Yuki & Moto Press

Programming Blockchains Step-by-Step

(Crypto) Hash

(Crypto) Block

(Crypto) Block with Proof-of-Work

Blockchain

Blockchain Broken?

Timestamping

Mining, Mining, Mining

Bitcoin, Bitcoin, Bitcoin

(Crypto) Block with Transactions (Tx)

References / Links

Contents

Let’s build blockchains from scratch (zero) step by step.

(Crypto) Hash

Let’s start with crypto hashes

Classic Bitcoin uses the SHA256 hash algorithm. Let’s try

require 'digest' Digest :: SHA256 . hexdigest ( 'Hello, Cryptos!' )

resulting in

#=> "33eedea60b0662c66c289ceba71863a864cf84b00e10002ca1069bf58f9362d5"

Try some more

Digest :: SHA256 . hexdigest ( 'Hello, Cryptos! - Hello, Cryptos! - Hello, Cryptos!' ) #=> "c4b5e2b9685062ecca5d0f6f6ba605b3f99eafed3a3729d2ae1ccaa2b440b1cc" Digest :: SHA256 . hexdigest ( 'Your Name Here' ) #=> "39459289c09c33a7b516bef926c1873c6ecd2e6db09218b065d7465b6736f801" Digest :: SHA256 . hexdigest ( 'Data Data Data Data' ) #=> "a7bbfc531b2ecf641b9abcd7ad8e50267e1c873e5a396d1919f504973090565a"

Note: The resulting hash is always 256-bit in size or 64 hex(adecimal) chars (0-9,a-f) in length even if the input is less than 256-bit or much bigger than 256-bit:

Digest :: SHA256 . hexdigest ( << TXT ) Data Data Data Data Data Data Data Data Data Data Data Data Data Data Data Data Data Data Data Data Data Data Data Data Data Data Data Data Data Data TXT #=> "c51023e2c874b6cf46cb0acef183ee1c05f14746636352d1b2cb9fc6aa5c3cee" ## use String#length Digest :: SHA256 . hexdigest ( 'Hello, Cryptos!' ). length # => 64 Digest :: SHA256 . hexdigest ( 'Hello, Cryptos! - Hello, Cryptos! - Hello, Cryptos!' ). length # => 64

Note: 1 hex char is 4-bits, 2 hex chars are 4x2=8 bits and 64 hex chars are 4x64=256 bits.

Hexa(decimal) chart:

binary hex (2^4=16) decimal binary hex (2^4=16) decimal 0000 0 0 1000 8 8 0001 1 1 1001 9 9 0010 2 2 1010 a 10 0011 3 3 1011 b 11 0100 4 4 1100 c 12 0101 5 5 1101 d 13 0110 6 6 1110 e 14 0111 7 7 1111 f 15

Let’s convert from hex (base 16) to decimal (integer) number (base 10)

hex = Digest :: SHA256 . hexdigest ( 'Hello, Cryptos!' ) #=> "33eedea60b0662c66c289ceba71863a864cf84b00e10002ca1069bf58f9362d5" hex . to_i ( 16 ) #=> 23490001543365037720284007500157053051505610714786813679598750288695740555989

and convert to 256-bits (32-bytes) binary number (base 2) as a string:

hex . to_i ( 16 ). to_s ( 2 ) # => "0011 0011 1110 1110 1101 1110 1010 0110 0000 1011 0000 0110 0110 0010 1100 0110 # 0110 1100 0010 1000 1001 1100 1110 1011 1010 0111 0001 1000 0110 0011 1010 1000 # 0110 0100 1100 1111 1000 0100 1011 0000 0000 1110 0001 0000 0000 0000 0010 1100 # 1010 0001 0000 0110 1001 1011 1111 0101 1000 1111 1001 0011 0110 0010 1101 0101"

Trivia Quiz: What’s SHA256?

(A) Still Hacking Anyway

(B) Secure Hash Algorithm

(C) Sweet Home Austria

(D) Super High Aperture

A: SHA256 == Secure Hash Algorithms 256 Bits

SHA256 is a (secure) hashing algorithm designed by the National Security Agency (NSA) of the United States of America (USA).

Find out more @ Secure Hash Algorithms (SHA) @ Wikipedia.

