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Diffstat (limited to 'rand/rand_isaac/src/isaac.rs')
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diff --git a/rand/rand_isaac/src/isaac.rs b/rand/rand_isaac/src/isaac.rs new file mode 100644 index 0000000..2bfdd94 --- /dev/null +++ b/rand/rand_isaac/src/isaac.rs @@ -0,0 +1,484 @@ +// 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()); + } + } +} |