Signatures and Bitcoin flavoured crypto written in pure Elixir. Curvy is an implementation of secp256k1, an elliptic curve that can be used in signature schemes, asymmetric encryption and ECDH shared secrets.

Highlights

• Pure Elixir implementation of secp256k1 - no external dependencies
• Fast ECDSA cryptography using Jacobian Point mathematics
• Supports deterministic ECDSA signatures as per RFC 6979
• Securely generate random ECDSA keypairs
• Compute ECDH shared secrets

Installation

The package can be installed by adding curvy to your list of dependencies in mix.exs.

def deps do
  [
    {:curvy, "~> 0.3.0"}
  ]
end

Usage

1. Key generation

Create random ECDSA keypairs.

iex> key = Curvy.generate_key()
%Curvy.Key{
  crv: :secp256k1,
  point: %Curvy.Point{},
  private_key: <<>>
}

ECDSA Keypairs can by converted to public and private key binaries.

iex> Curvy.Key.to_privkey(key)
<<privkey::binery-size(32)>>

iex> Curvy.Key.to_pubkey(key)
<<privkey::binary-size(33)>>

iex> Curvy.Key.to_pubkey(key, compressed: false)
<<privkey::binary-size(65)>>

2. Sign messages

Sign arbitrary messages with a private key. Signatures are deterministic as per RFC 6979.

iex> sig = Curvy.sign("hello", key)
<<sig::binary-size(71)>>

iex> sig = Curvy.sign("hello", compact: true)
<<sig::binary-size(65)>>

iex> sig = Curvy.sign("hello", compact: true, encoding: :base64)
"IEnXUDXZ3aghwXaq1zu9ax2zJj7N+O4gGREmWBmrldwrIb9B7QuicjwPrrv3ocPpxYO7uCxcw+DR/FcHR9b/YjM="

3. Verify signatures

Verify a signature against the message and a public key.

iex> sig = Curvy.verify(sig, "hello", key)
true

iex> sig = Curvy.verify(sig, "hello", wrongkey)
false

# Returns :error if the signature cannot be decoded
iex> sig = Curvy.verify("notasig", "hello", key)
:error

4. Recover the public key from a signature

It's possible to recover the public key from a compact signature when given with the signed message.

iex> sig = Curvy.sign("hello", key, compact: true)
iex> recovered = Curvy.recover_key(sig, "hello")
iex> recovered.point == key.point
true

The same can be done with DER encoded signatures if the recovery ID is known.

iex> {sig, recovery_id} = Curvy.sign("hello", key, recovery: true)
iex> recovered = Curvy.recover_key(sig, "hello", recovery_id: recovery_id)
iex> recovered.point == key.point
true

5. ECDH shared secrets

ECDH shared secrets are computed by multiplying a public key with a private key. The operation yields the same result in both directions.

iex> s1 = Curvy.get_shared_secret(key1, key2)
iex> s2 = Curvy.get_shared_secret(key2, key1)
iex> s1 == s2
true