Format code using 'cargo fmt'

Signed-off-by: Michael Lodder <redmike7@gmail.com>

.gitignore

@@ -7,5 +7,9 @@
 # Executables
 *.exe
 
+# Folders
+.idea
+
 # Generated by Cargo
 /target/
+Cargo.lock

.travis.yml

@@ -0,0 +1,18 @@
+language: rust
+rust:
+- nightly
+before_script:
+- |
+  pip install 'travis-cargo<0.2' --user &&
+  export PATH=$HOME/.local/bin:$PATH
+script:
+- |
+  travis-cargo build &&
+  travis-cargo test &&
+  travis-cargo bench
+addons:
+  apt:
+    packages:
+    - libcurl4-openssl-dev
+    - libelf-dev
+    - libdw-dev

Cargo.toml

@@ -0,0 +1,26 @@
+[package]
+name = "pumpkin"
+version = "2.0.1"
+authors = ["Zach Dziura <zcdziura@gmail.com>"]
+description = "A cryptographically secure prime number generator"
+repository = "https://github.com/zcdziura/pumpkin"
+homepage = "https://zcdziura.github.io/pumpkin/pumpkin"
+keywords = ["prime", "number", "cryptography", "generator"]
+license = "Unlicense/MIT"
+readme = "README.md"
+
+[dependencies]
+clippy = {version = "0.0.*", optional = true}
+custom_derive = "0.1"
+newtype_derive = "0.1"
+ramp = "0.5"
+rand = "0.6"
+
+[lib]
+name = "pumpkin"
+path = "src/lib.rs"
+doctest = false
+
+[features]
+dev = ["clippy"]
+unstable = []

LICENSE

@@ -1,28 +0,0 @@
-Copyright (c) 2015, Zach Dziura
-All rights reserved.
-
-Redistribution and use in source and binary forms, with or without
-modification, are permitted provided that the following conditions are met:
-
-* Redistributions of source code must retain the above copyright notice, this
-  list of conditions and the following disclaimer.
-
-* Redistributions in binary form must reproduce the above copyright notice,
-  this list of conditions and the following disclaimer in the documentation
-  and/or other materials provided with the distribution.
-
-* Neither the name of pumpkin nor the names of its
-  contributors may be used to endorse or promote products derived from
-  this software without specific prior written permission.
-
-THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
-AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
-IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
-DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE
-FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
-DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR
-SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
-CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY,
-OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
-OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
-

LICENSE.md

@@ -0,0 +1,25 @@
+The MIT License (MIT)
+=====================
+
+Copyright © `2015` `Zachary Dziura`
+
+Permission is hereby granted, free of charge, to any person
+obtaining a copy of this software and associated documentation
+files (the “Software”), to deal in the Software without
+restriction, including without limitation the rights to use,
+copy, modify, merge, publish, distribute, sublicense, and/or sell
+copies of the Software, and to permit persons to whom the
+Software is furnished to do so, subject to the following
+conditions:
+
+The above copyright notice and this permission notice shall be
+included in all copies or substantial portions of the Software.
+
+THE SOFTWARE IS PROVIDED “AS IS”, WITHOUT WARRANTY OF ANY KIND,
+EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES
+OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
+NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT
+HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY,
+WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
+FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR
+OTHER DEALINGS IN THE SOFTWARE.

README.md

@@ -0,0 +1,120 @@
+# 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
+```

UNLICENSE.md

@@ -0,0 +1,27 @@
+Unlicense (Public Domain)
+============================
+
+This is free and unencumbered software released into the public domain.
+
+Anyone is free to copy, modify, publish, use, compile, sell, or
+distribute this software, either in source code form or as a compiled
+binary, for any purpose, commercial or non-commercial, and by any
+means.
+
+In jurisdictions that recognize copyright laws, the author or authors
+of this software dedicate any and all copyright interest in the
+software to the public domain. We make this dedication for the benefit
+of the public at large and to the detriment of our heirs and
+successors. We intend this dedication to be an overt act of
+relinquishment in perpetuity of all present and future rights to this
+software under copyright law.
+
+THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
+EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF
+MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT.
+IN NO EVENT SHALL THE AUTHORS BE LIABLE FOR ANY CLAIM, DAMAGES OR
+OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE,
+ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR
+OTHER DEALINGS IN THE SOFTWARE.
+
+For more information, please refer to &lt;<http://unlicense.org/>&gt;

WAIVER

@@ -0,0 +1,5 @@
+I dedicate any and all copyright interest in this software to the
+public domain. I make this dedication for the benefit of the public at
+large and to the detriment of my heirs and successors. I intend this
+dedication to be an overt act of relinquishment in perpetuity of all
+present and future rights to this software under copyright law.

