 8-byte word entries from the work vector Vx, ytwo 8-byte word entries from padded message mOutput:V_{a}, V_{b}, V_{c}, V_{d}the modified versions of VV_{a}, V_{b}, V_{c}, V_{d}_{a}← V_{a}+ V_{b}+ xwith inputV_{d}← (V_{d}xorV_{a})rotateright32 V_{c}← V_{c}+ V_{d}no inputV_{b}← (V_{b}xorV_{c})rotateright24 V_{a}← V_{a}+ V_{b}+ ywith inputV_{d}← (V_{d}xorV_{a})rotateright16 V_{c}← V_{c}+ V_{d}no inputV_{b}← (V_{b}xorV_{c})rotateright63Result← V_{a}, V_{b}, V_{c}, V_{d}End FunctionMix

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 an avalanche 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

- Argon2, the winner of the Password Hashing Competition uses BLAKE2b
- Chef's Habitat deployment system uses BLAKE2b for package signing
^{[9]} - FreeBSD Ports package management tool uses BLAKE2b
- GNU Core Utilities implements BLAKE2b in its b2sum command
^{[10]} - IPFS allows use of BLAKE2b for tree hashing
- librsync uses BLAKE2b
^{[11]} - Noise (cryptographic protocol), which is used in WhatsApp includes BLAKE2 as an option.
^{[12]}^{[citation needed]} - 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+
^{[13]} - 7zip can generate the BLAKE2sp signature for each file in the Explorer shell via "CRC SHA" context menu, and choosing '*'
- rmlint uses BLAKE2b for duplicate file detection
^{[14]} - WireGuard uses BLAKE2s for hashing
^{[15]} - Zcash, a cryptocurrency, uses BLAKE2b in the Equihash proof of work, and as a key derivation function
- NANO, a cryptocurrency, uses BLAKE2b in the proof of work, for hashing digital signatures and as a key derivation function
^{[16]}^{[17]}^{[18]}

In addition to the reference implementation,^{[5]} the following cryptography libraries provide implementations of BLAKE2:

General | |
---|---|

Designers | Jack O'Connor, Samuel Neves, Jean-Philippe Aumasson, Zooko Wilcox-O'Hearn |

First published | January 9, 2020; 17 months ago (2020-01-09) |

Derived from | Bao, BLAKE2 |

Detail | |

Digest sizes | 256 bits, arbitrarily extensible |

Structure | Merkle tree |

Rounds | 7 |

Speed | 0.49 cpb on Cascade Lake-SP with AVX-512^{[19]} |

**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.^{[20]} It was announced on January 9th, 2020 at Real World Crypto.^{[citation needed]}

BLAKE3 is a single algorithm with many desirable features (parallelism, XOF, KDF, PRF and MAC), 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 (both SIMD and multithreading) on large files. The official Rust and C implementations^{[21]} are dual-licensed as public domain (CC0) and the Apache License.^{[22]}

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.^{[23]} In addition to providing parallelism, the Merkle tree format also allows for verified streaming (on-the-fly verifying) and incremental updates.^{[21]}

**^**Aumasson, Jean-Philippe (2021).*Crypto Dictionary: 500 Tasty Tidbits for the Curious Cryptographer*. No Starch Press. ISBN 9781718501409.**^**"BLAKE2 – an alternative to MD5/SHA-1".**^**O'Whielacronx, Zooko (21 December 2012). "introducing BLAKE2 – an alternative to SHA-3, SHA-2 and MD5".- ^
^{a}^{b}"BLAKE2".*blake2.net*. - ^
^{a}^{b}"BLAKE2 official implementations". Retrieved 7 July 2019. **^**Aumasson, Jean-Philippe; Neves, Samuel; Wilcox-O’Hearn, Zooko; Winnerlein, Christian (2013). "BLAKE2: simpler, smaller, fast as MD5" (PDF).*Cryptology ePrint Archive*. IACR.**^**"BLAKE2X" (PDF).**^**Saarinen, M-J; Aumasson, J-P (November 2015).*The BLAKE2 Cryptographic Hash and Message Authentication Code (MAC)*. IETF. doi:10.17487/RFC7693. RFC 7693. Retrieved 4 December 2015.**^**Habitat Internals: Cryptography**^**"coreutils/src/blake2/".*github.com*.**^**"librsync/src/blake2/".*github.com*.**^**"WhatsApp Security Whitepaper" (PDF).**^**"WinRAR archiver, a powerful tool to process RAR and ZIP files".*rarsoft.com*.**^**"rmlint — rmlint documentation".**^**"WireGuard: Next Generation Kernel Network Tunnel" (PDF).**^**"work".*docs.nano.org*.**^**"signatures".*docs.nano.org*.**^**"key derivation".*docs.nano.org*.**^**"BLAKE3 – one function, fast everywhere" (PDF).**^**"An earlier version of Bao specified its own custom tree mode, which eventually grew into BLAKE3".- ^
^{a}^{b}"BLAKE3 official implementations". Retrieved 12 January 2020. **^**"This work is released into the public domain with CC0 1.0. Alternatively, it is licensed under the Apache License 2.0".**^**Aumasson, Jean-Philippe (2020).*Too Much Crypto*(PDF). Real World Crypto Symposium.

- The BLAKE web site
- The BLAKE2 web site
- The BLAKE3 web site
- VHDL implementation of BLAKE, developed by the Cryptographic Engineering Research Group (CERG) at George Mason University

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