A (secure) hash is also known as:

Digital (Crypto) Fingerprint == (Secure) Hash

Digital (Crypto) Digest == (Secure) Hash

Digital (Crypto) Checksum == (Secure) Hash

(Crypto) Block

Let’s build blocks (secured) with crypto hashes. First let’s define a block class:

require 'digest' require 'pp' ## pp = pretty print class Block attr_reader :data attr_reader :hash def initialize ( data ) @data = data @hash = Digest :: SHA256 . hexdigest ( data ) end end

And let’s mine (build) some blocks with crypto hashes:

pp Block . new ( 'Hello, Cryptos!' ) #=> #<Block:0x1ef9a68 # @data="Hello, Cryptos!", # @hash="33eedea60b0662c66c289ceba71863a864cf84b00e10002ca1069bf58f9362d5"> pp Block . new ( 'Hello, Cryptos! - Hello, Cryptos! - Hello, Cryptos!' ) #=> <Block:0x1eebdd0 # @data="Hello, Cryptos! - Hello, Cryptos! - Hello, Cryptos!", # @hash="c4b5e2b9685062ecca5d0f6f6ba605b3f99eafed3a3729d2ae1ccaa2b440b1cc"> pp Block . new ( 'Your Name Here' ) #=> #<Block:0x1eeac78 # @data="Your Name Here", # @hash="39459289c09c33a7b516bef926c1873c6ecd2e6db09218b065d7465b6736f801"> pp Block . new ( 'Data Data Data Data' ) #=> <Block:0x1ee9b98 # @data="Data Data Data Data", # @hash="a7bbfc531b2ecf641b9abcd7ad8e50267e1c873e5a396d1919f504973090565a">

Note: All the hashes (checksums/digests/fingerprints) are the same as above! Same input e.g. 'Hello, Cryptos!' , same hash e.g. 33eedea60b0662c66c289ceba71863a864cf84b00e10002ca1069bf58f9362d5 , same length e.g. 64 hex chars!

And the biggie:

pp Block . new ( << TXT ) Data Data Data Data Data Data Data Data Data Data Data Data Data Data Data Data Data Data Data Data Data Data Data Data Data Data Data Data Data Data TXT # => #<Block:0x1e489a8 # @data=" Data Data Data Data Data Data

# Data Data Data Data Data Data

# Data Data Data Data Data Data

# Data Data Data Data Data Data

# Data Data Data Data Data Data

", # @hash="c51023e2c874b6cf46cb0acef183ee1c05f14746636352d1b2cb9fc6aa5c3cee">

(Crypto) Block with Proof-of-Work

Let’s add a proof-of-work to the block and hash. and let’s start mining to find the nonce (=Number used ONCE) and let’s start with the “hard-coded” difficulty of two leading zeros ‘00’.

In classic bitcoin you have to compute a hash that starts with leading zeros ( 00 ). The more leading zeros the harder (more difficult) to compute. Let’s keep it easy to compute and let’s start with two leading zeros ( 00 ), that is, 16^2 = 256 possibilities (^1,2). Three leading zeros ( 000 ) would be 16^3 = 4 096 possibilities and four zeros ( 0000 ) would be 16^4 = 65 536 and so on.

(1): 16 possibilities because it’s a hex or hexadecimal or base 16 number, that is, 0 1 2 3 4 5 6 7 8 9 a (10) b (11) c (12) d (13) e (14) f (15).

(2): A random secure hash algorithm needs on average 256 tries (might be lets say 305 tries, for example, because it’s NOT a perfect statistic distribution of possibilities).

require 'digest' require 'pp' ## pp = pretty print class Block attr_reader :data attr_reader :hash attr_reader :nonce # number used once - lucky (mining) lottery number def initialize ( data ) @data = data @nonce , @hash = compute_hash_with_proof_of_work end def compute_hash_with_proof_of_work ( difficulty = '00' ) nonce = 0 loop do hash = Digest :: SHA256 . hexdigest ( " #{ nonce }#{ data } " ) if hash . start_with? ( difficulty ) return [ nonce , hash ] ## bingo! proof of work if hash starts with leading zeros (00) else nonce += 1 ## keep trying (and trying and trying) end end # loop end # method compute_hash_with_proof_of_work end # class Block