WAIVER.sigs

@@ -0,0 +1,19 @@
+@zcdziura's signature
+keyserver: sks-keyservers.net
+fingerprint: 0xC936A812AF607321
+-----BEGIN PGP SIGNATURE-----
+
+iQIcBAABCgAGBQJXK3Z2AAoJENNfKjTk1jvtfTQP/0PnIWai7tpg+8YfTf+FTBjI
+hH8X1KquM6Kt58m+9bSpJAyaA42MYRmPd0UlyKq0UfR9EV9Dyme72cQCUQlNEkuh
+tXp1mqQ9wSTy7SGy43vGje2F76WPjGYR9zwrS/+EN771LbQEaYvsI75uIc5ynWnN
+op6w9XA9jLDdLPiXb+lli/7uAiSOZgLBqj6M8nTs6ii94kkHgEgZyHpyYe8kJNRq
+SUbldrJmH//vKbS7HSvgkPJ/ok2c04ZmZ7B3sa0997r36ubwM/SscqWTvZkGy3uj
+PCJh4m+gcHLiNasWucSL/y2oym7Px7DzmCibvT2pA0wa7zcjhIRc5ksnSDXfYafe
+XrTeuy/6cP5Trep9jzDf4wnAWhRzLZzy0LGHGYsSd5//6n3qFn2XFNyy769qYLu6
+8anCbpk40XNDLyEDlHB+lFCCe0KG/K5sg49CoxTsdLoiwyKqGpC7cjEQ15RoFtRQ
+JEvVJKs36fcAYalkfa4+OWt5TeoTAm/kg1erz6SwnNiL9n4MQ+0hLjm0WtpEpJqG
+V2XYi7tSIpfVFi+lvtxfoOGL+9nZpd6s6JarhdBPFFFang70I9wpXwVZDbSML89q
+KYnx3XVTxBhV6sumlJQ40wBGAisXLfJ4VpS1uj5JIx01d36Lgv6z80i6CiHTnIvz
+HFbm9XcS6pooPZOOxTrp
+=LwYG
+-----END PGP SIGNATURE-----

examples/multiply.rs

@@ -0,0 +1,11 @@
+extern crate pumpkin;
+
+use pumpkin::prime;
+
+fn main() {
+    let p = prime::new(1024).unwrap();
+    let q = prime::new(1024).unwrap();
+    let n = p * q;
+
+    println!("The product of 'p' and 'q' is: {}", n);
+}

