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// 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()); } } }