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Monthly Downloads: 17,580
Programming language: Elixir
License: MIT License
Tags: Text And Numbers    
Latest version: v0.1.24

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README

Caustic Cryptocurrency Library

Caustic is an Elixir cryptocurrency library which contains algorithms used in Bitcoin, Ethereum, and other blockchains. It also includes a rich cryptography, number theory, and general mathematics class library. You can use Caustic to quickly implement your own crypto wallet or client. With the low-level math library, you can have fun with exploratory mathematics.

Warning: This library is developed for learning purposes. Please do not use for production.

Documentation

https://hexdocs.pm/caustic/

Installation

Add to mix.exs of your Elixir project:

defp deps do
  [
    {:caustic, "~> 0.1.22"}
  ]
end

And then run:

mix deps.get

Usage

Cryptocurrency

You can generate Bitcoin private keys.

privkey = Caustic.Secp256k1.generate_private_key()
# 55129182198667841522063226112743062531539377180872956850932941251085402073984

privkey_base58check = Caustic.Utils.base58check_encode(<<privkey::size(256)>>, :private_key_wif, convert_from_hex: false)
# 5Jjxv41cLxb3hBZRr5voBB7zj77MDo7QVVLf3XgK2tpdAoTNq9n

You can then digitally sign a message.

pubkey = Caustic.Secp256k1.public_key(privkey)
# {6316467786437337873577388437635743649101330733943708346103893494005928771381, 36516277665018688612645564779200795235396005730419130160033716279021320193545}

message = "Hello, world!!!"
hash = Caustic.Utils.hash256(message)
signature = Caustic.Secp256k1.ecdsa_sign(hash, privkey)
Caustic.Secp256k1.ecdsa_verify?(pubkey, hash, signature) # true

Number theory

Caustic has many functions to deal with integers and their properties. For example you can do primality testing.

first_primes = 1..20 |> Enum.filter(&Caustic.Utils.prime?/1)
# [2, 3, 5, 7, 11, 13, 17, 19]

So 7 is supposed to be a prime. Let's confirm by finding its divisors:

Caustic.Utils.divisors 7
# [1, 7]

This is in contrast to 6 for example, which has divisors other than 1 and itself:

Caustic.Utils.divisors 6
# [1, 2, 3, 6]

The sum of 6's divisors other than itself (its proper divisors) equals to 6 again. Those kinds of numbers are called perfect numbers.

Caustic.Utils.proper_divisors 6    
# [1, 2, 3]
Caustic.Utils.proper_divisors_sum 6                               
# 6
Caustic.Utils.perfect? 6
# true

We can easily find other perfect numbers.

1..10000 |> Enum.filter(&Caustic.Utils.perfect?/1)
# [6, 28, 496, 8128]

There aren't that many of them, it seems...

Now back to our list of first primes. You can find the primitive roots of those primes:

first_primes |> Enum.map(&{&1, Caustic.Utils.primitive_roots(&1)})
# [
#   {2, [1]},
#   {3, [2]},
#   {5, [2, 3]},
#   {7, [3, 5]},
#   {11, [2, 6, 7, 8]},
#   {13, [2, 6, 7, 11]},
#   {17, [3, 5, 6, 7, 10, 11, 12, 14]},
#   {19, [2, 3, 10, 13, 14, 15]}
# ]

We can see that 5 is a primitive root of 7. It means that repeated exponentiation of 5 modulo 7 will generate all numbers relatively prime to 7. Let's confirm it:

Caustic.Utils.order_multiplicative 5, 7
# 6
1..6 |> Enum.map(&Caustic.Utils.pow_mod(5, &1, 7))
# [5, 4, 6, 2, 3, 1]

First we check the order of 5 modulo 7. It is 6, which means that 56 = 1 (mod 7), so further repeated multiplication (57 etc.) will just repeat previous values.

Then we calculate 51 to 56 (mod 7), and as expected it cycles through all numbers relatively prime to 7 because 5 is a primitive root of 7.

For more examples, please see the documentation of Caustic.Utils.

Contribute

Please send pull requests to https://github.com/agro1986/caustic

Contact

@agro1986 on Twitter