src/common.rs

@@ -0,0 +1,333 @@
+use ramp::traits::Integer;
+use ramp::{Int, RandomInt};
+
+use rand::rngs::OsRng;
+use rand::thread_rng;
+
+use error::{Error, Result};
+
+pub fn two() -> Int {
+    Int::from(2_usize)
+}
+pub fn three() -> Int {
+    Int::from(3_usize)
+}
+
+static SMALL_PRIMES: [u32; 2047] = [
+    3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97,
+    101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193,
+    197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271, 277, 281, 283, 293, 307,
+    311, 313, 317, 331, 337, 347, 349, 353, 359, 367, 373, 379, 383, 389, 397, 401, 409, 419, 421,
+    431, 433, 439, 443, 449, 457, 461, 463, 467, 479, 487, 491, 499, 503, 509, 521, 523, 541, 547,
+    557, 563, 569, 571, 577, 587, 593, 599, 601, 607, 613, 617, 619, 631, 641, 643, 647, 653, 659,
+    661, 673, 677, 683, 691, 701, 709, 719, 727, 733, 739, 743, 751, 757, 761, 769, 773, 787, 797,
+    809, 811, 821, 823, 827, 829, 839, 853, 857, 859, 863, 877, 881, 883, 887, 907, 911, 919, 929,
+    937, 941, 947, 953, 967, 971, 977, 983, 991, 997, 1009, 1013, 1019, 1021, 1031, 1033, 1039,
+    1049, 1051, 1061, 1063, 1069, 1087, 1091, 1093, 1097, 1103, 1109, 1117, 1123, 1129, 1151, 1153,
+    1163, 1171, 1181, 1187, 1193, 1201, 1213, 1217, 1223, 1229, 1231, 1237, 1249, 1259, 1277, 1279,
+    1283, 1289, 1291, 1297, 1301, 1303, 1307, 1319, 1321, 1327, 1361, 1367, 1373, 1381, 1399, 1409,
+    1423, 1427, 1429, 1433, 1439, 1447, 1451, 1453, 1459, 1471, 1481, 1483, 1487, 1489, 1493, 1499,
+    1511, 1523, 1531, 1543, 1549, 1553, 1559, 1567, 1571, 1579, 1583, 1597, 1601, 1607, 1609, 1613,
+    1619, 1621, 1627, 1637, 1657, 1663, 1667, 1669, 1693, 1697, 1699, 1709, 1721, 1723, 1733, 1741,
+    1747, 1753, 1759, 1777, 1783, 1787, 1789, 1801, 1811, 1823, 1831, 1847, 1861, 1867, 1871, 1873,
+    1877, 1879, 1889, 1901, 1907, 1913, 1931, 1933, 1949, 1951, 1973, 1979, 1987, 1993, 1997, 1999,
+    2003, 2011, 2017, 2027, 2029, 2039, 2053, 2063, 2069, 2081, 2083, 2087, 2089, 2099, 2111, 2113,
+    2129, 2131, 2137, 2141, 2143, 2153, 2161, 2179, 2203, 2207, 2213, 2221, 2237, 2239, 2243, 2251,
+    2267, 2269, 2273, 2281, 2287, 2293, 2297, 2309, 2311, 2333, 2339, 2341, 2347, 2351, 2357, 2371,
+    2377, 2381, 2383, 2389, 2393, 2399, 2411, 2417, 2423, 2437, 2441, 2447, 2459, 2467, 2473, 2477,
+    2503, 2521, 2531, 2539, 2543, 2549, 2551, 2557, 2579, 2591, 2593, 2609, 2617, 2621, 2633, 2647,
+    2657, 2659, 2663, 2671, 2677, 2683, 2687, 2689, 2693, 2699, 2707, 2711, 2713, 2719, 2729, 2731,
+    2741, 2749, 2753, 2767, 2777, 2789, 2791, 2797, 2801, 2803, 2819, 2833, 2837, 2843, 2851, 2857,
+    2861, 2879, 2887, 2897, 2903, 2909, 2917, 2927, 2939, 2953, 2957, 2963, 2969, 2971, 2999, 3001,
+    3011, 3019, 3023, 3037, 3041, 3049, 3061, 3067, 3079, 3083, 3089, 3109, 3119, 3121, 3137, 3163,
+    3167, 3169, 3181, 3187, 3191, 3203, 3209, 3217, 3221, 3229, 3251, 3253, 3257, 3259, 3271, 3299,
+    3301, 3307, 3313, 3319, 3323, 3329, 3331, 3343, 3347, 3359, 3361, 3371, 3373, 3389, 3391, 3407,
+    3413, 3433, 3449, 3457, 3461, 3463, 3467, 3469, 3491, 3499, 3511, 3517, 3527, 3529, 3533, 3539,
+    3541, 3547, 3557, 3559, 3571, 3581, 3583, 3593, 3607, 3613, 3617, 3623, 3631, 3637, 3643, 3659,
+    3671, 3673, 3677, 3691, 3697, 3701, 3709, 3719, 3727, 3733, 3739, 3761, 3767, 3769, 3779, 3793,
+    3797, 3803, 3821, 3823, 3833, 3847, 3851, 3853, 3863, 3877, 3881, 3889, 3907, 3911, 3917, 3919,
+    3923, 3929, 3931, 3943, 3947, 3967, 3989, 4001, 4003, 4007, 4013, 4019, 4021, 4027, 4049, 4051,
+    4057, 4073, 4079, 4091, 4093, 4099, 4111, 4127, 4129, 4133, 4139, 4153, 4157, 4159, 4177, 4201,
+    4211, 4217, 4219, 4229, 4231, 4241, 4243, 4253, 4259, 4261, 4271, 4273, 4283, 4289, 4297, 4327,
+    4337, 4339, 4349, 4357, 4363, 4373, 4391, 4397, 4409, 4421, 4423, 4441, 4447, 4451, 4457, 4463,
+    4481, 4483, 4493, 4507, 4513, 4517, 4519, 4523, 4547, 4549, 4561, 4567, 4583, 4591, 4597, 4603,
+    4621, 4637, 4639, 4643, 4649, 4651, 4657, 4663, 4673, 4679, 4691, 4703, 4721, 4723, 4729, 4733,
+    4751, 4759, 4783, 4787, 4789, 4793, 4799, 4801, 4813, 4817, 4831, 4861, 4871, 4877, 4889, 4903,
+    4909, 4919, 4931, 4933, 4937, 4943, 4951, 4957, 4967, 4969, 4973, 4987, 4993, 4999, 5003, 5009,
+    5011, 5021, 5023, 5039, 5051, 5059, 5077, 5081, 5087, 5099, 5101, 5107, 5113, 5119, 5147, 5153,
+    5167, 5171, 5179, 5189, 5197, 5209, 5227, 5231, 5233, 5237, 5261, 5273, 5279, 5281, 5297, 5303,
+    5309, 5323, 5333, 5347, 5351, 5381, 5387, 5393, 5399, 5407, 5413, 5417, 5419, 5431, 5437, 5441,
+    5443, 5449, 5471, 5477, 5479, 5483, 5501, 5503, 5507, 5519, 5521, 5527, 5531, 5557, 5563, 5569,
+    5573, 5581, 5591, 5623, 5639, 5641, 5647, 5651, 5653, 5657, 5659, 5669, 5683, 5689, 5693, 5701,
