Falcon

Falcon: It's a post-quantum cryptography library for digital signatures based on the Falcon algorithm.

Introduction

Falcon is a post-quantum digital signature scheme selected by NIST as part of its efforts to develop cryptographic standards resilient to quantum attacks. It is based on NTRU lattices and offers an optimal balance between security and efficiency.

Features

Post-quantum security: Based on the Quantum Random Oracle model.
Optimized efficiency: Compact key and signature sizes.
Elixir implementation via NIF: Native C code integration for optimal performance.
Compatible with Falcon-512 and Falcon-1024.

Signature Padding Optimization

Falcon signatures include an initial 41-byte padding, which is automatically reconstructed during the verification process. This means the padding can be safely removed when storing or transmitting signatures, reducing their overall size without affecting security or validity.

Key Considerations:

Storage & Transmission Efficiency: Removing the padding reduces signature size while maintaining integrity.
Compatibility: Since the verification process restores the removed bytes, there is no impact on the correctness of signature validation.
Implementation Details: Ensure the padding is removed consistently, and validate that the verification method correctly regenerates it.

This optimization offers a practical way to minimize storage and transmission overhead while preserving Falcon’s cryptographic strength.

Compilation & Testing

Compiled and tested on Linux x64.

Details

Security	LOGN
Falcon-512	9
Falcon-1024	10

Key and Signature Sizes

Falcon-512

Component	Size (bytes)
Public key	897
Private key	1281
Signature	~625 (666)

Note: The maximum signature size is 625 bytes, as the first 41 characters <<57, 0, 0, 0...>> are removed.

Falcon-1024

Component	Size (bytes)
Public key	1793
Private key	2305
Signature	~1239 (1280)

Note: The maximum signature size is 1239 bytes, as the first 41 characters <<58, 0, 0, 0...>> are removed.

Installation & Compilation

Before compiling, make sure to install build-essential and erlang-dev.

mix deps.get
mix compile

Usage

To add the library to your project, include the following dependency in mix.exs: def deps do [

{:ex_falcon, "~> 0.1.0"}

] end

Example

msg = "Hello world!"
{:ok, pubkey, privkey} = Falcon.gen_key_pair()
{:ok, signature} = Falcon.sign(privkey, msg)
:ok = Falcon.verify(msg, signature, pubkey)

# Generate from seed
{:ok, pubkey, privkey} = Falcon.gen_keys_from_seed("your_seed")
# Generate public key from private key
{:ok, pubkey2} = Falcon.gen_pub_key(privkey)
pubkey == pubkey2

# Falcon1024 test
{:ok, pub, priv} = Falcon1024.gen_key_pair()
{:ok, signature} = Falcon1024.sign(priv, msg)
:ok = Falcon1024.verify(msg, signature, pub)

Testing

Run the following commands to test Falcon-512 and Falcon-1024:

mix run test/falcon_512_test.exs
mix run test/falcon_1024_test.exs