qfall-math 0.1.1

// Copyright © 2023 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, Zq},
    rational::Q,
    utils::sample::discrete_gauss::{DiscreteGaussianIntegerSampler, LookupTableSetting, TAILCUT},
};

impl Zq {
    /// Chooses a [`Zq`] instance chosen according to the discrete Gaussian distribution
    /// in `[center - ⌈6 * s⌉ , center + ⌊ 6 * s⌋ ]`.
    ///
    /// This function samples discrete Gaussians according to the definition of
    /// SampleZ in [GPV08](https://citeseerx.ist.psu.edu/document?repid=rep1&type=pdf&doi=d9f54077d568784c786f7b1d030b00493eb3ae35).
    ///
    /// Parameters:
    /// - `modulus`: specifies the modulus of the new [`Zq`] element
    /// - `center`: specifies the position of the center with peak probability
    /// - `s`: specifies the Gaussian parameter, which is proportional
    ///   to the standard deviation `sigma * sqrt(2 * pi) = s`
    ///
    /// Returns new [`Zq`] sample chosen according to the specified discrete Gaussian
    /// distribution or a [`MathError`] if the specified parameters were not chosen
    /// appropriately, i.e. `s < 0`.
    ///
    /// # Examples
    /// ```
    /// use qfall_math::integer_mod_q::Zq;
    ///
    /// let sample = Zq::sample_discrete_gauss(17, 0, 1).unwrap();
    /// ```
    ///
    /// # Errors and Failures
    /// - Returns a [`MathError`] of type [`InvalidIntegerInput`](MathError::InvalidIntegerInput)
    ///   if `s < 0`.
    ///
    /// # Panics ...
    /// - if `modulus` is smaller than `2`.
    ///
    /// This function implements SampleZ according to:
    /// - \[1\] Gentry, Craig and Peikert, Chris and Vaikuntanathan, Vinod (2008).
    ///   Trapdoors for hard lattices and new cryptographic constructions.
    ///   In: Proceedings of the fortieth annual ACM symposium on Theory of computing.
    ///   <https://dl.acm.org/doi/pdf/10.1145/1374376.1374407>
    pub fn sample_discrete_gauss(
        modulus: impl Into<Modulus>,
        center: impl Into<Q>,
        s: impl Into<Q>,
    ) -> Result<Self, MathError> {
        let modulus: Modulus = modulus.into();
        let center: Q = center.into();
        let s: Q = s.into();

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

        let sample = dgis.sample_z();
        Ok(Zq::from((&sample, &modulus)))
    }
}

#[cfg(test)]
mod test_sample_discrete_gauss {
    use crate::{integer::Z, integer_mod_q::Zq, rational::Q};

    // Appropriate interval and invalid inputs were tested in
    // utils::sample::discrete_gauss::test_sample_z and are thus omitted here.

    /// 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() {
        let z = Z::from(2);
        let q = Q::from(2);

        let _ = Zq::sample_discrete_gauss(17u64, 7u8, 1u16);
        let _ = Zq::sample_discrete_gauss(17u16, 7u16, 1u8);
        let _ = Zq::sample_discrete_gauss(17u8, 7u32, 1u32);
        let _ = Zq::sample_discrete_gauss(17u32, 7u64, 1u64);
        let _ = Zq::sample_discrete_gauss(17i16, 7i8, 1i64);
        let _ = Zq::sample_discrete_gauss(17i8, 7i16, 1i32);
        let _ = Zq::sample_discrete_gauss(17i64, 7i32, 1i16);
        let _ = Zq::sample_discrete_gauss(17i32, 7i64, 1i8);
        let _ = Zq::sample_discrete_gauss(17, q.clone(), 1i64);
        let _ = Zq::sample_discrete_gauss(z.clone(), 0i8, z.clone());
        let _ = Zq::sample_discrete_gauss(17, z.clone(), q.clone());
        let _ = Zq::sample_discrete_gauss(17, 1f32, 1f64);
        let _ = Zq::sample_discrete_gauss(17, 1f64, 1f32);

        // With references
        let _ = Zq::sample_discrete_gauss(17i64, 7i32, 1i16);
        let _ = Zq::sample_discrete_gauss(17i32, 7i64, 1i8);
        let _ = Zq::sample_discrete_gauss(17, &q, 1i64);
        let _ = Zq::sample_discrete_gauss(&z, 0i8, &z);
        let _ = Zq::sample_discrete_gauss(17, &z, &q);
    }

    /// Roughly checks the collected samples are distributed
    /// according to the discrete Gaussian distribution.
    ///
    /// This test could possibly fail for a truly uniform distribution
    /// with probability smaller than 1/1000.
    #[test]
    fn distribution() {
        let mut counts = [0; 20];
        // count sampled instances
        for _ in 0..200 {
            let sample = Zq::sample_discrete_gauss(20, 0, 2).unwrap();
            let sample_int = i64::try_from(&sample.get_representative_least_nonnegative_residue())
                .unwrap() as usize;
            counts[sample_int] += 1;
        }

        let expl_text = String::from("This test can fail with probability close to 0. 
        It fails if the sampled occurrences do not look like a typical discrete Gaussian random distribution. 
        If this happens, rerun the tests several times and check whether this issue comes up again.");

        // Check that the sampled occurrences roughly look
        // like a discrete Gaussian distribution
        assert!(counts[0] > 70, "{expl_text}");
        assert!(counts[0] < 130, "{expl_text}");
        assert!(counts[19] > 20, "{expl_text}");
        assert!(counts[19] < 70, "{expl_text}");
        assert!(counts[1] > 20, "{expl_text}");
        assert!(counts[1] < 70, "{expl_text}");
        assert!(counts[18] < 20, "{expl_text}");
        assert!(counts[2] < 20, "{expl_text}");
        for count in counts.iter().take(18).skip(3) {
            assert!(count < &10, "{expl_text}");
        }
    }
}