+    5711, 5717, 5737, 5741, 5743, 5749, 5779, 5783, 5791, 5801, 5807, 5813, 5821, 5827, 5839, 5843,
+    5849, 5851, 5857, 5861, 5867, 5869, 5879, 5881, 5897, 5903, 5923, 5927, 5939, 5953, 5981, 5987,
+    6007, 6011, 6029, 6037, 6043, 6047, 6053, 6067, 6073, 6079, 6089, 6091, 6101, 6113, 6121, 6131,
+    6133, 6143, 6151, 6163, 6173, 6197, 6199, 6203, 6211, 6217, 6221, 6229, 6247, 6257, 6263, 6269,
+    6271, 6277, 6287, 6299, 6301, 6311, 6317, 6323, 6329, 6337, 6343, 6353, 6359, 6361, 6367, 6373,
+    6379, 6389, 6397, 6421, 6427, 6449, 6451, 6469, 6473, 6481, 6491, 6521, 6529, 6547, 6551, 6553,
+    6563, 6569, 6571, 6577, 6581, 6599, 6607, 6619, 6637, 6653, 6659, 6661, 6673, 6679, 6689, 6691,
+    6701, 6703, 6709, 6719, 6733, 6737, 6761, 6763, 6779, 6781, 6791, 6793, 6803, 6823, 6827, 6829,
+    6833, 6841, 6857, 6863, 6869, 6871, 6883, 6899, 6907, 6911, 6917, 6947, 6949, 6959, 6961, 6967,
+    6971, 6977, 6983, 6991, 6997, 7001, 7013, 7019, 7027, 7039, 7043, 7057, 7069, 7079, 7103, 7109,
+    7121, 7127, 7129, 7151, 7159, 7177, 7187, 7193, 7207, 7211, 7213, 7219, 7229, 7237, 7243, 7247,
+    7253, 7283, 7297, 7307, 7309, 7321, 7331, 7333, 7349, 7351, 7369, 7393, 7411, 7417, 7433, 7451,
+    7457, 7459, 7477, 7481, 7487, 7489, 7499, 7507, 7517, 7523, 7529, 7537, 7541, 7547, 7549, 7559,
+    7561, 7573, 7577, 7583, 7589, 7591, 7603, 7607, 7621, 7639, 7643, 7649, 7669, 7673, 7681, 7687,
+    7691, 7699, 7703, 7717, 7723, 7727, 7741, 7753, 7757, 7759, 7789, 7793, 7817, 7823, 7829, 7841,
+    7853, 7867, 7873, 7877, 7879, 7883, 7901, 7907, 7919, 7927, 7933, 7937, 7949, 7951, 7963, 7993,
+    8009, 8011, 8017, 8039, 8053, 8059, 8069, 8081, 8087, 8089, 8093, 8101, 8111, 8117, 8123, 8147,
+    8161, 8167, 8171, 8179, 8191, 8209, 8219, 8221, 8231, 8233, 8237, 8243, 8263, 8269, 8273, 8287,
+    8291, 8293, 8297, 8311, 8317, 8329, 8353, 8363, 8369, 8377, 8387, 8389, 8419, 8423, 8429, 8431,
+    8443, 8447, 8461, 8467, 8501, 8513, 8521, 8527, 8537, 8539, 8543, 8563, 8573, 8581, 8597, 8599,
+    8609, 8623, 8627, 8629, 8641, 8647, 8663, 8669, 8677, 8681, 8689, 8693, 8699, 8707, 8713, 8719,
+    8731, 8737, 8741, 8747, 8753, 8761, 8779, 8783, 8803, 8807, 8819, 8821, 8831, 8837, 8839, 8849,
+    8861, 8863, 8867, 8887, 8893, 8923, 8929, 8933, 8941, 8951, 8963, 8969, 8971, 8999, 9001, 9007,
+    9011, 9013, 9029, 9041, 9043, 9049, 9059, 9067, 9091, 9103, 9109, 9127, 9133, 9137, 9151, 9157,
+    9161, 9173, 9181, 9187, 9199, 9203, 9209, 9221, 9227, 9239, 9241, 9257, 9277, 9281, 9283, 9293,
+    9311, 9319, 9323, 9337, 9341, 9343, 9349, 9371, 9377, 9391, 9397, 9403, 9413, 9419, 9421, 9431,
+    9433, 9437, 9439, 9461, 9463, 9467, 9473, 9479, 9491, 9497, 9511, 9521, 9533, 9539, 9547, 9551,
+    9587, 9601, 9613, 9619, 9623, 9629, 9631, 9643, 9649, 9661, 9677, 9679, 9689, 9697, 9719, 9721,
+    9733, 9739, 9743, 9749, 9767, 9769, 9781, 9787, 9791, 9803, 9811, 9817, 9829, 9833, 9839, 9851,
+    9857, 9859, 9871, 9883, 9887, 9901, 9907, 9923, 9929, 9931, 9941, 9949, 9967, 9973, 10007,
+    10009, 10037, 10039, 10061, 10067, 10069, 10079, 10091, 10093, 10099, 10103, 10111, 10133,
+    10139, 10141, 10151, 10159, 10163, 10169, 10177, 10181, 10193, 10211, 10223, 10243, 10247,
+    10253, 10259, 10267, 10271, 10273, 10289, 10301, 10303, 10313, 10321, 10331, 10333, 10337,
+    10343, 10357, 10369, 10391, 10399, 10427, 10429, 10433, 10453, 10457, 10459, 10463, 10477,
+    10487, 10499, 10501, 10513, 10529, 10531, 10559, 10567, 10589, 10597, 10601, 10607, 10613,
+    10627, 10631, 10639, 10651, 10657, 10663, 10667, 10687, 10691, 10709, 10711, 10723, 10729,
+    10733, 10739, 10753, 10771, 10781, 10789, 10799, 10831, 10837, 10847, 10853, 10859, 10861,
+    10867, 10883, 10889, 10891, 10903, 10909, 10937, 10939, 10949, 10957, 10973, 10979, 10987,
+    10993, 11003, 11027, 11047, 11057, 11059, 11069, 11071, 11083, 11087, 11093, 11113, 11117,
+    11119, 11131, 11149, 11159, 11161, 11171, 11173, 11177, 11197, 11213, 11239, 11243, 11251,
+    11257, 11261, 11273, 11279, 11287, 11299, 11311, 11317, 11321, 11329, 11351, 11353, 11369,
+    11383, 11393, 11399, 11411, 11423, 11437, 11443, 11447, 11467, 11471, 11483, 11489, 11491,
+    11497, 11503, 11519, 11527, 11549, 11551, 11579, 11587, 11593, 11597, 11617, 11621, 11633,
+    11657, 11677, 11681, 11689, 11699, 11701, 11717, 11719, 11731, 11743, 11777, 11779, 11783,
+    11789, 11801, 11807, 11813, 11821, 11827, 11831, 11833, 11839, 11863, 11867, 11887, 11897,
+    11903, 11909, 11923, 11927, 11933, 11939, 11941, 11953, 11959, 11969, 11971, 11981, 11987,
+    12007, 12011, 12037, 12041, 12043, 12049, 12071, 12073, 12097, 12101, 12107, 12109, 12113,
+    12119, 12143, 12149, 12157, 12161, 12163, 12197, 12203, 12211, 12227, 12239, 12241, 12251,
