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// Copyright (c) Facebook, Inc. and its affiliates.
//
// This source code is licensed under the MIT license found in the
// LICENSE file in the root directory of this source tree.
use alloc::vec::Vec;
use math::{FieldElement, StarkField};
use crate::{errors::RandomCoinError, Digest, ElementHasher, RandomCoin};
// DEFAULT RANDOM COIN IMPLEMENTATION
// ================================================================================================
/// Pseudo-random element generator for finite fields, which is a default implementation of the
/// RandomCoin trait.
///
/// A random coin can be used to draw elements uniformly at random from the specified base field
/// or from any extension of the base field.
///
/// Internally we use a cryptographic hash function (which is specified via the `H` type parameter),
/// to draw elements from the field. The coin works roughly as follows:
/// - The internal state of the coin consists of a `seed` and a `counter`. At instantiation
/// time, the `seed` is set to a hash of the provided bytes, and the `counter` is set to 0.
/// - To draw the next element, we increment the `counter` and compute hash(`seed` || `counter`).
/// If the resulting value is a valid field element, we return the result; otherwise we try
/// again until a valid element is found or the number of allowed tries is exceeded.
/// - We can also re-seed the coin with a new value. During the reseeding procedure, the
/// seed is set to hash(`old_seed` || `new_seed`), and the counter is reset to 0.
///
/// # Examples
/// ```
/// # use winter_crypto::{RandomCoin, DefaultRandomCoin, Hasher, hashers::Blake3_256};
/// # use math::fields::f128::BaseElement;
/// // initial elements for seeding the random coin
/// let seed = &[BaseElement::new(1), BaseElement::new(2), BaseElement::new(3), BaseElement::new(4)];
///
/// // instantiate a random coin using BLAKE3 as the hash function
/// let mut coin = DefaultRandomCoin::<Blake3_256<BaseElement>>::new(seed);
///
/// // should draw different elements each time
/// let e1 = coin.draw::<BaseElement>().unwrap();;
/// let e2 = coin.draw::<BaseElement>().unwrap();;
/// assert_ne!(e1, e2);
///
/// let e3 = coin.draw::<BaseElement>().unwrap();;
/// assert_ne!(e1, e3);
/// assert_ne!(e2, e3);
///
/// // should draw same elements for the same seed
/// let mut coin2 = DefaultRandomCoin::<Blake3_256<BaseElement>>::new(seed);
/// let mut coin1 = DefaultRandomCoin::<Blake3_256<BaseElement>>::new(seed);
/// let e1 = coin1.draw::<BaseElement>().unwrap();;
/// let e2 = coin2.draw::<BaseElement>().unwrap();;
/// assert_eq!(e1, e2);
///
/// // should draw different elements based on seed
/// let mut coin1 = DefaultRandomCoin::<Blake3_256<BaseElement>>::new(seed);
/// let seed = &[BaseElement::new(2), BaseElement::new(3), BaseElement::new(4), BaseElement::new(5)];
/// let mut coin2 = DefaultRandomCoin::<Blake3_256<BaseElement>>::new(seed);
/// let e1 = coin1.draw::<BaseElement>().unwrap();;
/// let e2 = coin2.draw::<BaseElement>().unwrap();;
/// assert_ne!(e1, e2);
/// ```
pub struct DefaultRandomCoin<H: ElementHasher> {
seed: H::Digest,
counter: u64,
}
impl<H: ElementHasher> DefaultRandomCoin<H> {
/// Updates the state by incrementing the counter and returns hash(seed || counter)
fn next(&mut self) -> H::Digest {
self.counter += 1;
H::merge_with_int(self.seed, self.counter)
}
}
impl<B: StarkField, H: ElementHasher<BaseField = B>> RandomCoin for DefaultRandomCoin<H> {
type BaseField = B;
type Hasher = H;
// CONSTRUCTOR
// --------------------------------------------------------------------------------------------
/// Returns a new random coin instantiated with the provided `seed`.
fn new(seed: &[Self::BaseField]) -> Self {
let seed = H::hash_elements(seed);
Self { seed, counter: 0 }
}
// RESEEDING
// --------------------------------------------------------------------------------------------
/// Reseeds the coin with the specified data by setting the new seed to hash(`seed` || `data`).
