qfall_math/integer_mod_q/poly_over_zq/sample/

binomial.rs

// Copyright 2023 Jan Niklas Siemer
//
// This file is part of qFALL-math.
//
// qFALL-math is free software: you can redistribute it and/or modify it under
// the terms of the Mozilla Public License Version 2.0 as published by the
// Mozilla Foundation. See <https://mozilla.org/en-US/MPL/2.0/>.

//! This module contains algorithms for sampling
//! according to the binomial distribution.

use crate::{
    error::MathError,
    integer::Z,
    integer_mod_q::{Modulus, PolyOverZq},
    macros::seeded::seedable_function,
    rational::Q,
    traits::SetCoefficient,
    utils::{index::evaluate_index, sample::binomial::BinomialSampler},
};
use std::fmt::Display;

impl PolyOverZq {
    seedable_function!(
        /// Generates a [`PolyOverZq`] instance of maximum degree `max_degree` and
        /// coefficients chosen according to the binomial distribution
        /// parameterized by `n` and `p`.
        ///
        /// Parameters:
        /// - `max_degree`: specifies the length of the polynomial,
        ///   i.e. the number of coefficients
        /// - `modulus`: specifies the [`Modulus`] of the new [`PolyOverZq`] instance
        /// - `n`: specifies the number of trials
        /// - `p`: specifies the probability of success
        #[seeded]
        /// - `seed`: specifies the 256-bit seed of the PRNG used for sampling
        #[optionally_seeded]
        /// - `seed`: specifies an optional 256-bit seed of the PRNG used for sampling.
        #[optionally_seeded]
        ///   If `None` is provided, a fresh [`ThreadRng`](rand::rngs::ThreadRng) is used instead.
        ///
        /// Returns a fresh [`PolyOverZq`] instance with each value sampled
        ///     according to the binomial distribution or a [`MathError`]
        ///     if `n < 0`, `p ∉ (0,1)`, `n` does not fit into an [`i64`],
        ///     or `max_degree` is negative or does not into an [`i64`].
        ///
        /// # Examples
        /// ```
        /// use qfall_math::integer_mod_q::PolyOverZq;
        ///
        #[unseeded]
        /// let sample = PolyOverZq::sample_binomial(2, 7, 2, 0.5).unwrap();
        #[seeded]
        /// let sample = PolyOverZq::sample_binomial_seeded(2, 7, 2, 0.5, [42; 32]).unwrap();
        /// ```
        ///
        /// # Errors and Failures
        /// - Returns a [`MathError`] of type [`InvalidIntegerInput`](MathError::InvalidIntegerInput)
        ///   if `n < 0`.
        /// - Returns a [`MathError`] of type [`InvalidInterval`](MathError::InvalidInterval)
        ///   if `p ∉ (0,1)`.
        /// - Returns a [`MathError`] of type [`ConversionError`](MathError::ConversionError)
        ///   if `n` does not fit into an [`i64`].
        /// - Returns a [`MathError`] of type [`OutOfBounds`](MathError::OutOfBounds) if
        ///   the `max_degree` is negative or it does not fit into an [`i64`].
        pub(crate) fn sample_binomial(
            max_degree: impl TryInto<i64> + Display,
            modulus: impl Into<Modulus>,
            n: impl Into<Z>,
            p: impl Into<Q>,
            seed: Option<[u8; 32]>,
        ) -> Result<Self, MathError> {
            Self::sample_binomial_with_offset_optionally_seeded(max_degree, 0, modulus, n, p, seed)
        }
    );