And let’s mine (build) some blocks with crypto hashes with a “hard-coded” difficulty of two leading zeros ‘00’:

pp Block . new ( 'Hello, Cryptos!' ) #=> #<Block:0x1d84b50 # @data="Hello, Cryptos!", # @hash="00ecb8b247998f9ddd15d2a5693777ee0041d138fa3bc5c1f6ccc12ec1cfece4", # @nonce=143> pp Block . new ( 'Hello, Cryptos! - Hello, Cryptos! - Hello, Cryptos!' ) #=> #<Block:0x1d67f18 # @data="Hello, Cryptos! - Hello, Cryptos! - Hello, Cryptos!", # @hash="0014406a868d202e2c6c3896af997e189daafc9df1878f9824cba2050fda199f", # @nonce=59> pp Block . new ( 'Your Name Here' ) #=> #<Block:0x1d64270 # @data="Your Name Here", # @hash="0012c3a90e58c9569ef0c036e6220c86c7c253ac94c0eb0064bf98df59acdfad", # @nonce=57> pp Block . new ( 'Data Data Data Data' ) #=> #<Block:0x139b828 # @data="Data Data Data Data", # @hash="00e2da510b97434713d63234f3ba2d816c8d52f29f9ffd267423c39d9ced7a70", # @nonce=73>

See the difference? Now all hashes start with ‘00’ e.g.

Block Hash with Proof-of-Work #1 00ecb8b247998f9ddd15d2a5693777ee0041d138fa3bc5c1f6ccc12ec1cfece4 #2 0014406a868d202e2c6c3896af997e189daafc9df1878f9824cba2050fda199f #3 0012c3a90e58c9569ef0c036e6220c86c7c253ac94c0eb0064bf98df59acdfad #4 00e2da510b97434713d63234f3ba2d816c8d52f29f9ffd267423c39d9ced7a70

That’s the magic of the proof-of-work. You have done the work, that is, found the lucky lottery number used once (nonce) and proof is the hash with the matching difficulty, that is, the two leading zeros 00 .

In the first block the compute_hash_with_proof_of_work tried 143 nonces until finding the matching lucky number. The stat(istic)s for all blocks are:

Block Loops / Number of Hash calculations #1 143 #2 59 #3 57 #4 73

The lucky nonce for block #1 is 143:

Try:

Digest :: SHA256 . hexdigest ( '0Hello, Cryptos!' ) # keep trying... # => "8954dec596f0baa0cb6b8cc9f5837037d4380e28338ccccdf5f00658010caf07" Digest :: SHA256 . hexdigest ( '1Hello, Cryptos!' ) # keep trying... # => "831c988d0745d1f02cf790c3b3d9c9f610ddb7d36d5b96c7b3413ccd1b6f46e1" Digest :: SHA256 . hexdigest ( '2Hello, Cryptos!' ) # keep trying... # => "ac6ccb11092f867dc5f10daaebcd7938f90d1627a7e277b940cdd2e4881ea712" # ...

Now try:

Digest :: SHA256 . hexdigest ( '143Hello, Cryptos!' ) # bingo!!! # => "00ecb8b247998f9ddd15d2a5693777ee0041d138fa3bc5c1f6ccc12ec1cfece4"

Let’s try a difficulty of four leading zeros ‘0000’.

Note: One hex char is 4-bits, thus, ‘0’ in hex (base16) is ‘0000’ in binary (base2) and, thus, ‘00’ in hex (base16) is 2x4=8 zeros in binary (base2) e.g. ‘0000 0000’ and, thus, ‘0000’ in hex (base16) is 4x4=16 zeros in binary (base) e.g. ‘0000 0000 0000 0000’

Change the “hard-coded” difficulty from 00 to 0000 e.g.

