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Bitcoin, Bitcoin, Bitcoin

Let's calculate the classic bitcoin (crypto) block hash from scratch (zero). Let's start with the genesis block, that is block #0 with the unique block hash id 000000000019d6689c085ae165831e934ff763ae46a2a6c172b3f1b60a8ce26f.

Note: You can search and browse bitcoin blocks using (online) block explorers. Example:

The classic bitcoin (crypto) block hash gets calculated from the 80-byte block header:

Field Size (Bytes) Comments
version 4 byte Block version number
prev 32 byte 256-bit hash of the previous block header
merkleroot 32 byte 256-bit hash of all transactions in the block
time 4 bytes Current timestamp as seconds since 1970-01-01 00:00
bits 4 bytes Current difficulty target in compact binary format
nonce 4 bytes 32-bit number of the (mined) lucky lottery number used once

Note: 32 byte x 8 bit = 256 bit

Using the data for the genesis block the setup is:

version    = 1
prev       = '0000000000000000000000000000000000000000000000000000000000000000'
merkleroot = '4a5e1e4baab89f3a32518a88c31bc87f618f76673e2cc77ab2127b7afdeda33b'
time       = 1231006505
bits       = '1d00ffff'
nonce      = 2083236893

Remember: To convert from Epoch time (seconds since January 1st, 1970) to classic time use:

Time.at( 1231006505 ).utc
#=> "2009-01-03 18:15:05"

Yes, the bitcoin classic started on January 3rd, 2009 at 18h 15m 5s (2009-01-03 18:15:05). Or in the other direction use:

Time.utc( 2009, 1, 3, 18, 15, 5 ).to_i
#=> 1231006505

What's UTC? Coordinated Universal Time is the "standard" world time. Note: UTC does NOT observe daylight saving time.

Binary Bytes - Little End(ian) vs Big End(ian)

In theory calculating the block hash is as easy as:

## pseudo-code
header = "..."           # 80 bytes (binary)
d1 = sha256( header )
d2 = sha256( d1 )
d2.to_s                  # convert 32-byte (256-bit) binary to hex string
#=> "000000000019d6689c085ae165831e934ff763ae46a2a6c172b3f1b60a8ce26f"

Note: Classic bitcoin uses a double hash, that is, for even higher security the hash gets hashed twice with the SHA256 algorithm e.g. sha256(sha256(header)).

In practice let's deal with the different byte order conversions from big endian (most significant bit first) to little endian (least significant bit first) and back again.

Tip: Read more about Endianness @ Wikipedia.

Let's put together the (binary) 80-byte header using the int4 and hex32 big-endian to little-endian byte order (to binary bytes) conversion helpers:

header =
   int4( version       ) +
  hex32( prev          ) +
  hex32( merkleroot    ) +
   int4( time          ) +
   int4( bits.to_i(16) ) +
   int4( nonce         )

header.size
#=> 80

bin_to_hex( header )
# => "01000000" +
#    "0000000000000000000000000000000000000000000000000000000000000000" +
#    "3ba3edfd7a7b12b27ac72c3e67768f617fc81bc3888a51323a9fb8aa4b1e5e4a" +
#    "29ab5f49" +
#    "ffff001d" +
#    "1dac2b7c"

And run the hash calculations:

d1 = Digest::SHA256.digest( header )
d2 = Digest::SHA256.digest( d1 )
bin_to_hex32( d2 )
#=> '000000000019d6689c085ae165831e934ff763ae46a2a6c172b3f1b60a8ce26f'

Bingo! The resulting block hash is 000000000019d6689c085ae165831e934ff763ae46a2a6c172b3f1b60a8ce26f.

Let's backtrack and add the missing binary conversion helpers, that is, int4, hex32, bin_to_hex32 and bin_to_hex.

def int4( num )   ##  integer 4 byte(32bit) to binary (little endian)
  [num].pack( 'V' )
end

def hex32( hex )   ## hex string 32 byte(256bit) / 64 hex chars to binary
  [hex].pack( 'H*' ).reverse     ## change byte order (w/ reverse)
end

def bin_to_hex32( bytes )
  bytes.reverse.unpack( 'H*' )[0]   ## note: change byte order (w/ reverse)
end

def bin_to_hex( bytes )
  bytes.unpack( 'H*' )[0]
end

To convert integers (4 bytes / 32 bit) to binary bytes (in little endian) use:

int4( version )
#=> "\x01\x00\x00\x00"
bin_to_hex( int4( version ))
#=> "01000000"

compare to "classic" hex string (in big endian):

pp "%08x" % version  
#=> "00000001"

What's better? Big-endian 00000001 or little-endian 01000000? What's better? Ruby or Python? Red or Blue? Bitshilling or Bitcoin?

Let's celebrate that there's more than one way to do it :-). Onwards.

