# Pumpkin

A random number generator for generating large prime numbers, suitable for cryptography.

## What's up with the name?

Since I began writing this library around Halloween of 2015, I wanted to choose
a name that was vaguely related to the holiday. Because "pumpkin" and "prime"
both begin with the letter 'p', I decided to use that.

## Purpose

`pumpkin` is a cryptographically-secure, random number generator, useful for
generating large prime numbers (at least 512-bits long). On the back-end,
`pumpkin` uses the wonderful [ramp](https://crates.io/crates/ramp) library for
storing the large numbers. `pumpkin` generates primes very quickly. In our
testing, primes were generated anywhere between 1s and 5s on average, though
of course your mileage may vary.

## Installation

Add the following to your `Cargo.toml` file:

```
pumpkin = "2.0.*"
```

Note that `pumpkin` requires the `nightly` Rust compiler.

## Example

```rust
extern crate pumpkin;

use pumpkin::Prime;

fn main() {
    let p = Prime::new(2048); // Generate a new 2048-bit prime number
    let q = Prime::new(2048);
    let e = p * q;

    println!("{}", e);

    /*
     * 75222035638256552797269351238215022250546763213674706... Some massive
     * 4096-bit number.
     */
}
```

You can also initialize your own `OsRng` and generate `Prime`s from that.

```rust
extern crate pumpkin;
extern crate rand;

use pumpkin::Prime;

use rand::OsRng;

fn main() {
    let mut rngesus = match OsRng::new() {
        Ok(rng) => rng,
        Err(e) => panic!("Error trying to initializing RNG: {}", e)
    };

    let p = Prime::from_rng(2048, &mut rngesus);
    let q = Prime::from_rng(2048, &mut rngesus);

    let e = p * q;

    println!("{}", e);

    /*
     * 75222035638256552797269351238215022250546763213674706... Some massive
     * 4096-bit number.
     */
}
```

## Explanation
`Primes` are generated in much the same way as primes generated by `GnuPG`:

  1) Create a large candidate number of a given bit-length. All `Primes` must
  be at least 512-bits long.

  2) Divide the candidate number by the first 1,000 prime numbers.

  3) Test the candidate number with [Fermat's Little
Theorem](https://www.wikiwand.com/en/Fermat's_little_theorem).

  4) Finally, run five iterations of the [Miller-Rabin Primality
Test](https://www.wikiwand.com/en/Miller%E2%80%93Rabin_primality_test).

`Primes` are seeded by `rand::OsRng`, which receives its entropy via the
operating system's entropy source (such as `/dev/urandom`). Thus, because we
can be confident that the generated candidate number is truly random (or as
close to truly random as the user can hope), we don't need to do more than five
iterations of the Miller-Rabin test to ensure primality.

`Primes` are simple "newtype" structs; that is, it is a tuple-like struct
surrounding `ramp's` `Int` type. `Primes` have all of the basic algebraic and logical
operators implemented, thus allowing you to do any operation that you would
require.

## Contributing

`pumpkin` is dual-licenced under the MIT and Unlicense. Should you wish to
contribute updates to the project, please consider signing the included `WAVER`
file with your cryptographic digital signature (as allowed by your country's
laws). Doing so will release your changes back into the public domain to be used
freely by all. I did so with this project, and it would mean a lot if you did
too!

To sign the `WAIVER`, execute the following commands:

```
$ gpg -sba -u $YOUR_SIGNING_KEY WAIVER
$ cat WAIVER.asc >> WAIVER.sigs && rm WAIVER.asc
```