qfall_math/integer_mod_q/z_q/

get.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/>.

//! Get elements of [`Zq`] like its [`Z`] value and [`Modulus`].

use crate::{
    integer::Z,
    integer_mod_q::{Modulus, Zq},
};

impl Zq {
    /// Returns the [`Z`] value of the [`Zq`] element.
    ///
    /// The representation in the range `[0, modulus)` is returned.
    /// Use [`Zq::get_representative_least_absolute_residue`] if they should be
    /// in the range `(-⌈modulus/2⌉, ⌊modulus/2⌋]`.
    ///
    /// # Examples
    /// ```
    /// use qfall_math::integer_mod_q::Zq;
    /// use qfall_math::integer::Z;
    /// let zq_value = Zq::from((4, 7));
    ///
    /// let z_value = zq_value.get_representative_least_nonnegative_residue();
    ///
    /// assert_eq!(Z::from(4), z_value);
    /// ```
    pub fn get_representative_least_nonnegative_residue(&self) -> Z {
        self.value.clone()
    }

    /// Returns the [`Z`] value of the [`Zq`] element with the representatives close to `0`.
    ///
    /// The output value is in the range `(-⌈modulus/2⌉, ⌊modulus/2⌋]`,
    /// i.e. `[-(modulus-1)/2, (modulus-1)/2]` for odd moduli and `(-modulus/2, modulus/2]` for even moduli.
    /// Hence, the positive representative is chosen for the element `modulus/2` of even moduli.
    /// Use [`Zq::get_representative_least_nonnegative_residue`] if they should be
    /// in the range `[0, modulus)`.
    ///
    /// # Examples
    /// ```
    /// use qfall_math::integer_mod_q::Zq;
    /// use qfall_math::integer::Z;
    /// let zq_value = Zq::from((5, 7));
    ///
    /// let z_value = zq_value.get_representative_least_absolute_residue();
    ///
    /// assert_eq!(Z::from(-2), z_value);
    /// ```
    pub fn get_representative_least_absolute_residue(&self) -> Z {
        let mod_z = Z::from(&self.modulus);
        let mod_half = mod_z.div_floor(2);
        if self.value > mod_half {
            &self.value - mod_z
        } else {
            self.value.clone()
        }
    }

    /// Returns the [`Modulus`] of the [`Zq`] element.
    ///
    /// # Examples
    /// ```
    /// use qfall_math::integer_mod_q::{Zq, Modulus};
    /// use std::str::FromStr;
    /// let value = Zq::from((4, 7));
    /// let cmp = Modulus::from(7);
    ///
    /// let modulus = value.get_mod();
    ///
    /// assert_eq!(cmp, modulus);
    /// ```
    pub fn get_mod(&self) -> Modulus {
        self.modulus.clone()
    }
}

#[cfg(test)]
mod test_get_representative_least_nonnegative_residue {
    use super::{Z, Zq};

    /// Check whether `get_representative_least_nonnegative_residue` outputs the correct value for small values
    #[test]
    fn get_small() {
        let value_0 = Zq::from((2, 20));
        let value_1 = Zq::from((-2, 20));

        let res_0 = value_0.get_representative_least_nonnegative_residue();
        let res_1 = value_1.get_representative_least_nonnegative_residue();

        assert_eq!(res_0, Z::from(2));
        assert_eq!(res_1, Z::from(18));
    }

    /// Check whether `get_representative_least_nonnegative_residue` outputs the correct value for large values
    #[test]
    fn get_large() {
        let value_0 = Zq::from((i64::MAX, u64::MAX));
        let value_1 = Zq::from((i64::MIN, u64::MAX));

        let res_0 = value_0.get_representative_least_nonnegative_residue();
        let res_1 = value_1.get_representative_least_nonnegative_residue();

        assert_eq!(res_0, Z::from(i64::MAX));
        assert_eq!(res_1, Z::from(i64::MAX));
    }
}

#[cfg(test)]
mod test_get_representative_least_absolute_residue {
    use super::{Z, Zq};

    /// Check whether `get_representative_least_absolute_residue` outputs the correct value for small values
    #[test]
    fn get_small() {
        let value_0 = Zq::from((2, 20));
        let value_1 = Zq::from((-2, 20));

        let res_0 = value_0.get_representative_least_absolute_residue();
        let res_1 = value_1.get_representative_least_absolute_residue();

        assert_eq!(res_0, Z::from(2));
        assert_eq!(res_1, Z::from(-2));
    }

    /// Check whether `get_representative_least_absolute_residue` outputs the correct value for large values
    #[test]
    fn get_large() {
        let value_0 = Zq::from((i64::MAX, u64::MAX));
        let value_1 = Zq::from((u64::MAX - 1, u64::MAX));

        let res_0 = value_0.get_representative_least_absolute_residue();
        let res_1 = value_1.get_representative_least_absolute_residue();

        assert_eq!(res_0, Z::from(i64::MAX));
        assert_eq!(res_1, Z::from(-1));
    }

    /// Check whether `get_representative_least_absolute_residue` outputs the correct value for special cases
    #[test]
    fn get_special() {
        let value_0 = Zq::from((10, 20));
        let value_1 = Zq::from((0, 20));
        let value_2 = Zq::from((11, 21));

        let res_0 = value_0.get_representative_least_absolute_residue();
        let res_1 = value_1.get_representative_least_absolute_residue();
        let res_2 = value_2.get_representative_least_absolute_residue();

        assert_eq!(res_0, Z::from(10));
        assert_eq!(res_1, Z::from(0));
        assert_eq!(res_2, Z::from(-10));
    }

    /// Checks whether an element of the upper half is mapped to its negative representative,
    /// i.e. `256 mod 257` to `-1`.
    #[test]
    fn upper_half_negative() {
        let value = Zq::from((256, 257));

        let res = value.get_representative_least_absolute_residue();

        assert_eq!(Z::MINUS_ONE, res);
    }

    /// Checks whether every element is mapped into `(-⌈modulus/2⌉, ⌊modulus/2⌋]`
    /// according to `mod±` as defined in FIPS 204 for an odd and an even modulus.
    #[test]
    fn full_range() {
        for modulus in [256, 257] {
            for value in 0..modulus {
                let expected = if value > modulus / 2 {
                    value - modulus
                } else {
                    value
                };

                let res = Zq::from((value, modulus)).get_representative_least_absolute_residue();

                assert_eq!(Z::from(expected), res);
            }
        }
    }
}

#[cfg(test)]
mod test_get_mod {
    use super::{Modulus, Zq};

    /// Check whether `get_mod` outputs the correct modulus for small moduli
    #[test]
    fn get_small() {
        let value = Zq::from((2, 20));

        let modulus = value.get_mod();

        assert_eq!(modulus, Modulus::from(20));
    }

    /// Check whether `get_mod` outputs the correct modulus for large moduli
    #[test]
    fn get_large() {
        let value = Zq::from((2, u64::MAX));

        let modulus = value.get_mod();

        assert_eq!(modulus, Modulus::from(u64::MAX));
    }
}