// Copyright 2018 Developers of the Rand project.
// Copyright 2013-2018 The Rust Project Developers.
//
// Licensed under the Apache License, Version 2.0 <LICENSE-APACHE or
// https://www.apache.org/licenses/LICENSE-2.0> or the MIT license
// <LICENSE-MIT or https://opensource.org/licenses/MIT>, at your
// option. This file may not be copied, modified, or distributed
// except according to those terms.
//! The ISAAC random number generator.
use core::{fmt, slice};
use core::num::Wrapping as w;
use rand_core::{RngCore, SeedableRng, Error, le};
use rand_core::block::{BlockRngCore, BlockRng};
use isaac_array::IsaacArray;
#[allow(non_camel_case_types)]
type w32 = w<u32>;
const RAND_SIZE_LEN: usize = 8;
const RAND_SIZE: usize = 1 << RAND_SIZE_LEN;
/// A random number generator that uses the ISAAC algorithm.
///
/// ISAAC stands for "Indirection, Shift, Accumulate, Add, and Count" which are
/// the principal bitwise operations employed. It is the most advanced of a
/// series of array based random number generator designed by Robert Jenkins
/// in 1996[^1][^2].
///
/// ISAAC is notably fast and produces excellent quality random numbers for
/// non-cryptographic applications.
///
/// In spite of being designed with cryptographic security in mind, ISAAC hasn't
/// been stringently cryptanalyzed and thus cryptographers do not not
/// consensually trust it to be secure. When looking for a secure RNG, prefer
/// [`Hc128Rng`] instead, which, like ISAAC, is an array-based RNG and one of
/// the stream-ciphers selected the by eSTREAM contest.
///
/// In 2006 an improvement to ISAAC was suggested by Jean-Philippe Aumasson,
/// named ISAAC+[^3]. But because the specification is not complete, because
/// there is no good implementation, and because the suggested bias may not
/// exist, it is not implemented here.
///
/// ## Overview of the ISAAC algorithm:
/// (in pseudo-code)
///
/// ```text
/// Input: a, b, c, s[256] // state
/// Output: r[256] // results
///
/// mix(a,i) = a ^ a << 13 if i = 0 mod 4
/// a ^ a >> 6 if i = 1 mod 4
/// a ^ a << 2 if i = 2 mod 4
/// a ^ a >> 16 if i = 3 mod 4
///
/// c = c + 1
/// b = b + c
///
/// for i in 0..256 {
/// x = s_[i]
/// a = f(a,i) + s[i+128 mod 256]
/// y = a + b + s[x>>2 mod 256]
/// s[i] = y
/// b = x + s[y>>10 mod 256]
/// r[i] = b
/// }
/// ```
///
/// Numbers are generated in blocks of 256. This means the function above only
/// runs once every 256 times you ask for a next random number. In all other
/// circumstances the last element of the results array is returned.
///
/// ISAAC therefore needs a lot of memory, relative to other non-crypto RNGs.
/// 2 * 256 * 4 = 2 kb to hold the state and results.
///
/// This implementation uses [`BlockRng`] to implement the [`RngCore`] methods.
///
/// ## References
/// [^1]: Bob Jenkins, [*ISAAC: A fast cryptographic random number generator*](
/// http://burtleburtle.net/bob/rand/isaacafa.html)
///
/// [^2]: Bob Jenkins, [*ISAAC and RC4*](
/// http://burtleburtle.net/bob/rand/isaac.html)
///
/// [^3]: Jean-Philippe Aumasson, [*On the pseudo-random generator ISAAC*](
/// https://eprint.iacr.org/2006/438)
///
/// [`Hc128Rng`]: ../../rand_hc/struct.Hc128Rng.html
/// [`BlockRng`]: ../../rand_core/block/struct.BlockRng.html
/// [`RngCore`]: ../../rand_core/trait.RngCore.html
#[derive(Clone, Debug)]
#[cfg_attr(feature="serde1", derive(Serialize, Deserialize))]
pub struct IsaacRng(BlockRng<IsaacCore>);
impl RngCore for IsaacRng {
#[inline(always)]
fn next_u32(&mut self) -> u32 {
self.0.next_u32()
}
#[inline(always)]
fn next_u64(&mut self) -> u64 {
self.0.next_u64()
}
fn fill_bytes(&mut self, dest: &mut [u8]) {
self.0.fill_bytes(dest)
}
fn try_fill_bytes(&mut self, dest: &mut [u8]) -> Result<(), Error> {
self.0.try_fill_bytes(dest)
}
}
impl SeedableRng for IsaacRng {
type Seed = <IsaacCore as SeedableRng>::Seed;
fn from_seed(seed: Self::Seed) -> Self {
IsaacRng(BlockRng::<IsaacCore>::from_seed(seed))
}
/// Create an ISAAC random number generator using an `u64` as seed.