def compute_hash_with_proof_of_work ( difficulty = '0000' ) ... end

and rerun or let’s mine blocks again:

pp Block . new ( 'Hello, Cryptos!' ) #=> #<Block:0x1ef4b60 # @data="Hello, Cryptos!", # @hash="0000a1ee5cb18c8d9fff5262b6dcb1bc95d54a331713e247f699f158f2022143", # @nonce=26762> pp Block . new ( 'Hello, Cryptos! - Hello, Cryptos! - Hello, Cryptos!' ) #=> #<Block:0x1f4c160 # @data="Hello, Cryptos! - Hello, Cryptos! - Hello, Cryptos!", # @hash="0000b27eeebe56b2daafeb935454d0e3f423fc7f5ac7a99e952f9b80475ef6c3", # @nonce=68419> pp Block . new ( 'Your Name Here' ) #=> #<Block:0x1ee8800 # @data="Your Name Here", # @hash="00000e59a4a7fb35d0d03def6ce31f503c208e6c291dcc9a217a7278ad1b95ce", # @nonce=23416> pp Block . new ( 'Data Data Data Data' ) # => #<Block:0x1f7a960 # @data="Data Data Data Data", # @hash="00000e3cff496c5afc18645dba31ae9ba5c6077e5a5d980d8512e4581e7d61ec", # @nonce=15353>

See the difference? Now all hashes start with ‘0000’ e.g.

Block Hash with Proof-of-Work #1 0000a1ee5cb18c8d9fff5262b6dcb1bc95d54a331713e247f699f158f2022143 #2 0000b27eeebe56b2daafeb935454d0e3f423fc7f5ac7a99e952f9b80475ef6c3 #3 00000e59a4a7fb35d0d03def6ce31f503c208e6c291dcc9a217a7278ad1b95ce #4 00000e3cff496c5afc18645dba31ae9ba5c6077e5a5d980d8512e4581e7d61ec

The nonce hash calculation stat(istic)s for all blocks are:

Block Loops / Number of Hash calculations #1 26 762 #2 68 419 #3 23 416 #4 15 353

In the first block the compute_hash_with_proof_of_work now tried 26 762 nonces (compare 143 nonces with difficulty ‘00’) until finding the matching lucky number.

Now try it with the latest difficulty in bitcoin, that is, with 24 leading zeros - just kidding. You will need trillions of mega zillions of hash calculations and all minining computers in the world will need all together about ten (10) minutes to find the lucky number used once (nonce) and mine the next block.

Let’s retry the ‘0000’ difficulty hash calculations “by hand”:

Digest :: SHA256 . hexdigest ( '26762Hello, Cryptos!' ) #=> "0000a1ee5cb18c8d9fff5262b6dcb1bc95d54a331713e247f699f158f2022143" Digest :: SHA256 . hexdigest ( '68419Hello, Cryptos! - Hello, Cryptos! - Hello, Cryptos!' ) #=> "0000b27eeebe56b2daafeb935454d0e3f423fc7f5ac7a99e952f9b80475ef6c3" Digest :: SHA256 . hexdigest ( '23416Your Name Here' ) #=> "00000e59a4a7fb35d0d03def6ce31f503c208e6c291dcc9a217a7278ad1b95ce" Digest :: SHA256 . hexdigest ( '15353Data Data Data Data' ) #=> "00000e3cff496c5afc18645dba31ae9ba5c6077e5a5d980d8512e4581e7d61ec"

Blockchain

Blockchain! Blockchain! Blockchain!

Let’s link the (crypto) blocks together into a chain of blocks, that is, blockchain, to revolutionize the world one block at a time.

Trivia Quiz: What’s the unique id(entifier) of a block?

(A) (Secure) Hash

(B) Block Hash

(C) Digital (Crypto) Digest

A: All of the above :-). (Secure) hash == block hash == digital (crypto) digest.

Thus, add the (secure) hash of the prev(ious) block to the new block and the hash calculation e.g.:

Digest :: SHA256 . hexdigest ( " #{ nonce }#{ prev }#{ data } " )

Bingo! Blockchain! Blockchain! Blockchain! All together now:

require 'digest' require 'pp' ## pp = pretty print class Block attr_reader :data attr_reader :prev # prev(ious) (block) hash attr_reader :hash attr_reader :nonce # number used once - lucky (mining) lottery number def initialize ( data , prev ) @data = data @prev = prev @nonce , @hash = compute_hash_with_proof_of_work end def compute_hash_with_proof_of_work ( difficulty = '0000' ) nonce = 0 loop do hash = Digest :: SHA256 . hexdigest ( " #{ nonce }#{ prev }#{ data } " ) if hash . start_with? ( difficulty ) return [ nonce , hash ] ## bingo! proof of work if hash starts with leading zeros (00) else nonce += 1 ## keep trying (and trying and trying) end end # loop end # method compute_hash_with_proof_of_work end # class Block

Note: For the first block, that is, the genesis block, there’s no prev(ious) block. What (block) hash to use? Let’s follow the classic bitcoin convention and lets use all zeros eg. 0000000000000000000000000000000000000000000000000000000000000000 .