    seedable_function!(
        /// Generates a [`PolyOverZq`] instance of maximum degree `max_degree` and
        /// coefficients chosen according to the binomial distribution
        /// parameterized by `n` and `p` with given `offset`.
        ///
        /// Parameters:
        /// - `max_degree`: specifies the length of the polynomial,
        ///   i.e. the number of coefficients
        /// - `offset`: specifies an offset applied to each sample
        ///   collected from the binomial distribution
        /// - `modulus`: specifies the [`Modulus`] of the new [`PolyOverZq`] instance
        /// - `n`: specifies the number of trials
        /// - `p`: specifies the probability of success
        #[seeded]
        /// - `seed`: specifies the 256-bit seed of the PRNG used for sampling
        #[optionally_seeded]
        /// - `seed`: specifies an optional 256-bit seed of the PRNG used for sampling.
        #[optionally_seeded]
        ///   If `None` is provided, a fresh [`ThreadRng`](rand::rngs::ThreadRng) is used instead.
        ///
        /// Returns a fresh [`PolyOverZq`] instance with each value sampled
        /// according to the binomial distribution or a [`MathError`]
        /// if `n < 0`, `p ∉ (0,1)`, `n` does not fit into an [`i64`],
        /// or `max_degree` is negative or does not into an [`i64`].
        ///
        /// # Examples
        /// ```
        /// use qfall_math::integer_mod_q::PolyOverZq;
        ///
        #[unseeded]
        /// let sample = PolyOverZq::sample_binomial_with_offset(2, -1, 7, 2, 0.5).unwrap();
        #[seeded]
        /// let sample = PolyOverZq::sample_binomial_with_offset_seeded(2, -1, 7, 2, 0.5, [42; 32]).unwrap();
        /// ```
        ///
        /// # Errors and Failures
        /// - Returns a [`MathError`] of type [`InvalidIntegerInput`](MathError::InvalidIntegerInput)
        ///   if `n < 0`.
        /// - Returns a [`MathError`] of type [`InvalidInterval`](MathError::InvalidInterval)
        ///   if `p ∉ (0,1)`.
        /// - Returns a [`MathError`] of type [`ConversionError`](MathError::ConversionError)
        ///   if `n` does not fit into an [`i64`].
        /// - Returns a [`MathError`] of type [`OutOfBounds`](MathError::OutOfBounds) if
        ///   the `max_degree` is negative or it does not fit into an [`i64`].
        ///
        /// # Panics ...
        /// - if `modulus` is smaller than `2`.
        pub(crate) fn sample_binomial_with_offset(
            max_degree: impl TryInto<i64> + Display,
            offset: impl Into<Z>,
            modulus: impl Into<Modulus>,
            n: impl Into<Z>,
            p: impl Into<Q>,
            seed: Option<[u8; 32]>,
        ) -> Result<Self, MathError> {
            let max_degree = evaluate_index(max_degree)?;
            let offset: Z = offset.into();
            let modulus: Modulus = modulus.into();
            let mut bin_sampler = BinomialSampler::init(n, p, seed)?;

            let mut poly_z = PolyOverZq::from(&modulus);

            for index in 0..=max_degree {
                let mut sample = bin_sampler.sample();
                sample += &offset;
                unsafe { poly_z.set_coeff_unchecked(index, sample) };
            }

            Ok(poly_z)
        }
    );
}

#[cfg(test)]
mod test_sample_binomial {
    use super::{PolyOverZq, Q, Z};
    use crate::traits::GetCoefficient;
    use crate::utils::sample::test_seed;

    // As all major tests regarding an appropriate binomial distribution,
    // whether the correct interval is kept, and if the errors are thrown correctly,
    // are performed in the `utils` module, we omit these tests here.

    /// Checks whether the boundaries of the interval are kept.
    #[test]
    fn boundaries_kept() {
        for seeded in [false, true] {
            for _ in 0..8 {
                let poly = PolyOverZq::sample_binomial_optionally_seeded(
                    0,
                    7,
                    2,
                    0.5,
                    seeded.then(test_seed),
                )
                .unwrap();
                let sample: Z = poly.get_coeff(0).unwrap();
                assert!(Z::ZERO <= sample || sample <= 2);
            }
        }
    }

    /// Checks whether the number of coefficients is correct.
    #[test]
    fn nr_coeffs() {
        for seeded in [false, true] {
            let degrees = [1, 3, 7, 15, 32, 120];
            for degree in degrees {
                let res = PolyOverZq::sample_binomial_optionally_seeded(
                    degree,
                    u64::MAX,
                    256,
                    0.99999,
                    seeded.then(test_seed),
                )
                .unwrap();

                assert_eq!(
                    degree,
                    res.get_degree(),
                    "This test can fail with probability close to 0."
                );
            }
        }
    }

    /// Checks whether providing a length smaller than `0` results in an error.
    #[test]
    fn invalid_max_degree() {
        for seeded in [false, true] {
            let res_0 = PolyOverZq::sample_binomial_optionally_seeded(
                -1,
                7,
                2,
                0.5,
                seeded.then(test_seed),
            );
            let res_1 = PolyOverZq::sample_binomial_optionally_seeded(
                i64::MIN,
                7,
                2,
                0.5,
                seeded.then(test_seed),
            );