+    12253, 12263, 12269, 12277, 12281, 12289, 12301, 12323, 12329, 12343, 12347, 12373, 12377,
+    12379, 12391, 12401, 12409, 12413, 12421, 12433, 12437, 12451, 12457, 12473, 12479, 12487,
+    12491, 12497, 12503, 12511, 12517, 12527, 12539, 12541, 12547, 12553, 12569, 12577, 12583,
+    12589, 12601, 12611, 12613, 12619, 12637, 12641, 12647, 12653, 12659, 12671, 12689, 12697,
+    12703, 12713, 12721, 12739, 12743, 12757, 12763, 12781, 12791, 12799, 12809, 12821, 12823,
+    12829, 12841, 12853, 12889, 12893, 12899, 12907, 12911, 12917, 12919, 12923, 12941, 12953,
+    12959, 12967, 12973, 12979, 12983, 13001, 13003, 13007, 13009, 13033, 13037, 13043, 13049,
+    13063, 13093, 13099, 13103, 13109, 13121, 13127, 13147, 13151, 13159, 13163, 13171, 13177,
+    13183, 13187, 13217, 13219, 13229, 13241, 13249, 13259, 13267, 13291, 13297, 13309, 13313,
+    13327, 13331, 13337, 13339, 13367, 13381, 13397, 13399, 13411, 13417, 13421, 13441, 13451,
+    13457, 13463, 13469, 13477, 13487, 13499, 13513, 13523, 13537, 13553, 13567, 13577, 13591,
+    13597, 13613, 13619, 13627, 13633, 13649, 13669, 13679, 13681, 13687, 13691, 13693, 13697,
+    13709, 13711, 13721, 13723, 13729, 13751, 13757, 13759, 13763, 13781, 13789, 13799, 13807,
+    13829, 13831, 13841, 13859, 13873, 13877, 13879, 13883, 13901, 13903, 13907, 13913, 13921,
+    13931, 13933, 13963, 13967, 13997, 13999, 14009, 14011, 14029, 14033, 14051, 14057, 14071,
+    14081, 14083, 14087, 14107, 14143, 14149, 14153, 14159, 14173, 14177, 14197, 14207, 14221,
+    14243, 14249, 14251, 14281, 14293, 14303, 14321, 14323, 14327, 14341, 14347, 14369, 14387,
+    14389, 14401, 14407, 14411, 14419, 14423, 14431, 14437, 14447, 14449, 14461, 14479, 14489,
+    14503, 14519, 14533, 14537, 14543, 14549, 14551, 14557, 14561, 14563, 14591, 14593, 14621,
+    14627, 14629, 14633, 14639, 14653, 14657, 14669, 14683, 14699, 14713, 14717, 14723, 14731,
+    14737, 14741, 14747, 14753, 14759, 14767, 14771, 14779, 14783, 14797, 14813, 14821, 14827,
+    14831, 14843, 14851, 14867, 14869, 14879, 14887, 14891, 14897, 14923, 14929, 14939, 14947,
+    14951, 14957, 14969, 14983, 15013, 15017, 15031, 15053, 15061, 15073, 15077, 15083, 15091,
+    15101, 15107, 15121, 15131, 15137, 15139, 15149, 15161, 15173, 15187, 15193, 15199, 15217,
+    15227, 15233, 15241, 15259, 15263, 15269, 15271, 15277, 15287, 15289, 15299, 15307, 15313,
+    15319, 15329, 15331, 15349, 15359, 15361, 15373, 15377, 15383, 15391, 15401, 15413, 15427,
+    15439, 15443, 15451, 15461, 15467, 15473, 15493, 15497, 15511, 15527, 15541, 15551, 15559,
+    15569, 15581, 15583, 15601, 15607, 15619, 15629, 15641, 15643, 15647, 15649, 15661, 15667,
+    15671, 15679, 15683, 15727, 15731, 15733, 15737, 15739, 15749, 15761, 15767, 15773, 15787,
+    15791, 15797, 15803, 15809, 15817, 15823, 15859, 15877, 15881, 15887, 15889, 15901, 15907,
+    15913, 15919, 15923, 15937, 15959, 15971, 15973, 15991, 16001, 16007, 16033, 16057, 16061,
+    16063, 16067, 16069, 16073, 16087, 16091, 16097, 16103, 16111, 16127, 16139, 16141, 16183,
+    16187, 16189, 16193, 16217, 16223, 16229, 16231, 16249, 16253, 16267, 16273, 16301, 16319,
+    16333, 16339, 16349, 16361, 16363, 16369, 16381, 16411, 16417, 16421, 16427, 16433, 16447,
+    16451, 16453, 16477, 16481, 16487, 16493, 16519, 16529, 16547, 16553, 16561, 16567, 16573,
+    16603, 16607, 16619, 16631, 16633, 16649, 16651, 16657, 16661, 16673, 16691, 16693, 16699,
+    16703, 16729, 16741, 16747, 16759, 16763, 16787, 16811, 16823, 16829, 16831, 16843, 16871,
+    16879, 16883, 16889, 16901, 16903, 16921, 16927, 16931, 16937, 16943, 16963, 16979, 16981,
+    16987, 16993, 17011, 17021, 17027, 17029, 17033, 17041, 17047, 17053, 17077, 17093, 17099,
+    17107, 17117, 17123, 17137, 17159, 17167, 17183, 17189, 17191, 17203, 17207, 17209, 17231,
+    17239, 17257, 17291, 17293, 17299, 17317, 17321, 17327, 17333, 17341, 17351, 17359, 17377,
+    17383, 17387, 17389, 17393, 17401, 17417, 17419, 17431, 17443, 17449, 17467, 17471, 17477,
+    17483, 17489, 17491, 17497, 17509, 17519, 17539, 17551, 17569, 17573, 17579, 17581, 17597,
+    17599, 17609, 17623, 17627, 17657, 17659, 17669, 17681, 17683, 17707, 17713, 17729, 17737,
+    17747, 17749, 17761, 17783, 17789, 17791, 17807, 17827, 17837, 17839, 17851, 17863,
+];
+
+/// Constructs a new prime number with the size of `bit_length` bits, sourced
+/// from an already-initialized `OsRng`.
+pub fn gen_prime(bit_length: usize, rngesus: &mut OsRng) -> Result {
+    if bit_length < 512 {
+        Err(Error::BitLength(bit_length))
+    } else {
+        let mut candidate: Int;
+
+        // In order to remove as much bias from the system as possible, test