///
/// # Examples
/// ```
/// # use winter_crypto::{RandomCoin, DefaultRandomCoin, Hasher, hashers::Blake3_256};
/// # use math::fields::f128::BaseElement;
/// // initial elements for seeding the random coin
/// let seed = &[BaseElement::new(1), BaseElement::new(2), BaseElement::new(3), BaseElement::new(4)];
///
/// let mut coin1 = DefaultRandomCoin::<Blake3_256<BaseElement>>::new(seed);
/// let mut coin2 = DefaultRandomCoin::<Blake3_256<BaseElement>>::new(seed);
///
/// // should draw the same element form both coins
/// let e1 = coin1.draw::<BaseElement>().unwrap();
/// let e2 = coin2.draw::<BaseElement>().unwrap();;
/// assert_eq!(e1, e2);
///
/// // after reseeding should draw different elements
/// coin2.reseed(Blake3_256::<BaseElement>::hash(&[2, 3, 4, 5]));
/// let e1 = coin1.draw::<BaseElement>().unwrap();;
/// let e2 = coin2.draw::<BaseElement>().unwrap();;
/// assert_ne!(e1, e2);
/// ```
fn reseed(&mut self, data: H::Digest) {
self.seed = H::merge(&[self.seed, data]);
self.counter = 0;
}
// PUBLIC ACCESSORS
// --------------------------------------------------------------------------------------------
/// Computes hash(`seed` || `value`) and returns the number of leading zeros in the resulting
/// value if it is interpreted as an integer in big-endian byte order.
fn check_leading_zeros(&self, value: u64) -> u32 {
let new_seed = H::merge_with_int(self.seed, value);
let bytes = new_seed.as_bytes();
let seed_head = u64::from_le_bytes(bytes[..8].try_into().unwrap());
seed_head.trailing_zeros()
}
// DRAW METHODS
// --------------------------------------------------------------------------------------------
/// Returns the next pseudo-random field element.
///
/// # Errors
/// Returns an error if a valid field element could not be generated after 1000 calls to the
/// PRNG.
fn draw<E: FieldElement>(&mut self) -> Result<E, RandomCoinError> {
for _ in 0..1000 {
// get the next pseudo-random value and take the first ELEMENT_BYTES from it
let value = self.next();
let bytes = &value.as_bytes()[..E::ELEMENT_BYTES];
// check if the bytes can be converted into a valid field element; if they can,
// return; otherwise try again
if let Some(element) = E::from_random_bytes(bytes) {
return Ok(element);
}
}
Err(RandomCoinError::FailedToDrawFieldElement(1000))
}
/// Returns a vector of integers selected from the range [0, domain_size) after reseeding
/// the PRNG with the specified `nonce` by setting the new seed to hash(`seed` || `nonce`).
///
/// # Errors
/// Returns an error if the specified number of integers could not be generated after 1000
/// calls to the PRNG.
///
/// # Panics
/// Panics if:
/// - `domain_size` is not a power of two.
/// - `num_values` is greater than or equal to `domain_size`.
///
/// # Examples
/// ```
/// # use std::collections::HashSet;
/// # use winter_crypto::{RandomCoin, DefaultRandomCoin, Hasher, hashers::Blake3_256};
/// # use math::fields::f128::BaseElement;
/// // initial elements for seeding the random coin
/// let seed = &[BaseElement::new(1), BaseElement::new(2), BaseElement::new(3), BaseElement::new(4)];
///
/// let mut coin = DefaultRandomCoin::<Blake3_256<BaseElement>>::new(seed);
///
/// let num_values = 20;
/// let domain_size = 64;
/// let nonce = 0;
/// let values = coin.draw_integers(num_values, domain_size, nonce).unwrap();
///
/// assert_eq!(num_values, values.len());
///
/// for value in values {
/// assert!(value < domain_size);
/// }
/// ```
fn draw_integers(
&mut self,
num_values: usize,
domain_size: usize,
nonce: u64,
) -> Result<Vec<usize>, RandomCoinError> {
assert!(domain_size.is_power_of_two(), "domain size must be a power of two");
assert!(num_values < domain_size, "number of values must be smaller than domain size");
// reseed with nonce
self.seed = H::merge_with_int(self.seed, nonce);
self.counter = 0;
// determine how many bits are needed to represent valid values in the domain
let v_mask = (domain_size - 1) as u64;
// draw values from PRNG until we get as many unique values as specified by num_queries
let mut values = Vec::new();
for _ in 0..1000 {
// get the next pseudo-random value and read the first 8 bytes from it
let bytes: [u8; 8] = self.next().as_bytes()[..8].try_into().unwrap();
// convert to integer and limit the integer to the number of bits which can fit
// into the specified domain
let value = (u64::from_le_bytes(bytes) & v_mask) as usize;
values.push(value);
if values.len() == num_values {
break;
}
}
if values.len() < num_values {
return Err(RandomCoinError::FailedToDrawIntegers(num_values, values.len(), 1000));
}
Ok(values)
}
}