/// If `seed == 0` this will produce the same stream of random numbers as
/// the reference implementation when used unseeded.
fn seed_from_u64(seed: u64) -> Self {
IsaacRng(BlockRng::<IsaacCore>::seed_from_u64(seed))
}
fn from_rng<S: RngCore>(rng: S) -> Result<Self, Error> {
BlockRng::<IsaacCore>::from_rng(rng).map(|rng| IsaacRng(rng))
}
}
impl IsaacRng {
/// Create an ISAAC random number generator using an `u64` as seed.
/// If `seed == 0` this will produce the same stream of random numbers as
/// the reference implementation when used unseeded.
#[deprecated(since="0.6.0", note="use SeedableRng::seed_from_u64 instead")]
pub fn new_from_u64(seed: u64) -> Self {
Self::seed_from_u64(seed)
}
}
/// The core of `IsaacRng`, used with `BlockRng`.
#[derive(Clone)]
#[cfg_attr(feature="serde1", derive(Serialize, Deserialize))]
pub struct IsaacCore {
#[cfg_attr(feature="serde1",serde(with="super::isaac_array::isaac_array_serde"))]
mem: [w32; RAND_SIZE],
a: w32,
b: w32,
c: w32,
}
// Custom Debug implementation that does not expose the internal state
impl fmt::Debug for IsaacCore {
fn fmt(&self, f: &mut fmt::Formatter) -> fmt::Result {
write!(f, "IsaacCore {{}}")
}
}
impl BlockRngCore for IsaacCore {
type Item = u32;
type Results = IsaacArray<Self::Item>;
/// Refills the output buffer, `results`. See also the pseudocode desciption
/// of the algorithm in the [`IsaacRng`] documentation.
///
/// Optimisations used (similar to the reference implementation):
///
/// - The loop is unrolled 4 times, once for every constant of mix().
/// - The contents of the main loop are moved to a function `rngstep`, to
/// reduce code duplication.
/// - We use local variables for a and b, which helps with optimisations.
/// - We split the main loop in two, one that operates over 0..128 and one
/// over 128..256. This way we can optimise out the addition and modulus
/// from `s[i+128 mod 256]`.
/// - We maintain one index `i` and add `m` or `m2` as base (m2 for the
/// `s[i+128 mod 256]`), relying on the optimizer to turn it into pointer
/// arithmetic.
/// - We fill `results` backwards. The reference implementation reads values
/// from `results` in reverse. We read them in the normal direction, to
/// make `fill_bytes` a memcopy. To maintain compatibility we fill in
/// reverse.