            assert!(res_0.is_err());
            assert!(res_1.is_err());
        }
    }

    /// Checks whether `sample_binomial` is available for all types
    /// implementing [`Into<Z>`], i.e. u8, u16, u32, u64, i8, ...
    /// and [`Into<Q>`], i.e. u8, u16, i8, i16, f32, f64, ...
    #[test]
    fn availability() {
        for seeded in [false, true] {
            let _ = PolyOverZq::sample_binomial_optionally_seeded(
                1,
                7u8,
                1u16,
                7u8,
                seeded.then(test_seed),
            );
            let _ = PolyOverZq::sample_binomial_optionally_seeded(
                1,
                7u16,
                1u32,
                7u16,
                seeded.then(test_seed),
            );
            let _ = PolyOverZq::sample_binomial_optionally_seeded(
                1,
                7u32,
                1u64,
                7u32,
                seeded.then(test_seed),
            );
            let _ = PolyOverZq::sample_binomial_optionally_seeded(
                1,
                7u64,
                1i8,
                7u64,
                seeded.then(test_seed),
            );
            let _ = PolyOverZq::sample_binomial_optionally_seeded(
                1,
                7i8,
                1i16,
                7i8,
                seeded.then(test_seed),
            );
            let _ = PolyOverZq::sample_binomial_optionally_seeded(
                1,
                7i16,
                1i32,
                7i16,
                seeded.then(test_seed),
            );
            let _ = PolyOverZq::sample_binomial_optionally_seeded(
                1,
                7i32,
                1i64,
                7i32,
                seeded.then(test_seed),
            );
            let _ = PolyOverZq::sample_binomial_optionally_seeded(
                1,
                7i64,
                Z::ONE,
                7i64,
                seeded.then(test_seed),
            );
            let _ = PolyOverZq::sample_binomial_optionally_seeded(
                1,
                7,
                1u8,
                0.5f32,
                seeded.then(test_seed),
            );
            let _ = PolyOverZq::sample_binomial_optionally_seeded(
                1,
                7,
                1u8,
                0.5f64,
                seeded.then(test_seed),
            );
            let _ = PolyOverZq::sample_binomial_optionally_seeded(
                1,
                7,
                1,
                Q::from((1, 2)),
                seeded.then(test_seed),
            );

            // explicitly checks the existence of the unseeded and the seeded function
            if seeded {
                let _ = PolyOverZq::sample_binomial_seeded(1, 7u8, 1u16, 7u8, test_seed());
            } else {
                let _ = PolyOverZq::sample_binomial(1, 7u8, 1u16, 7u8);
            }
        }
    }

    /// Checks whether the same seed results in the same sample.
    #[test]
    fn same_seed_same_sample() {
        use crate::integer_mod_q::PolyOverZq;
        let sample_0 = PolyOverZq::sample_binomial_seeded(2, 7, 2, 0.5, [42; 32]).unwrap();
        let sample_1 = PolyOverZq::sample_binomial_seeded(2, 7, 2, 0.5, [42; 32]).unwrap();

        assert_eq!(sample_0, sample_1);
    }

    /// Checks whether the seeded variant outputs the known sample for a fixed seed.
    #[test]
    fn known_answer() {
        use crate::integer_mod_q::PolyOverZq;
        let sample = PolyOverZq::sample_binomial_seeded(2, 7, 2, 0.5, [42; 32]).unwrap();

        assert_eq!("3  0 2 1 mod 7", sample.to_string());
    }
}

#[cfg(test)]
mod test_sample_binomial_with_offset {
    use super::{PolyOverZq, Q, Z};
    use crate::traits::GetCoefficient;
    use crate::utils::sample::test_seed;

    // As all major tests regarding an appropriate binomial distribution,
    // whether the correct interval is kept, and if the errors are thrown correctly,
    // are performed in the `utils` module, we omit these tests here.

    /// Checks whether the boundaries of the interval are kept.
    #[test]
    fn boundaries_kept() {
        for seeded in [false, true] {
            for _ in 0..8 {
                let poly = PolyOverZq::sample_binomial_with_offset_optionally_seeded(
                    0,
                    -1,
                    7,
                    2,
                    0.5,
                    seeded.then(test_seed),
                )
                .unwrap();
                let sample: Z = poly.get_coeff(0).unwrap();
                assert!(Z::MINUS_ONE <= sample || sample <= Z::ONE);
            }
        }
    }