+        // 500 potential candidates at a time before re-seeding the candidate
+        // with a new random number.
+        loop {
+            candidate = rngesus.gen_uint(bit_length);
+
+            // We first want to make sure that the candidate is in the appropriate
+            // size range before continuing. This can easily be done by setting the
+            // two most significant bits of the candidate number to 1.
+            candidate.set_bit(1, true);
+            candidate.set_bit(2, true);
+
+            // Next, flip the least significant bit to 1, to make sure the candidate
+            // is odd (no sense in testing primality on an even number, after all).
+            candidate.set_bit(bit_length as u32, true);
+
+            if is_prime(&candidate) {
+                return Ok(candidate);
+            }
+        }
+    }
+}
+
+/// Runs the following three tests on a given `candidate` to determine
+/// primality:
+///
+/// 1. Divide the candidate by the first 2048 small prime numbers.
+/// 2. Run Fermat's Little Theorem against the candidate.
+/// 3. Run fifteen rounds of the Miller-Rabin test on the candidate.
+///
+/// Should the candidate number pass all three tests, then you can be
+/// reasonably sure that the candidate is prime.
+pub fn is_prime(candidate: &Int) -> bool {
+    // First, iterate through the array of small primes and divide the
+    // candidate. If the candidate divides any of them, then we know the number
+    // is a multiple of that prime; that is, the candidate is composite.
+
+    if *candidate == Int::from(2) {
+        return true;
+    }
+
+    if !candidate.is_odd() {
+        return false;
+    }
+
+    for p in SMALL_PRIMES.into_iter() {
+        let prime: Int = Int::from(*p);
+        let (_, r) = candidate.divmod(&prime);
+
+        if r == Int::zero() {
+            return *candidate == prime;
+        }
+    }
+
+    // Second, do a Fermat test on the candidate
+    if !fermat(candidate) {
+        return false;
+    }
+
+    // Finally, do a Miller-Rabin test
+    // See https://eprint.iacr.org/2018/749.pdf for good choices on appropriate number of tests
+    if !miller_rabin(candidate, 15) {
+        return false;
+    }
+
+    true
+}
+
+fn fermat(candidate: &Int) -> bool {
+    // Perform Fermat's little theorem on the candidate to determine probable
+    // primality.
+    let random = thread_rng().gen_int_range(&Int::one(), candidate);
+
+    let result = mod_exp(&random, &(candidate - 1), candidate);
+
+    result == Int::one()
+}
+
+fn mod_exp(base: &Int, exponent: &Int, modulus: &Int) -> Int {
+    let mut result = Int::one();
+    let mut base = base.clone();
+    let mut exponent = exponent.clone();
+
+    while exponent > Int::zero() {
+        if exponent.trailing_zeros() == 0 {
+            result = (&base * result) % modulus;
+        }
+
+        base = base.pow_mod(&two(), modulus);
+        exponent >>= 1;
+    }
+
+    result
+}
+
+fn miller_rabin(candidate: &Int, limit: usize) -> bool {
+    // Perform the Miller-Rabin test on the candidate, 'limit' times.
+    let (s, d) = rewrite(candidate);
+
+    for _ in 0..limit {
+        let basis = thread_rng().gen_int_range(&two(), candidate);
+        let mut x = mod_exp(&basis, &d, candidate);
+
+        if x == Int::one() || x == (candidate - 1) {
+            continue;
+        } else {
+            for _ in Int::one()..s - 1 {
+                x = mod_exp(&x, &two(), candidate);
+                if x == Int::one() {
+                    return false;
+                } else if x == candidate - 1 {
+                    break;
+                }
+            }
+            return false;
+        }
+    }
+
+    true
+}
+
+fn rewrite(candidate: &Int) -> (Int, Int) {
+    let mut d = candidate - 1_usize;
+    let mut s = Int::zero();
+
+    while d.trailing_zeros() == 0 {
+        //
+        d = &d >> 1;
+        s = &s + 1;
+    }
+
+    (s, d)
+}
+
+#[cfg(test)]
+mod tests {
+    extern crate ramp;
+
+    use super::{fermat, miller_rabin};
+    use ramp::Int;
+
+    #[test]
+    fn test_fermat_prime() {
+        let candidate = Int::from(65537);
+        let result = fermat(&candidate);
+        assert_eq!(result, true);
+    }
+
+    #[test]
+    fn test_fermat_not_prime() {
+        let candidate = Int::from(65535);
+        let result = fermat(&candidate);
+        assert_eq!(result, false);
+    }
+
+    #[test]
+    fn test_miller_rabin_prime() {
+        let candidate = Int::from(65537);
+        let result = miller_rabin(&candidate, 64);
+        assert_eq!(result, true);
+    }
+
+    #[test]
+    fn test_miller_rabin_not_prime() {
+        let candidate = Int::from(65535);
+        let result = miller_rabin(&candidate, 64);
+        assert_eq!(result, false);
+    }
+}