///
/// [`IsaacRng`]: struct.IsaacRng.html
fn generate(&mut self, results: &mut IsaacArray<Self::Item>) {
self.c += w(1);
// abbreviations
let mut a = self.a;
let mut b = self.b + self.c;
const MIDPOINT: usize = RAND_SIZE / 2;
#[inline]
fn ind(mem:&[w32; RAND_SIZE], v: w32, amount: usize) -> w32 {
let index = (v >> amount).0 as usize % RAND_SIZE;
mem[index]
}
#[inline]
fn rngstep(mem: &mut [w32; RAND_SIZE],
results: &mut [u32; RAND_SIZE],
mix: w32,
a: &mut w32,
b: &mut w32,
base: usize,
m: usize,
m2: usize) {
let x = mem[base + m];
*a = mix + mem[base + m2];
let y = *a + *b + ind(&mem, x, 2);
mem[base + m] = y;
*b = x + ind(&mem, y, 2 + RAND_SIZE_LEN);
results[RAND_SIZE - 1 - base - m] = (*b).0;
}
let mut m = 0;
let mut m2 = MIDPOINT;
for i in (0..MIDPOINT/4).map(|i| i * 4) {
rngstep(&mut self.mem, results, a ^ (a << 13), &mut a, &mut b, i + 0, m, m2);
rngstep(&mut self.mem, results, a ^ (a >> 6 ), &mut a, &mut b, i + 1, m, m2);
rngstep(&mut self.mem, results, a ^ (a << 2 ), &mut a, &mut b, i + 2, m, m2);
rngstep(&mut self.mem, results, a ^ (a >> 16), &mut a, &mut b, i + 3, m, m2);
}
m = MIDPOINT;
m2 = 0;
for i in (0..MIDPOINT/4).map(|i| i * 4) {
rngstep(&mut self.mem, results, a ^ (a << 13), &mut a, &mut b, i + 0, m, m2);
rngstep(&mut self.mem, results, a ^ (a >> 6 ), &mut a, &mut b, i + 1, m, m2);
rngstep(&mut self.mem, results, a ^ (a << 2 ), &mut a, &mut b, i + 2, m, m2);
rngstep(&mut self.mem, results, a ^ (a >> 16), &mut a, &mut b, i + 3, m, m2);
}
self.a = a;
self.b = b;
}
}
impl IsaacCore {
/// Create a new ISAAC random number generator.
///
/// The author Bob Jenkins describes how to best initialize ISAAC here:
/// <https://rt.cpan.org/Public/Bug/Display.html?id=64324>
/// The answer is included here just in case:
///
/// "No, you don't need a full 8192 bits of seed data. Normal key sizes will
/// do fine, and they should have their expected strength (eg a 40-bit key
/// will take as much time to brute force as 40-bit keys usually will). You
/// could fill the remainder with 0, but set the last array element to the
/// length of the key provided (to distinguish keys that differ only by
/// different amounts of 0 padding). You do still need to call `randinit()`
/// to make sure the initial state isn't uniform-looking."
/// "After publishing ISAAC, I wanted to limit the key to half the size of
/// `r[]`, and repeat it twice. That would have made it hard to provide a
/// key that sets the whole internal state to anything convenient. But I'd
/// already published it."
///
/// And his answer to the question "For my code, would repeating the key
/// over and over to fill 256 integers be a better solution than
/// zero-filling, or would they essentially be the same?":
/// "If the seed is under 32 bytes, they're essentially the same, otherwise
/// repeating the seed would be stronger. randinit() takes a chunk of 32
/// bytes, mixes it, and combines that with the next 32 bytes, et cetera.
/// Then loops over all the elements the same way a second time."
#[inline]
fn init(mut mem: [w32; RAND_SIZE], rounds: u32) -> Self {
fn mix(a: &mut w32, b: &mut w32, c: &mut w32, d: &mut w32,
e: &mut w32, f: &mut w32, g: &mut w32, h: &mut w32) {
*a ^= *b << 11; *d += *a; *b += *c;
*b ^= *c >> 2; *e += *b; *c += *d;
*c ^= *d << 8; *f += *c; *d += *e;
*d ^= *e >> 16; *g += *d; *e += *f;
*e ^= *f << 10; *h += *e; *f += *g;
*f ^= *g >> 4; *a += *f; *g += *h;
*g ^= *h << 8; *b += *g; *h += *a;
*h ^= *a >> 9; *c += *h; *a += *b;
}
// These numbers are the result of initializing a...h with the
// fractional part of the golden ratio in binary (0x9e3779b9)
// and applying mix() 4 times.