Genesis. A new blockchain is born!

b0 = Block . new ( 'Hello, Cryptos!' , '0000000000000000000000000000000000000000000000000000000000000000' ) #=> #<Block:0x4d11ce0 # @data="Hello, Cryptos!", # @hash="000047954e7d5877b6dea6915c48e84579b5c64fb58d5b6488863c241f1ce2af", # @nonce=24287, # @prev="0000000000000000000000000000000000000000000000000000000000000000">

Let’s mine (build) some more blocks linked (chained) together with crypto hashes:

b1 = Block . new ( 'Hello, Cryptos! - Hello, Cryptos!' , '000047954e7d5877b6dea6915c48e84579b5c64fb58d5b6488863c241f1ce2af' ) # -or- b1 = Block . new ( 'Hello, Cryptos! - Hello, Cryptos!' , b0 . hash ) #=> #<Block:0x4dce620 # @data="Hello, Cryptos! - Hello, Cryptos!", # @hash="00002acb41e00fb252b8fedeed7d4a629dafb28517bcf6235b90367ee6f63a7f", # @nonce=191453, # @prev="000047954e7d5877b6dea6915c48e84579b5c64fb58d5b6488863c241f1ce2af"> b2 = Block . new ( 'Your Name Here' , b1 . hash ) #=> #<Block:0x4d9d798 # @data="Your Name Here", # @hash="0000d85423bc8d3ccda0e83ddd6e7e9d6a30f393b73705409b481be57eeaad37", # @nonce=109213, # @prev="00002acb41e00fb252b8fedeed7d4a629dafb28517bcf6235b90367ee6f63a7f"> b3 = Block . new ( 'Data Data Data Data' , b2 . hash ) #=> #<Block:0x46cfc80 # @data="Data Data Data Data", # @hash="000000c652265dcf44f0b18911435100f4677bdc468f8f1dd85910d581b3542d", # @nonce=129257, # @prev="0000d85423bc8d3ccda0e83ddd6e7e9d6a30f393b73705409b481be57eeaad37">

Let’s store all blocks together (in an array):

blockchain = [ b0 , b1 , b2 , b3 ] pp blockchain ## pretty print (pp) blockchain #=> [#<Block:0x4d010a8 # @data="Hello, Cryptos!", # @hash="000047954e7d5877b6dea6915c48e84579b5c64fb58d5b6488863c241f1ce2af", # @nonce=24287, # @prev="0000000000000000000000000000000000000000000000000000000000000000">, # #<Block:0x4685388 # @data="Hello, Cryptos! - Hello, Cryptos!", # @hash="00002acb41e00fb252b8fedeed7d4a629dafb28517bcf6235b90367ee6f63a7f", # @nonce=191453, # @prev="000047954e7d5877b6dea6915c48e84579b5c64fb58d5b6488863c241f1ce2af">, # #<Block:0x4d6d120 # @data="Your Name Here", # @hash="0000d85423bc8d3ccda0e83ddd6e7e9d6a30f393b73705409b481be57eeaad37", # @nonce=109213, # @prev="00002acb41e00fb252b8fedeed7d4a629dafb28517bcf6235b90367ee6f63a7f">, # #<Block:0x469ec30 # @data="Data Data Data Data", # @hash="000000c652265dcf44f0b18911435100f4677bdc468f8f1dd85910d581b3542d", # @nonce=129257, # @prev="0000d85423bc8d3ccda0e83ddd6e7e9d6a30f393b73705409b481be57eeaad37">]

Note: If you want to change the data in block b1, for examples, you have to change all the blocks on top (that is, b2 and b3) too and update their hashes too! With every block added breaking the chain gets harder and harder and harder (not to say practically impossible!). That’s the magic of the blockchain - it’s (almost) unbreakable if you have many shared / cloned copies. The data gets more secure with every block added (on top), …

Blockchain Broken?