To convert a hex string (32 byte / 256 bit / 64 hex chars) to binary bytes (in little endian) use:

hex32( merkleroot )
#=> ";\xA3\xED\xFDz{\x12\xB2z\xC7,>gv\x8Fa\x7F\xC8\e\xC3\x88\x8A..."
bin_to_hex( hex32( merkleroot ))
#=> "3ba3edfd7a7b12b27ac72c3e67768f617fc81bc3888a51323a9fb8aa4b1e5e4a"

and to convert back from binary bytes (in little endian) to a hex string use:

bin_to_hex32( hex32( merkleroot ))   # to little-endian and binary and back again
#=> "4a5e1e4baab89f3a32518a88c31bc87f618f76673e2cc77ab2127b7afdeda33b"

What's better? Big-endian 4a5e1e4baab89f3a32518a88c31bc87f618f76673e2cc77ab2127b7afdeda33b or little-endian 3ba3edfd7a7b12b27ac72c3e67768f617fc81bc3888a51323a9fb8aa4b1e5e4a?

What's that pack/unpack magic? See the ruby documentation for Array#pack and String#unpack for the binary data packing and unpacking machinery

To sum up all together now. Let's use the Block #125552 used as a sample in the Bitcoin Block hashing algorithm wiki page:

version    =  1
prev       = '00000000000008a3a41b85b8b29ad444def299fee21793cd8b9e567eab02cd81'
merkleroot = '2b12fcf1b09288fcaff797d71e950e71ae42b91e8bdb2304758dfcffc2b620e3'
time       =  1305998791     ## 2011-05-21 17:26:31
bits       = '1a44b9f2'
nonce      =  2504433986

header =  int4( version       ) +
         hex32( prev          ) +
         hex32( merkleroot    ) +
          int4( time          ) +
          int4( bits.to_i(16) ) +
          int4( nonce         )

d1 = Digest::SHA256.digest( header )
d2 = Digest::SHA256.digest( d1 )
bin_to_hex32( d2 )
#=> "00000000000000001e8d6829a8a21adc5d38d0a473b144b6765798e61f98bd1d"

Bonus. For easy (re)use let's package up the bitcoin block header code into a class:

require 'digest'

module Bitcoin
  class Header
    attr_reader :version
    attr_reader :prev
    attr_reader :merkleroot
    attr_reader :time
    attr_reader :bits
    attr_reader :nonce

    def initialize( version, prev, merkleroot, time, bits, nonce )
       @version    = version
       @prev       = prev
       @merkleroot = merkleroot
       @time       = time
       @bits       = bits
       @nonce      = nonce
    end

    ## lets add a convenience c'tor helper
    def self.from_hash( h )
      new( h[:version],
           h[:prev],
           h[:merkleroot],
           h[:time],
           h[:bits],
           h[:nonce] )
    end

    def to_bin
       i4( version )       +
      h32( prev )          +
      h32( merkleroot )    +
       i4( time )          +
       i4( bits.to_i(16) ) +
       i4( nonce )
    end

    def hash
      bytes = sha256(sha256( to_bin ))
      bin_to_h32( bytes )
    end

    def sha256( bytes )
       Digest::SHA256.digest( bytes )
    end

    ## binary pack/unpack conversion helpers
    def i4( num )   ##  integer (4 byte / 32bit) to binary (in little endian)
      [num].pack( 'V' )
    end

    def h32( hex )   ## hex string (32 byte / 256 bit / 64 hex chars) to binary
      [hex].pack( 'H*' ).reverse     ## change byte order (w/ reverse)
    end

    def bin_to_h32( bytes )
      bytes.reverse.unpack( 'H*' )[0]   ## note: change byte order (w/ reverse)
    end
  end # class Header
end # module Bitcoin

and let's test drive it with the genesis block #0 and block #125552:

b0 =
Bitcoin::Header.from_hash(
  version:     1,
  prev:       '0000000000000000000000000000000000000000000000000000000000000000',
  merkleroot: '4a5e1e4baab89f3a32518a88c31bc87f618f76673e2cc77ab2127b7afdeda33b',
  time:        1231006505,
  bits:       '1d00ffff',
  nonce:       2083236893 )

b0.hash
#=> "000000000019d6689c085ae165831e934ff763ae46a2a6c172b3f1b60a8ce26f"

b125552 =
Bitcoin::Header.from_hash(
  version:     1,
  prev:       '00000000000008a3a41b85b8b29ad444def299fee21793cd8b9e567eab02cd81',
  merkleroot: '2b12fcf1b09288fcaff797d71e950e71ae42b91e8bdb2304758dfcffc2b620e3',
  time:        1305998791,
  bits:       '1a44b9f2',
  nonce:       2504433986 )

b125552.hash
#=> "00000000000000001e8d6829a8a21adc5d38d0a473b144b6765798e61f98bd1d"