let mut a = w(0x1367df5a);
let mut b = w(0x95d90059);
let mut c = w(0xc3163e4b);
let mut d = w(0x0f421ad8);
let mut e = w(0xd92a4a78);
let mut f = w(0xa51a3c49);
let mut g = w(0xc4efea1b);
let mut h = w(0x30609119);
// Normally this should do two passes, to make all of the seed effect
// all of `mem`
for _ in 0..rounds {
for i in (0..RAND_SIZE/8).map(|i| i * 8) {
a += mem[i ]; b += mem[i+1];
c += mem[i+2]; d += mem[i+3];
e += mem[i+4]; f += mem[i+5];
g += mem[i+6]; h += mem[i+7];
mix(&mut a, &mut b, &mut c, &mut d,
&mut e, &mut f, &mut g, &mut h);
mem[i ] = a; mem[i+1] = b;
mem[i+2] = c; mem[i+3] = d;
mem[i+4] = e; mem[i+5] = f;
mem[i+6] = g; mem[i+7] = h;
}
}
Self { mem, a: w(0), b: w(0), c: w(0) }
}
}
impl SeedableRng for IsaacCore {
type Seed = [u8; 32];
fn from_seed(seed: Self::Seed) -> Self {
let mut seed_u32 = [0u32; 8];
le::read_u32_into(&seed, &mut seed_u32);
// Convert the seed to `Wrapping<u32>` and zero-extend to `RAND_SIZE`.
let mut seed_extended = [w(0); RAND_SIZE];
for (x, y) in seed_extended.iter_mut().zip(seed_u32.iter()) {
*x = w(*y);
}
Self::init(seed_extended, 2)
}
/// Create an ISAAC random number generator using an `u64` as seed.
/// If `seed == 0` this will produce the same stream of random numbers as
/// the reference implementation when used unseeded.
fn seed_from_u64(seed: u64) -> Self {
let mut key = [w(0); RAND_SIZE];
key[0] = w(seed as u32);
key[1] = w((seed >> 32) as u32);
// Initialize with only one pass.
// A second pass does not improve the quality here, because all of the
// seed was already available in the first round.
// Not doing the second pass has the small advantage that if
// `seed == 0` this method produces exactly the same state as the
// reference implementation when used unseeded.
Self::init(key, 1)
}
fn from_rng<R: RngCore>(mut rng: R) -> Result<Self, Error> {
// Custom `from_rng` implementation that fills a seed with the same size
// as the entire state.
let mut seed = [w(0u32); RAND_SIZE];
unsafe {
let ptr = seed.as_mut_ptr() as *mut u8;
let slice = slice::from_raw_parts_mut(ptr, RAND_SIZE * 4);
rng.try_fill_bytes(slice)?;
}
for i in seed.iter_mut() {
*i = w(i.0.to_le());
}
Ok(Self::init(seed, 2))
}
}
#[cfg(test)]
mod test {
use rand_core::{RngCore, SeedableRng};
use super::IsaacRng;
#[test]
fn test_isaac_construction() {
// Test that various construction techniques produce a working RNG.
