qfall_math/integer_mod_q/poly_over_zq/sample/

discrete_gauss.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 discrete Gaussian distribution.

use crate::{
    error::MathError,
    integer_mod_q::{Modulus, PolyOverZq},
    macros::seeded::seedable_function,
    rational::Q,
    traits::SetCoefficient,
    utils::{
        index::evaluate_index,
        sample::discrete_gauss::{DiscreteGaussianIntegerSampler, LookupTableSetting, TAILCUT},
    },
};
use std::fmt::Display;

impl PolyOverZq {
    seedable_function!(
        /// Initializes a new [`PolyOverZq`] with maximum degree `max_degree`
        /// and with each entry sampled independently according to the
        /// discrete Gaussian distribution, using [`Z::sample_discrete_gauss`](crate::integer::Z::sample_discrete_gauss).
        ///
        /// Parameters:
        /// - `max_degree`: specifies the included maximal degree the created [`PolyOverZq`] should have
        /// - `modulus`: specififes the [`Modulus`] over which the ring of integer coefficients is defined
        /// - `center`: specifies the positions of the center with peak probability
        /// - `s`: specifies the Gaussian parameter, which is proportional
        ///   to the standard deviation `sigma * sqrt(2 * pi) = s`
        #[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 of maximum degree `max_degree`
        /// with coefficients chosen independently according the discrete Gaussian distribution or
        /// a [`MathError`] if `s < 0`.
        ///
        /// # Examples
        /// ```
        /// use qfall_math::integer_mod_q::PolyOverZq;
        ///
        #[unseeded]
        /// let sample = PolyOverZq::sample_discrete_gauss(2, 17, 0, 1).unwrap();
        #[seeded]
        /// let sample = PolyOverZq::sample_discrete_gauss_seeded(2, 17, 0, 1, [42; 32]).unwrap();
        /// ```
        ///
        /// # Errors and Failures
        /// - Returns a [`MathError`] of type [`InvalidIntegerInput`](MathError::InvalidIntegerInput)
        ///   if `s < 0`.
        ///
        /// # Panics ...
        /// - if `max_degree` is negative, or does not fit into an [`i64`].
        /// - if `modulus` is smaller than `2`.
        pub(crate) fn sample_discrete_gauss(
            max_degree: impl TryInto<i64> + Display,
            modulus: impl Into<Modulus>,
            center: impl Into<Q>,
            s: impl Into<Q>,
            seed: Option<[u8; 32]>,
        ) -> Result<Self, MathError> {
            let max_degree = evaluate_index(max_degree).unwrap();
            let modulus = modulus.into();

            let center = center.into();
            let s = s.into();
            let mut poly = PolyOverZq::from(&modulus);

            let mut dgis = DiscreteGaussianIntegerSampler::init(
                &center,
                &s,
                unsafe { TAILCUT },
                LookupTableSetting::FillOnTheFly,
                seed,
            )?;

            for index in 0..=max_degree {
                let sample = dgis.sample_z();
                unsafe { poly.set_coeff_unchecked(index, sample) };
            }
            Ok(poly)
        }
    );
}

#[cfg(test)]
mod test_sample_discrete_gauss {
    use crate::utils::sample::test_seed;
    use crate::{integer::Z, integer_mod_q::PolyOverZq, rational::Q, traits::GetCoefficient};

    /// Checks whether `sample_discrete_gauss` is available for all types
    /// implementing [`Into<Z>`], i.e. u8, u16, u32, u64, i8, ...
    /// or [`Into<Q>`], i.e. u8, i16, f32, Z, Q, ...
    #[test]
    fn availability() {
        for seeded in [false, true] {
            let center = Q::ZERO;
            let s = Q::ONE;

