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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.

BLAKE
General
DesignersJean-Philippe Aumasson, Luca Henzen, Willi Meier, Raphael C.-W. Phan
SuccessorsBLAKE2
CertificationSHA-3 finalist
Detail
Digest sizes224, 256, 384 or 512 bits
StructureHAIFA construction
Rounds14 or 16
Speed8.4 cpb on Core 2 for BLAKE-256; 7.8 cpb for BLAKE-512

HistoryEdit

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.

AlgorithmEdit

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.

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.

TweaksEdit

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 digestsEdit

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

BLAKE2Edit

BLAKE2
General
DesignersJean-Philippe Aumasson, Samuel Neves, Zooko Wilcox-O'Hearn, Christian Winnerlein
Derived fromBLAKE
Detail
Digest sizesup to 64 bytes (BLAKE2b); up to 32 bytes (BLAKE2s); arbitrary (BLAKE2X)
Rounds10 or 12
Speed3.5 cpb on Core i5 (Ivy Bridge) for BLAKE2b[1]

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.[2] A reference implementation is available under CC0, the OpenSSL License, and the Apache Public License 2.0.[3][4]

BLAKE2b is faster than MD5, SHA-1, SHA-2, and SHA-3, on 64-bit x64 and ARM architectures.[3] BLAKE2 provides security superior to SHA-2 and similar to that of SHA-3: immunity to length extension, indifferentiability from a random oracle, etc.[5]

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).[6]

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.[7]

Initialization vectorEdit

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 algorithmEdit

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

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

CompressEdit

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

MixEdit

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, VdEnd Function Mix

Example digestsEdit

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

Users of BLAKE2Edit

ImplementationsEdit

In addition to the reference implementation,[4] the following cryptography libraries provide implementations of BLAKE2:

ReferencesEdit

  1. ^ "BLAKE2 – an alternative to MD5/SHA-1".
  2. ^ O'Whielacronx, Zooko (21 December 2012). "introducing BLAKE2 – an alternative to SHA-3, SHA-2 and MD5".
  3. ^ a b "BLAKE2". blake2.net.
  4. ^ a b "BLAKE2 official implementations". Retrieved 7 July 2019.
  5. ^ Aumasson, Jean-Philippe; Neves, Samuel; Wilcox-O’Hearn, Zooko; Winnerlein, Christian (2013). "BLAKE2: simpler, smaller, fast as MD5" (PDF). Cryptology ePrint Archive. IACR.
  6. ^ "BLAKE2X" (PDF).
  7. ^ 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.
  8. ^ Habitat Internals: Cryptography
  9. ^ "coreutils/src/blake2/". github.com.
  10. ^ "librsync/src/blake2/". github.com.
  11. ^ "WhatsApp Security Whitepaper" (PDF).
  12. ^ "WinRAR archiver, a powerful tool to process RAR and ZIP files". rarsoft.com.
  13. ^ "WireGuard: Next Generation Kernel Network Tunnel" (PDF).

External linksEdit