let seed = [1,0,0,0, 23,0,0,0, 200,1,0,0, 210,30,0,0,
0,0,0,0, 0,0,0,0, 0,0,0,0, 0,0,0,0];
let mut rng1 = IsaacRng::from_seed(seed);
assert_eq!(rng1.next_u32(), 2869442790);
let mut rng2 = IsaacRng::from_rng(rng1).unwrap();
assert_eq!(rng2.next_u32(), 3094074039);
}
#[test]
fn test_isaac_true_values_32() {
let seed = [1,0,0,0, 23,0,0,0, 200,1,0,0, 210,30,0,0,
57,48,0,0, 0,0,0,0, 0,0,0,0, 0,0,0,0];
let mut rng1 = IsaacRng::from_seed(seed);
let mut results = [0u32; 10];
for i in results.iter_mut() { *i = rng1.next_u32(); }
let expected = [
2558573138, 873787463, 263499565, 2103644246, 3595684709,
4203127393, 264982119, 2765226902, 2737944514, 3900253796];
assert_eq!(results, expected);
let seed = [57,48,0,0, 50,9,1,0, 49,212,0,0, 148,38,0,0,
0,0,0,0, 0,0,0,0, 0,0,0,0, 0,0,0,0];
let mut rng2 = IsaacRng::from_seed(seed);
// skip forward to the 10000th number
for _ in 0..10000 { rng2.next_u32(); }
for i in results.iter_mut() { *i = rng2.next_u32(); }
let expected = [
3676831399, 3183332890, 2834741178, 3854698763, 2717568474,
1576568959, 3507990155, 179069555, 141456972, 2478885421];
assert_eq!(results, expected);
}
#[test]
fn test_isaac_true_values_64() {
// As above, using little-endian versions of above values
let seed = [1,0,0,0, 23,0,0,0, 200,1,0,0, 210,30,0,0,
57,48,0,0, 0,0,0,0, 0,0,0,0, 0,0,0,0];
let mut rng = IsaacRng::from_seed(seed);
let mut results = [0u64; 5];
for i in results.iter_mut() { *i = rng.next_u64(); }
let expected = [
3752888579798383186, 9035083239252078381,18052294697452424037,
11876559110374379111, 16751462502657800130];
assert_eq!(results, expected);
}
#[test]
fn test_isaac_true_bytes() {
let seed = [1,0,0,0, 23,0,0,0, 200,1,0,0, 210,30,0,0,
57,48,0,0, 0,0,0,0, 0,0,0,0, 0,0,0,0];
let mut rng = IsaacRng::from_seed(seed);
let mut results = [0u8; 32];
rng.fill_bytes(&mut results);
// Same as first values in test_isaac_true_values as bytes in LE order
let expected = [82, 186, 128, 152, 71, 240, 20, 52,
45, 175, 180, 15, 86, 16, 99, 125,
101, 203, 81, 214, 97, 162, 134, 250,
103, 78, 203, 15, 150, 3, 210, 164];
assert_eq!(results, expected);
}
#[test]
fn test_isaac_new_uninitialized() {
// Compare the results from initializing `IsaacRng` with
// `seed_from_u64(0)`, to make sure it is the same as the reference
// implementation when used uninitialized.
// Note: We only test the first 16 integers, not the full 256 of the
// first block.
let mut rng = IsaacRng::seed_from_u64(0);
let mut results = [0u32; 16];
for i in results.iter_mut() { *i = rng.next_u32(); }
let expected: [u32; 16] = [
0x71D71FD2, 0xB54ADAE7, 0xD4788559, 0xC36129FA,
0x21DC1EA9, 0x3CB879CA, 0xD83B237F, 0xFA3CE5BD,
0x8D048509, 0xD82E9489, 0xDB452848, 0xCA20E846,
0x500F972E, 0x0EEFF940, 0x00D6B993, 0xBC12C17F];
assert_eq!(results, expected);
}
#[test]
fn test_isaac_clone() {
let seed = [1,0,0,0, 23,0,0,0, 200,1,0,0, 210,30,0,0,
57,48,0,0, 0,0,0,0, 0,0,0,0, 0,0,0,0];
let mut rng1 = IsaacRng::from_seed(seed);
let mut rng2 = rng1.clone();
for _ in 0..16 {
assert_eq!(rng1.next_u32(), rng2.next_u32());
}
}
#[test]
#[cfg(feature="serde1")]
fn test_isaac_serde() {
use bincode;
use std::io::{BufWriter, BufReader};
let seed = [1,0,0,0, 23,0,0,0, 200,1,0,0, 210,30,0,0,
57,48,0,0, 0,0,0,0, 0,0,0,0, 0,0,0,0];
let mut rng = IsaacRng::from_seed(seed);
let buf: Vec<u8> = Vec::new();
let mut buf = BufWriter::new(buf);
bincode::serialize_into(&mut buf, &rng).expect("Could not serialize");
let buf = buf.into_inner().unwrap();
let mut read = BufReader::new(&buf[..]);
let mut deserialized: IsaacRng = bincode::deserialize_from(&mut read).expect("Could not deserialize");
for _ in 0..300 { // more than the 256 buffered results
assert_eq!(rng.next_u32(), deserialized.next_u32());
}
}
}