| // 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_hc128/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()); |
| } |
| } |
| } |