    /// Checks whether the number of coefficients is correct.
    #[test]
    fn nr_coeffs() {
        for seeded in [false, true] {
            let degrees = [1, 3, 7, 15, 32, 120];
            for degree in degrees {
                let res = PolyOverZq::sample_binomial_with_offset_optionally_seeded(
                    degree,
                    1,
                    7,
                    2,
                    0.5,
                    seeded.then(test_seed),
                )
                .unwrap();

                assert_eq!(degree, res.get_degree());
            }
        }
    }

    /// Checks whether providing a length smaller than `0` results in an error.
    #[test]
    fn invalid_max_degree() {
        for seeded in [false, true] {
            let res_0 = PolyOverZq::sample_binomial_with_offset_optionally_seeded(
                -1,
                -1,
                7,
                2,
                0.5,
                seeded.then(test_seed),
            );
            let res_1 = PolyOverZq::sample_binomial_with_offset_optionally_seeded(
                i64::MIN,
                -1,
                7,
                2,
                0.5,
                seeded.then(test_seed),
            );

            assert!(res_0.is_err());
            assert!(res_1.is_err());
        }
    }

    /// Checks whether `sample_binomial_with_offset` is available for all types
    /// implementing [`Into<Z>`], i.e. u8, u16, u32, u64, i8, ...
    /// and [`Into<Q>`], i.e. u8, u16, i8, i16, f32, f64, ...
    #[test]
    fn availability() {
        for seeded in [false, true] {
            let _ = PolyOverZq::sample_binomial_with_offset_optionally_seeded(
                1,
                0,
                7u8,
                1u16,
                7u8,
                seeded.then(test_seed),
            );
            let _ = PolyOverZq::sample_binomial_with_offset_optionally_seeded(
                1,
                0,
                7u16,
                1u32,
                7u16,
                seeded.then(test_seed),
            );
            let _ = PolyOverZq::sample_binomial_with_offset_optionally_seeded(
                1,
                0,
                7u32,
                1u64,
                7u32,
                seeded.then(test_seed),
            );
            let _ = PolyOverZq::sample_binomial_with_offset_optionally_seeded(
                1,
                0,
                7u64,
                1i8,
                7u64,
                seeded.then(test_seed),
            );
            let _ = PolyOverZq::sample_binomial_with_offset_optionally_seeded(
                1,
                0,
                7i8,
                1i16,
                7i8,
                seeded.then(test_seed),
            );
            let _ = PolyOverZq::sample_binomial_with_offset_optionally_seeded(
                1,
                0,
                7i16,
                1i32,
                7i16,
                seeded.then(test_seed),
            );
            let _ = PolyOverZq::sample_binomial_with_offset_optionally_seeded(
                1,
                0,
                7i32,
                1i64,
                7i32,
                seeded.then(test_seed),
            );
            let _ = PolyOverZq::sample_binomial_with_offset_optionally_seeded(
                1,
                0,
                7i64,
                Z::ONE,
                7i64,
                seeded.then(test_seed),
            );
            let _ = PolyOverZq::sample_binomial_with_offset_optionally_seeded(
                1,
                0,
                7,
                1u8,
                0.5f32,
                seeded.then(test_seed),
            );
            let _ = PolyOverZq::sample_binomial_with_offset_optionally_seeded(
                1,
                0,
                7,
                1u8,
                0.5f64,
                seeded.then(test_seed),
            );
            let _ = PolyOverZq::sample_binomial_with_offset_optionally_seeded(
                1,
                0,
                7,
                1,
                Q::from((1, 2)),
                seeded.then(test_seed),
            );

            // explicitly checks the existence of the unseeded and the seeded function
            if seeded {
                let _ = PolyOverZq::sample_binomial_with_offset_seeded(
                    1,
                    0,
                    7u8,
                    1u16,
                    7u8,
                    test_seed(),
                );
            } else {
                let _ = PolyOverZq::sample_binomial_with_offset(1, 0, 7u8, 1u16, 7u8);
            }
        }
    }

    /// Checks whether the same seed results in the same sample.
    #[test]
    fn same_seed_same_sample() {
        use crate::integer_mod_q::PolyOverZq;
        let sample_0 =
            PolyOverZq::sample_binomial_with_offset_seeded(2, -1, 7, 2, 0.5, [42; 32]).unwrap();
        let sample_1 =
            PolyOverZq::sample_binomial_with_offset_seeded(2, -1, 7, 2, 0.5, [42; 32]).unwrap();

        assert_eq!(sample_0, sample_1);
    }

    /// Checks whether the seeded variant outputs the known sample for a fixed seed.
    #[test]
    fn known_answer() {
        use crate::integer_mod_q::PolyOverZq;
        let sample =
            PolyOverZq::sample_binomial_with_offset_seeded(2, -1, 7, 2, 0.5, [42; 32]).unwrap();

        assert_eq!("2  6 1 mod 7", sample.to_string());
    }
}