qfall-math 0.2.1

// 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::{PolyOverZ, Z},
    integer_mod_q::{ModulusPolynomialRingZq, PolynomialRingZq},
    macros::seeded::seedable_function,
    rational::Q,
};

impl PolynomialRingZq {
    seedable_function!(
        /// Generates a [`PolynomialRingZq`] instance of maximum degree `modulus.get_degree() - 1` and
        /// coefficients chosen according to the binomial distribution
        /// parameterized by `n` and `p`.
        ///
        /// Parameters:
        /// - `modulus`: specifies the [`ModulusPolynomialRingZq`] over which the
        ///   ring of polynomials modulo `modulus.get_q()` is defined
        /// - `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 [`PolynomialRingZq`] instance of length `modulus.get_degree() - 1`
        /// with coefficients chosen according to the binomial distribution or a [`MathError`]
        /// if `n < 0`, `p ∉ (0,1)`, `n` does not fit into an [`i64`].
        ///
        /// # Examples
        /// ```
        /// use qfall_math::integer_mod_q::{PolynomialRingZq, ModulusPolynomialRingZq};
        /// use std::str::FromStr;
        /// let modulus = ModulusPolynomialRingZq::from_str("3  1 2 1 mod 17").unwrap();
        ///
        #[unseeded]
        /// let sample = PolynomialRingZq::sample_binomial(&modulus, 2, 0.5).unwrap();
        #[seeded]
        /// let sample = PolynomialRingZq::sample_binomial_seeded(&modulus, 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`].
        ///
        /// # Panics ...
        /// - if the provided [`ModulusPolynomialRingZq`] has degree `0` or smaller.
        pub(crate) fn sample_binomial(
            modulus: &ModulusPolynomialRingZq,
            n: impl Into<Z>,
            p: impl Into<Q>,
            seed: Option<[u8; 32]>,
        ) -> Result<Self, MathError> {
            Self::sample_binomial_with_offset_optionally_seeded(modulus, 0, n, p, seed)
        }
    );

    seedable_function!(
        /// Generates a [`PolynomialRingZq`] instance of maximum degree `modulus.get_degree() - 1` and
        /// coefficients chosen according to the binomial distribution
        /// parameterized by `n` and `p` with given `offset`.
        ///
        /// Parameters:
        /// - `modulus`: specifies the [`ModulusPolynomialRingZq`] over which the
        ///   ring of polynomials modulo `modulus.get_q()` is defined
        /// - `offset`: specifies an offset applied to each sample
        ///   collected from the binomial distribution
        /// - `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 [`PolynomialRingZq`] instance of length `modulus.get_degree() - 1`
        /// with coefficients chosen according to the binomial distribution or a [`MathError`]
        /// if `n < 0`, `p ∉ (0,1)`, `n` does not fit into an [`i64`].
        ///
        /// # Examples
        /// ```
        /// use qfall_math::integer_mod_q::{PolynomialRingZq, ModulusPolynomialRingZq};
        /// use std::str::FromStr;
        /// let modulus = ModulusPolynomialRingZq::from_str("3  1 2 1 mod 17").unwrap();
        ///
        #[unseeded]
        /// let sample = PolynomialRingZq::sample_binomial_with_offset(&modulus, -1, 2, 0.5).unwrap();
        #[seeded]
        /// let sample = PolynomialRingZq::sample_binomial_with_offset_seeded(&modulus, -1, 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`].
        ///
        /// # Panics ...
        /// - if the provided [`ModulusPolynomialRingZq`] has degree `0` or smaller.
        pub(crate) fn sample_binomial_with_offset(
            modulus: &ModulusPolynomialRingZq,
            offset: impl Into<Z>,
            n: impl Into<Z>,
            p: impl Into<Q>,
            seed: Option<[u8; 32]>,
        ) -> Result<Self, MathError> {
            assert!(
                modulus.get_degree() > 0,
                "ModulusPolynomial of degree 0 is insufficient to sample over."
            );

            let poly_z = PolyOverZ::sample_binomial_with_offset_optionally_seeded(
                modulus.get_degree() - 1,
                offset,
                n,
                p,
                seed,
            )?;

            Ok(PolynomialRingZq {
                poly: poly_z,
                modulus: modulus.clone(),
            })
        }
    );
}

#[cfg(test)]
mod test_sample_binomial {
    use super::{PolynomialRingZq, Z};
    use crate::utils::sample::test_seed;
    use crate::{
        integer_mod_q::{ModulusPolynomialRingZq, PolyOverZq},
        traits::{GetCoefficient, SetCoefficient},
    };
    use std::str::FromStr;

    // 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] {
            let modulus = ModulusPolynomialRingZq::from_str("4  1 0 0 1 mod 17").unwrap();

            for _ in 0..8 {
                let poly = PolynomialRingZq::sample_binomial_optionally_seeded(
                    &modulus,
                    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 mut modulus = PolyOverZq::from((1, u64::MAX));
                modulus.set_coeff(degree, 1).unwrap();
                let modulus = ModulusPolynomialRingZq::from(&modulus);

                let res = PolynomialRingZq::sample_binomial_optionally_seeded(
                    &modulus,
                    256,
                    0.99999,
                    seeded.then(test_seed),
                )
                .unwrap();

                assert_eq!(
                    modulus.get_degree(),
                    res.get_degree() + 1,
                    "This test can fail with probability close to 0."
                );
            }
        }
    }