How do you know if anyone changed (broke) the (almost) unbreakable blockchain and changed some data in blocks? Let’s run tests checking up on the chained / linked (crypto) hashes:

b0 . prev == '0000000000000000000000000000000000000000000000000000000000000000' #=> true b1 . prev == b0 . hash #=> true b2 . prev == b1 . hash #=> true b3 . prev == b2 . hash #=> true

All true, true, true, true. All in order? What if someone changes the data but keeps the original (now fake non-matching) hash? Let’s run more tests checking up on the (crypto) hashes by recalculating (using nonce + prev + data ) right on the spot plus checking up on the proof-of-work difficulty (hash must start with 0000 ):

## shortcut convenience helper def sha256 ( data ) Digest :: SHA256 . hexdigest ( data ) end b0 . hash == sha256 ( " #{ b0 . nonce }#{ b0 . prev }#{ b0 . data } " ) # => true b1 . hash == sha256 ( " #{ b1 . nonce }#{ b1 . prev }#{ b1 . data } " ) # => true b2 . hash == sha256 ( " #{ b2 . nonce }#{ b2 . prev }#{ b2 . data } " ) # => true b3 . hash == sha256 ( " #{ b3 . nonce }#{ b3 . prev }#{ b3 . data } " ) # => true b0 . hash . start_with? ( '0000' ) # => true b1 . hash . start_with? ( '0000' ) # => true b2 . hash . start_with? ( '0000' ) # => true b3 . hash . start_with? ( '0000' ) # => true

All true, true, true, true, true, true, true, true. All in order? Yes. The blockchain is (almost) unbreakable.

Let’s try to break the unbreakable. Let’s change the block b1 from 'Hello, Cryptos!' to 'Hello, Koruptos!' :

b1 = Block . new ( 'Hello, Koruptos! - Hello, Koruptos!' , b0 . hash ) #=> #<Block:0x4daa9f8 # @data="Hello, Koruptos! - Hello, Koruptos!", # @hash="00000c915e240a2b386fc86ef6170261a19292b9fdebebce049c621da1ab7e8f", # @nonce=27889, # @prev="000047954e7d5877b6dea6915c48e84579b5c64fb58d5b6488863c241f1ce2af">

Now if you check:

b0 . prev == '0000000000000000000000000000000000000000000000000000000000000000' #=> true b1 . prev == b0 . hash #=> true b2 . prev == b1 . hash #=> false b3 . prev == b2 . hash #=> true

Fail! False! No longer all true. The chain is now broken. The chained / linked (crypto) hashes

b1.hash => 00002acb41e00fb252b8fedeed7d4a629dafb28517bcf6235b90367ee6f63a7f

=> b2.prev => 00000c915e240a2b386fc86ef6170261a19292b9fdebebce049c621da1ab7e8f

do no longer match. The only way to get the chained / linked (crypto) hashes back in order to true, true, true, true is to rebuild (remine) all blocks on top.

How can you make the blockchain even more secure? Link it to the real world! Let’s add a timestamp:

Time . now # => 2018-03-17 14:12:01 +0100

or in Epoch time (that is, seconds since January 1st, 1970)

Time . now . to_i # => 1521292321

Note: You can use Time.at to convert Epoch time back to the standard “classic” format:

Time . at ( 1521292321 ) # => 2018-03-17 14:12:01 +0100

Now the blockchain must always move forward, that is, you can only add a new block if the timestamp is bigger / younger than the previous block’s timestamp.

Unbreakable. Unbreakable. Unbreakable. What else?

Let’s add the proof-of-work difficulty (e.g. ‘00’, ‘000’, ‘0000’ etc.) to the hash to make the difficulty unbreakable / unchangeable too!

Last but not least let’s drop the “pre-calculated” hash attribute and let’s always calculate the hash on demand e.g.:

def hash Digest :: SHA256 . hexdigest ( " #{ nonce }#{ time }#{ difficulty }#{ prev }#{ data } " ) end

Remember: Calculating the block’s (crypto) hash is fast, fast, fast. What take’s time depending on the proof-of-work difficulty is finding the nonce, that is, the lucky number used once.