            let _ = PolyOverZq::sample_discrete_gauss_optionally_seeded(
                1u8,
                17u8,
                0f32,
                1u8,
                seeded.then(test_seed),
            );
            let _ = PolyOverZq::sample_discrete_gauss_optionally_seeded(
                1u16,
                17u16,
                0f64,
                1u16,
                seeded.then(test_seed),
            );
            let _ = PolyOverZq::sample_discrete_gauss_optionally_seeded(
                1u32,
                17u32,
                0f32,
                1u32,
                seeded.then(test_seed),
            );
            let _ = PolyOverZq::sample_discrete_gauss_optionally_seeded(
                1u64,
                17u64,
                0f64,
                1u64,
                seeded.then(test_seed),
            );
            let _ = PolyOverZq::sample_discrete_gauss_optionally_seeded(
                1i8,
                17u8,
                0f32,
                1i8,
                seeded.then(test_seed),
            );
            let _ = PolyOverZq::sample_discrete_gauss_optionally_seeded(
                1i8,
                17i8,
                0f32,
                1i16,
                seeded.then(test_seed),
            );
            let _ = PolyOverZq::sample_discrete_gauss_optionally_seeded(
                1i16,
                17i16,
                0f32,
                1i32,
                seeded.then(test_seed),
            );
            let _ = PolyOverZq::sample_discrete_gauss_optionally_seeded(
                1i32,
                17i32,
                0f64,
                1i64,
                seeded.then(test_seed),
            );
            let _ = PolyOverZq::sample_discrete_gauss_optionally_seeded(
                1i64,
                17i64,
                center,
                s,
                seeded.then(test_seed),
            );
            let _ = PolyOverZq::sample_discrete_gauss_optionally_seeded(
                1u8,
                17u8,
                0f32,
                1f64,
                seeded.then(test_seed),
            );

            // explicitly checks the existence of the unseeded and the seeded function
            if seeded {
                let _ = PolyOverZq::sample_discrete_gauss_seeded(1u8, 17u8, 0f32, 1u8, test_seed());
            } else {
                let _ = PolyOverZq::sample_discrete_gauss(1u8, 17u8, 0f32, 1u8);
            }
        }
    }

    /// Checks whether the boundaries of the interval are kept for small moduli.
    #[test]
    fn boundaries_kept_small() {
        for seeded in [false, true] {
            let modulus = 128;

            for _ in 0..32 {
                let poly = PolyOverZq::sample_discrete_gauss_optionally_seeded(
                    3,
                    modulus,
                    15,
                    1,
                    seeded.then(test_seed),
                )
                .unwrap();

                for i in 0..3 {
                    let sample: Z = poly.get_coeff(i).unwrap();
                    assert!(Z::ZERO <= sample);
                    assert!(sample < modulus);
                }
            }
        }
    }

    /// Checks whether the boundaries of the interval are kept for large moduli.
    #[test]
    fn boundaries_kept_large() {
        for seeded in [false, true] {
            let modulus = u64::MAX;

            for _ in 0..256 {
                let poly = PolyOverZq::sample_discrete_gauss_optionally_seeded(
                    3,
                    modulus,
                    1,
                    1,
                    seeded.then(test_seed),
                )
                .unwrap();

                for i in 0..3 {
                    let sample: Z = poly.get_coeff(i).unwrap();
                    assert!(Z::ZERO <= sample);
                    assert!(sample < modulus);
                }
            }
        }
    }

    /// 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_discrete_gauss_optionally_seeded(
                    degree,
                    u64::MAX,
                    i64::MAX,
                    1,
                    seeded.then(test_seed),
                )
                .unwrap();

                assert_eq!(
                    res.get_degree(),
                    degree,
                    "Could fail with negligible probability."
                );
            }
        }
    }

    /// Checks whether the maximum degree needs to be at least 0.
    #[test]
    fn invalid_max_degree() {
        for seeded in [false, true] {
            let result = std::panic::catch_unwind(|| {
                let _ = PolyOverZq::sample_discrete_gauss_optionally_seeded(
                    -1,
                    17,
                    0,
                    1,
                    seeded.then(test_seed),
                )
                .unwrap();
            });
            assert!(result.is_err());
        }
    }

    /// Checks whether too small modulus is insufficient.
    #[test]
    fn invalid_modulus() {
        for seeded in [false, true] {
            let result = std::panic::catch_unwind(|| {
                let _ = PolyOverZq::sample_discrete_gauss_optionally_seeded(
                    3,
                    1,
                    0,
                    1,
                    seeded.then(test_seed),
                )
                .unwrap();
            });
            assert!(result.is_err());
        }
    }

    /// 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_discrete_gauss_seeded(2, 17, 0, 1, [42; 32]).unwrap();
        let sample_1 = PolyOverZq::sample_discrete_gauss_seeded(2, 17, 0, 1, [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_discrete_gauss_seeded(2, 17, 0, 1, [42; 32]).unwrap();

        assert_eq!("1  1 mod 17", sample.to_string());
    }
}