    /// Checks whether 0 modulus polynomial is insufficient.
    #[test]
    fn invalid_modulus() {
        for seeded in [false, true] {
            let result = std::panic::catch_unwind(|| {
                let modulus = ModulusPolynomialRingZq::from_str("1  1 mod 17").unwrap();

                let _ = PolynomialRingZq::sample_binomial_optionally_seeded(
                    &modulus,
                    2,
                    0.5,
                    seeded.then(test_seed),
                );
            });
            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::{ModulusPolynomialRingZq, PolynomialRingZq};
        use std::str::FromStr;
        let modulus = ModulusPolynomialRingZq::from_str("3  1 2 1 mod 17").unwrap();
        let sample_0 =
            PolynomialRingZq::sample_binomial_seeded(&modulus, 2, 0.5, [42; 32]).unwrap();
        let sample_1 =
            PolynomialRingZq::sample_binomial_seeded(&modulus, 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::{ModulusPolynomialRingZq, PolynomialRingZq};
        use std::str::FromStr;
        let modulus = ModulusPolynomialRingZq::from_str("3  1 2 1 mod 17").unwrap();
        let sample = PolynomialRingZq::sample_binomial_seeded(&modulus, 2, 0.5, [42; 32]).unwrap();

        assert_eq!("2  0 2 / 3  1 2 1 mod 17", sample.to_string());
    }

    /// Checks whether the unseeded and the seeded function are available.
    #[test]
    fn availability() {
        use crate::integer_mod_q::{ModulusPolynomialRingZq, PolynomialRingZq};
        use std::str::FromStr;
        let modulus = ModulusPolynomialRingZq::from_str("3  1 2 1 mod 17").unwrap();

        // explicitly checks the existence of the unseeded and the seeded function
        let _ = PolynomialRingZq::sample_binomial(&modulus, 2, 0.5);
        let _ = PolynomialRingZq::sample_binomial_seeded(&modulus, 2, 0.5, test_seed());
    }
}

#[cfg(test)]
mod test_sample_binomial_with_offset {
    use super::{PolynomialRingZq, Z};
    use crate::utils::sample::test_seed;
    use crate::{
        integer_mod_q::{ModulusPolynomialRingZq, PolyOverZq},
        traits::{GetCoefficient, SetCoefficient},
    };
    use std::str::FromStr;

    // 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] {
            let modulus = ModulusPolynomialRingZq::from_str("4  1 0 0 1 mod 17").unwrap();

            for _ in 0..8 {
                let poly = PolynomialRingZq::sample_binomial_with_offset_optionally_seeded(
                    &modulus,
                    -1,
                    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 mut modulus = PolyOverZq::from((1, u64::MAX));
                modulus.set_coeff(degree, 1).unwrap();
                let modulus = ModulusPolynomialRingZq::from(&modulus);

                let res = PolynomialRingZq::sample_binomial_with_offset_optionally_seeded(
                    &modulus,
                    1,
                    2,
                    0.5,
                    seeded.then(test_seed),
                )
                .unwrap();

                assert_eq!(modulus.get_degree(), res.get_degree() + 1);
            }
        }
    }

    /// Checks whether 0 modulus polynomial is insufficient.
    #[test]
    fn invalid_modulus() {
        for seeded in [false, true] {
            let result = std::panic::catch_unwind(|| {
                let modulus = ModulusPolynomialRingZq::from_str("1  1 mod 17").unwrap();

                let _ = PolynomialRingZq::sample_binomial_with_offset_optionally_seeded(
                    &modulus,
                    -1,
                    2,
                    0.5,
                    seeded.then(test_seed),
                );
            });
            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::{ModulusPolynomialRingZq, PolynomialRingZq};
        use std::str::FromStr;
        let modulus = ModulusPolynomialRingZq::from_str("3  1 2 1 mod 17").unwrap();
        let sample_0 =
            PolynomialRingZq::sample_binomial_with_offset_seeded(&modulus, -1, 2, 0.5, [42; 32])
                .unwrap();
        let sample_1 =
            PolynomialRingZq::sample_binomial_with_offset_seeded(&modulus, -1, 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::{ModulusPolynomialRingZq, PolynomialRingZq};
        use std::str::FromStr;
        let modulus = ModulusPolynomialRingZq::from_str("3  1 2 1 mod 17").unwrap();
        let sample =
            PolynomialRingZq::sample_binomial_with_offset_seeded(&modulus, -1, 2, 0.5, [42; 32])
                .unwrap();

        assert_eq!("2  -1 1 / 3  1 2 1 mod 17", sample.to_string());
    }

    /// Checks whether the unseeded and the seeded function are available.
    #[test]
    fn availability() {
        use crate::integer_mod_q::{ModulusPolynomialRingZq, PolynomialRingZq};
        use std::str::FromStr;
        let modulus = ModulusPolynomialRingZq::from_str("3  1 2 1 mod 17").unwrap();

        // explicitly checks the existence of the unseeded and the seeded function
        let _ = PolynomialRingZq::sample_binomial_with_offset(&modulus, -1, 2, 0.5);
        let _ =
            PolynomialRingZq::sample_binomial_with_offset_seeded(&modulus, -1, 2, 0.5, test_seed());
    }
}