All together now. Resulting in:

require 'digest' require 'pp' ## pp = pretty print class Block attr_reader :data attr_reader :prev attr_reader :difficulty attr_reader :time attr_reader :nonce # number used once - lucky (mining) lottery number def hash Digest :: SHA256 . hexdigest ( " #{ nonce }#{ time }#{ difficulty }#{ prev }#{ data } " ) end def initialize ( data , prev , difficulty: '0000' ) @data = data @prev = prev @difficulty = difficulty @nonce , @time = compute_hash_with_proof_of_work ( difficulty ) end def compute_hash_with_proof_of_work ( difficulty = '00' ) nonce = 0 time = Time . now . to_i loop do hash = Digest :: SHA256 . hexdigest ( " #{ nonce }#{ time }#{ difficulty }#{ prev }#{ data } " ) if hash . start_with? ( difficulty ) return [ nonce , time ] ## bingo! proof of work if hash starts with leading zeros (00) else nonce += 1 ## keep trying (and trying and trying) end end # loop end # method compute_hash_with_proof_of_work end # class Block

Proof of the pudding. Let’s build a new (more secure) blockchain from scratch (zero). Genesis!

b0 = Block . new ( 'Hello, Cryptos!' , '0000000000000000000000000000000000000000000000000000000000000000' ) #=> #<Block:0x4d00700 # @data="Hello, Cryptos!", # @difficulty="0000", # @nonce=215028, # @prev="0000000000000000000000000000000000000000000000000000000000000000", # @time=1521292321>

Let’s mine (build) some more blocks linked (chained) together with crypto hashes:

b1 = Block . new ( 'Hello, Cryptos! - Hello, Cryptos!' , b0 . hash ) #=> #<Block:0x4ed7940 # @data="Hello, Cryptos! - Hello, Cryptos!", # @difficulty="0000", # @nonce=3264, # @prev="0000071b9c71675db90b0bb819236d76be97ac75f9f379d078456495133b18c6", # @time=1521292325> b2 = Block . new ( 'Your Name Here' , b1 . hash ) #=> #<Block:0x2f297e8 # @data="Your Name Here", # @difficulty="0000", # @nonce=81552, # @prev="0000a6f83a7883891afea2536891df228a1c527add36c1cc38999e566eeed6a7", # @time=1521292325> b3 = Block . new ( 'Data Data Data Data' , b2 . hash ) #=> #<Block:0x4dbd9d0 # @data="Data Data Data Data", # @difficulty="0000", # @nonce=43010, # @prev="00009b581870a4e0792f84786e1d089e32f2820459cd878298c6b62974afd0bc", # @time=1521292326>

Blockchain broken? Let’s run all the tests checking up on the chained / linked (crypto) hashes, timestamps, proof-of-work difficulty and more:

## shortcut convenience helper def sha256 ( data ) Digest :: SHA256 . hexdigest ( data ) end b0 . hash == sha256 ( " #{ b0 . nonce }#{ b0 . time }#{ b0 . difficulty }#{ b0 . prev }#{ b0 . data } " ) # => true b1 . hash == sha256 ( " #{ b1 . nonce }#{ b1 . time }#{ b1 . difficulty }#{ b1 . prev }#{ b1 . data } " ) # => true b2 . hash == sha256 ( " #{ b2 . nonce }#{ b2 . time }#{ b2 . difficulty }#{ b2 . prev }#{ b2 . data } " ) # => true b3 . hash == sha256 ( " #{ b3 . nonce }#{ b3 . time }#{ b3 . difficulty }#{ b3 . prev }#{ b3 . data } " ) # => true # check proof-of-work difficulty (e.g. '0000') b0 . hash . start_with? ( b0 . difficulty ) # => true b1 . hash . start_with? ( b1 . difficulty ) # => true b2 . hash . start_with? ( b2 . difficulty ) # => true b3 . hash . start_with? ( b3 . difficulty ) # => true ## check chained / linked hashes b0 . prev == '0000000000000000000000000000000000000000000000000000000000000000' #=> true b1 . prev == b0 . hash #=> true b2 . prev == b1 . hash #=> true b3 . prev == b2 . hash #=> true # check time moving forward; timestamp always greater/bigger/younger b1 . time > b0 . time #=> true b2 . time > b1 . time #=> true b3 . time > b2 . time #=> true Time . now . to_i > b3 . time ## back to the future (not yet) possible :-) #=> true

All true, true, true, true, true, true, true, true. All in order? Yes. The blockchain is (almost) unbreakable.