src/error.rs

@@ -0,0 +1,49 @@
+//! More coming soon
+
+use ramp::Int;
+
+use rand;
+use std::{error, fmt, result};
+
+/// Goddamn docs
+pub type Result = result::Result<Int, Error>;
+
+/// More goddamn docs
+#[derive(Debug)]
+pub enum Error {
+    /// Docs for a variant, are you kidding me??
+    OsRngInitialization(rand::Error),
+
+    /// Jesus fuck, people
+    BitLength(usize),
+}
+
+impl fmt::Display for Error {
+    fn fmt(&self, f: &mut fmt::Formatter) -> fmt::Result {
+        match *self {
+            Error::OsRngInitialization(ref err) => {
+                write!(f, "Error initializing the random number generator: {}", err)
+            }
+            Error::BitLength(length) => write!(
+                f,
+                "The given bit length is too small; must be at least 512: {}",
+                length
+            ),
+        }
+    }
+}
+
+impl error::Error for Error {
+    fn description(&self) -> &str {
+        match *self {
+            Error::OsRngInitialization(ref err) => err.description(),
+            Error::BitLength(_) => "The given bit length was less than 512",
+        }
+    }
+}
+
+impl From<rand::Error> for Error {
+    fn from(err: rand::Error) -> Error {
+        Error::OsRngInitialization(err)
+    }
+}

src/lib.rs

@@ -0,0 +1,99 @@
+#![feature(test)]
+#![deny(
+    missing_docs,
+    missing_debug_implementations,
+    missing_copy_implementations,
+    trivial_casts,
+    trivial_numeric_casts,
+    unsafe_code,
+    unused_import_braces,
+    unused_qualifications
+)]
+#![cfg_attr(feature = "dev", feature(plugin))]
+#![cfg_attr(feature = "dev", plugin(clippy))]
+
+//! A crate for generating large, cryptographically secure prime numbers.
+//! These numbers are seeded from the operating system's main source of
+//! entropy, ensuring proper randomness.
+//!
+//! Numbers are verified to be prime by running the following three tests
+//! during initialization:
+//!
+//! 1. Dividing the initial prime number candidate by the first 1,000 prime
+//! numbers, checking the remainder. Should the remainder ever be zero, then
+//! add two to the candidate and try again.
+//!
+//! 2. Run a Fermat Primality Test on the candidate. If it doesn't pass, add
+//! two to the candidate and goto Step 1.
+//!
+//! 3. Finally, complete five rounds of the Miller-Rabin Primality Test.
+//! Should any of the tests pass, add two to the candidate and goto Step 1.
+//!
+//! The preceding steps mirror those used by GnuPG, a leading PGP implementation
+//! used by thousands of users all across the world.
+//!
+//! The prime numbers must be AT LEAST 512-bits long. Attempting to generate a
+//! number less than 512-bits long will cause a panic.
+//!
+//! ## Example
+//!
+//! ```
+//! extern crate pumpkin;
+//!
+//! use pumpkin::prime;
+//!
+//! fn main() {
+//!     // Generate 2, 2048-bit primes
+//!     let p = prime::new(2048);
+//!     let q = prime::new(2048);
+//!
+//!     let n = p * q;
+//!     println!("{}", n); // Some 4096-bit composite number
+//! }
+//! ```
+
+#[allow(unused_imports)]
+#[macro_use]
+extern crate custom_derive;
+#[allow(unused_imports)]
+#[macro_use]
+extern crate newtype_derive;
+extern crate ramp;
+extern crate rand;
+extern crate test;
+
+mod common;
+pub mod error;
+pub mod prime;
+pub mod safe_prime;
+
+#[cfg(test)]
+mod tests {
+    use super::{prime, safe_prime};
+    use rand::rngs::OsRng;
+    use test::Bencher;
+
+    #[bench]
+    fn bench_generate_512_bit_prime(b: &mut Bencher) {
+        let mut rngesus = OsRng::new().unwrap();
+        b.iter(|| prime::from_rng(512, &mut rngesus));
+    }
+
+    #[bench]
+    fn bench_generate_1024_bit_prime(b: &mut Bencher) {
+        let mut rngesus = OsRng::new().unwrap();
+        b.iter(|| prime::from_rng(1024, &mut rngesus));
+    }
+
+    #[bench]
+    fn bench_generate_2048_bit_prime(b: &mut Bencher) {
+        let mut rngesus = OsRng::new().unwrap();
+        b.iter(|| prime::from_rng(2048, &mut rngesus));
+    }
+
+    #[bench]
+    fn bench_generate_512_bit_safe_prime(b: &mut Bencher) {
+        let mut rngesus = OsRng::new().unwrap();
+        b.iter(|| safe_prime::from_rng(512, &mut rngesus));
+    }
+}

src/prime.rs

@@ -0,0 +1,50 @@
+//! Generates cryptographically secure prime numbers.
+
+use rand::rngs::OsRng;
+
+pub use common::gen_prime as from_rng;
+use error::{Error, Result};
+
+/// Constructs a new prime number with a size of `bit_length` bits.
+///
+/// This will initialize an `OsRng` instance and call the
+/// `from_rng()` function.
+///
+/// Note: the `bit_length` MUST be at least 512-bits.
+pub fn new(bit_length: usize) -> Result {
+    if bit_length < 512 {
+        Err(Error::BitLength(bit_length))
+    } else {
+        let mut rngesus = OsRng::new()?;
+        Ok(from_rng(bit_length, &mut rngesus)?)
+    }
+}
+
+#[cfg(test)]
+mod tests {
+    use super::new;
+
+    #[test]
+    fn test_prime_bit_length_too_small() {
+        let p = new(511);
+        assert_eq!(
+            false,
+            match p {
+                Ok(_) => true,
+                Err(_) => false,
+            }
+        );
+    }
+
+    #[test]
+    fn test_prime() {
+        let p = new(512);
+        assert_eq!(
+            true,
+            match p {
+                Ok(_) => true,
+                Err(_) => false,
+            }
+        );
+    }
+}

src/safe_prime.rs

@@ -0,0 +1,112 @@
+//! Generates [safe prime numbers](https://www.wikiwand.com/en/Sophie_Germain_prime).
+
+use ramp::Int;
+
+use rand::rngs::OsRng;
+
+pub use common::{gen_prime, is_prime};
+use common::{three, two};
+use error::{Error, Result};
+
+/// Constructs a new `SafePrime` with a size of `bit_length` bits.
+///
+/// This will initialize an `OsRng` instance and call the
+/// `SafePrime::from_rng()` method.
+///
+/// Note: the `bit_length` MUST be at least 512-bits.
+pub fn new(bit_length: usize) -> Result {
+    if bit_length < 512 {
+        Err(Error::BitLength(bit_length))
+    } else {
+        let mut rngesus = OsRng::new()?;
+        Ok(from_rng(bit_length, &mut rngesus)?)
+    }
+}
+
+/// Checks if number is a safe prime
+pub fn is_safe_prime(candidate: &Int) -> bool {
+    // according to https://eprint.iacr.org/2003/186.pdf
+    // a safe prime is congruent to 2 mod 3
+    if (candidate % three()) == two() {
+        if is_prime(&candidate) {
+            // a safe prime satisfies (p-1)/2 is prime. Since a
+            // prime is odd, We just need to divide by 2
+            let candidate_p = candidate >> 1;
+            return is_prime(&candidate_p);
+        }
+    }
+    false
+}
+
+/// Constructs a new `SafePrime` with the size of `bit_length` bits, sourced
+/// from an already-initialized `OsRng`.
+pub fn from_rng(bit_length: usize, mut rngesus: &mut OsRng) -> Result {
+    if bit_length < 512 {
+        Err(Error::BitLength(bit_length))
+    } else {
+        let mut candidate: Int;
+
+        loop {
+            candidate = gen_prime(bit_length, &mut rngesus)?;
+
+            if is_safe_prime(&candidate) {
+                break;
+            }
+
+            candidate <<= 1;
+            candidate += 1;
+
+            if is_prime(&candidate) {
+                break;
+            }
+        }
+
+        Ok(candidate)
+    }
+}
+
+#[cfg(test)]
+mod tests {
+    use super::{is_safe_prime, new};
+    use ramp::Int;
+
+    #[test]
+    fn test_safe_prime_bit_length_too_small() {
+        let sp = new(511);
+        assert_eq!(
+            false,
+            match sp {
+                Ok(_) => true,
+                Err(_) => false,
+            }
+        );
+    }
+
+    #[test]
+    fn test_safe_prime() {
+        let sp = new(512);
+        assert_eq!(
+            true,
+            match sp {
+                Ok(_) => true,
+                Err(_) => false,
+            }
+        );
+    }
+
+    #[test]
+    fn test_is_safe_prime() {
+        //Numbers pulled from https://github.com/mikelodder7/cunningham_chain/blob/master/findings.md
+        //p0 is sophie german prime
+        let p0 = Int::from_str_radix("37313426856874901938110133384605074194791927500210707276948918975046371522830901596065044944558427864187196889881993164303255749681644627614963632713725183364319410825898054225147061624559894980555489070322738683900143562848200257354774040241218537613789091499134051387344396560066242901217378861764936185029", 10).unwrap();
+        assert!(!is_safe_prime(&p0));
+        let p1 = Int::from_str_radix("74626853713749803876220266769210148389583855000421414553897837950092743045661803192130089889116855728374393779763986328606511499363289255229927265427450366728638821651796108450294123249119789961110978140645477367800287125696400514709548080482437075227578182998268102774688793120132485802434757723529872370059", 10).unwrap();
+        assert!(is_safe_prime(&p1));
+        let p2 = Int::from_str_radix("149253707427499607752440533538420296779167710000842829107795675900185486091323606384260179778233711456748787559527972657213022998726578510459854530854900733457277643303592216900588246498239579922221956281290954735600574251392801029419096160964874150455156365996536205549377586240264971604869515447059744740119", 10).unwrap();
+        assert!(is_safe_prime(&p2));
+        let p3 = Int::from_str_radix("298507414854999215504881067076840593558335420001685658215591351800370972182647212768520359556467422913497575119055945314426045997453157020919709061709801466914555286607184433801176492996479159844443912562581909471201148502785602058838192321929748300910312731993072411098755172480529943209739030894119489480239", 10).unwrap();
+        assert!(is_safe_prime(&p3));
+        let p4 = Int::from_str_radix("4806876214089177439121678559764069543282270755154137981051366776821330958611719328037311759924923156830623290278296826263863902327008664143707117531049168010908663795201825132050017581985031718536424081509084930569115857201636971728388275433540277562846153879803474020036767852693656753257597801227199822164846876100177774044259379232968071371318658371230787073384750022830829873718254139779006439569882904712552834431199870749249168775012460891012776977366721903", 10).unwrap();
+        assert!(is_safe_prime(&p4));
+    }
+}