Mining, Mining, Mining

What’s your hash rate? Let’s find out. Let’s use a “stand-alone” version of the by now “classic” compute_hash_with_proof_of_work function:

require 'digest' def compute_hash_with_proof_of_work ( data , difficulty = '00' ) nonce = 0 loop do hash = Digest :: SHA256 . hexdigest ( " #{ nonce }#{ data } " ) if hash . start_with? ( difficulty ) return [ nonce , hash ] ## bingo! proof of work if hash starts with leading zeros (00) else nonce += 1 ## keep trying (and trying and trying) end end # loop end # method compute_hash_with_proof_of_work

Let’s try (run) benchmarks for the difficulty from 0 (4 bits) to 0000000 (28 bits). Remember: 0 in hex (base16, 2^4 bits) equals 0000 in binary (base2), thus, 0000000 in hex (base16) equals 0 x 4 x 7 = 28 zero bits in binary (base2). Example:

( 1 .. 7 ). each do | factor | difficulty = '0' * factor puts "difficulty: #{ difficulty } ( #{ difficulty . length * 4 } bits)" end # => difficulty: 0 (4 bits) # difficulty: 00 (8 bits) # difficulty: 000 (12 bits) # difficulty: 0000 (16 bits) # difficulty: 00000 (20 bits) # difficulty: 000000 (24 bits) # difficulty: 0000000 (28 bits)

Let’s add the hash proof-of-work hash computing machinery and re(run):

( 1 .. 7 ). each do | factor | difficulty = '0' * factor puts "Difficulty: #{ difficulty } ( #{ difficulty . length * 4 } bits)" puts "Starting search..." t1 = Time . now nonce , hash = compute_hash_with_proof_of_work ( 'Hello, Cryptos!' , difficulty ) t2 = Time . now delta = t2 - t1 puts "Elapsed Time: %.4f seconds, Hashes Calculated: %d" % [ delta , nonce ] if delta > 0 hashrate = Float ( nonce / delta ) puts "Hash Rate: %d hashes per second" % hashrate end puts end

Resulting on a “low-end” home computer:

Difficulty: 0 (4 bits) Starting search... Elapsed Time: 0.0156 seconds, Hashes Calculated: 56 Hash Rate: 3 588 hashes per second Difficulty: 00 (8 bits) Starting search... Elapsed Time: 0.0000 seconds, Hashes Calculated: 143 Hash Rate: Infinity ;-) Difficulty: 000 (12 bits) Starting search... Elapsed Time: 0.0313 seconds, Hashes Calculated: 3 834 Hash Rate: 122 684 hashes per second Difficulty: 0000 (16 bits) Starting search... Elapsed Time: 0.2656 seconds, Hashes Calculated: 26 762 Hash Rate: 100 753 hashes per second Difficulty: 00000 (20 bits) Starting search... Elapsed Time: 1.2031 seconds, Hashes Calculated: 118 592 Hash Rate: 98 569 hashes per second Difficulty: 000000 (24 bits) Starting search... Elapsed Time: 220.5767 seconds, Hashes Calculated: 21 554 046 Hash Rate: 97 716 hashes per second Difficulty: 0000000 (28 bits) Starting search...

To sum up the hash rate is about 100 000 hashes per second on a “low-end” home computer. What’s your hash rate? Run the benchmark on your machinery!

The search for the 28 bits difficulty proof-of-work hash is still running… expected to find the lucky number in the next hours…

Trivia Quiz: What’s the Hash Rate of the Bitcoin Classic Network?

A: About 25 million trillions of hashes per second (in March 2018)

Estimated number of tera hashes per second (trillions of hashes per second) the Bitcoin network is performing.

(Source: blockchain.info)

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"

(Crypto) Block with Transactions (Tx)

To be continued.

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