qfall_math/integer/z/sample/
discrete_gauss.rs

1// Copyright © 2023 Niklas Siemer
2//
3// This file is part of qFALL-math.
4//
5// qFALL-math is free software: you can redistribute it and/or modify it under
6// the terms of the Mozilla Public License Version 2.0 as published by the
7// Mozilla Foundation. See <https://mozilla.org/en-US/MPL/2.0/>.
8
9//! This module contains algorithms for sampling according to the discrete Gaussian distribution.
10
11use crate::{
12    error::MathError,
13    integer::Z,
14    rational::Q,
15    utils::sample::discrete_gauss::{DiscreteGaussianIntegerSampler, LookupTableSetting, TAILCUT},
16};
17
18impl Z {
19    /// Chooses a [`Z`] instance according to the discrete Gaussian distribution
20    /// in `[center - ⌈6 * s⌉ , center + ⌊6 * s⌋ ]`.
21    ///
22    /// This function samples discrete Gaussians according to the definition of
23    /// SampleZ in [GPV08](https://citeseerx.ist.psu.edu/document?repid=rep1&type=pdf&doi=d9f54077d568784c786f7b1d030b00493eb3ae35).
24    ///
25    /// Parameters:
26    /// - `n`: specifies the range from which is sampled
27    /// - `center`: specifies the position of the center with peak probability
28    /// - `s`: specifies the Gaussian parameter, which is proportional
29    ///   to the standard deviation `sigma * sqrt(2 * pi) = s`
30    ///
31    /// Returns new [`Z`] sample chosen according to the specified discrete Gaussian
32    /// distribution or a [`MathError`] if the specified parameters were not chosen
33    /// appropriately, i.e. `s < 0`.
34    ///
35    /// # Examples
36    /// ```
37    /// use qfall_math::integer::Z;
38    ///
39    /// let sample = Z::sample_discrete_gauss(0, 1).unwrap();
40    /// ```
41    ///
42    /// # Errors and Failures
43    /// - Returns a [`MathError`] of type [`InvalidIntegerInput`](MathError::InvalidIntegerInput)
44    ///   if `s < 0`.
45    ///
46    /// This function implements SampleZ according to:
47    /// - \[1\] Gentry, Craig and Peikert, Chris and Vaikuntanathan, Vinod (2008).
48    ///   Trapdoors for hard lattices and new cryptographic constructions.
49    ///   In: Proceedings of the fortieth annual ACM symposium on Theory of computing.
50    ///   <https://dl.acm.org/doi/pdf/10.1145/1374376.1374407>
51    pub fn sample_discrete_gauss(center: impl Into<Q>, s: impl Into<Q>) -> Result<Self, MathError> {
52        let center: Q = center.into();
53        let s: Q = s.into();
54
55        let mut dgis = DiscreteGaussianIntegerSampler::init(
56            &center,
57            &s,
58            unsafe { TAILCUT },
59            LookupTableSetting::NoLookup,
60        )?;
61
62        Ok(dgis.sample_z())
63    }
64}
65
66#[cfg(test)]
67mod test_sample_discrete_gauss {
68    use crate::{integer::Z, rational::Q};
69
70    // Appropriate interval and invalid inputs were tested in
71    // utils::sample::discrete_gauss::test_sample_z and are thus omitted here.
72
73    /// Checks whether `sample_discrete_gauss` is available for all types
74    /// implementing [`Into<Z>`], i.e. u8, u16, u32, u64, i8, ...
75    /// or [`Into<Q>`], i.e. u8, i16, f32, Z, Q, ...
76    #[test]
77    fn availability() {
78        let z = Z::from(2);
79        let q = Q::from(2);
80
81        let _ = Z::sample_discrete_gauss(7u8, 1u16);
82        let _ = Z::sample_discrete_gauss(7u16, 1u8);
83        let _ = Z::sample_discrete_gauss(7u32, 1u32);
84        let _ = Z::sample_discrete_gauss(7u64, 1u64);
85        let _ = Z::sample_discrete_gauss(7i8, 1i64);
86        let _ = Z::sample_discrete_gauss(7i16, 1i32);
87        let _ = Z::sample_discrete_gauss(7i32, 1i16);
88        let _ = Z::sample_discrete_gauss(7i64, 1i8);
89        let _ = Z::sample_discrete_gauss(&q, 1i64);
90        let _ = Z::sample_discrete_gauss(0i8, &z);
91        let _ = Z::sample_discrete_gauss(&z, &q);
92        let _ = Z::sample_discrete_gauss(1f32, 1f64);
93        let _ = Z::sample_discrete_gauss(1f64, 1f32);
94    }
95
96    /// Roughly checks the collected samples are distributed
97    /// according to the discrete Gaussian distribution.
98    ///
99    /// This test could possibly fail for a truly uniform distribution
100    /// with probability smaller than 1/1000.
101    #[test]
102    fn distribution() {
103        let mut counts = [0; 20];
104        // count sampled instances
105        for _ in 0..200 {
106            let sample = Z::sample_discrete_gauss(10, 2).unwrap();
107            let sample_int = i64::try_from(&sample).unwrap() as usize;
108            counts[sample_int] += 1;
109        }
110
111        let expl_text = String::from("This test can fail with probability close to 0. 
112        It fails if the sampled occurrences do not look like a typical discrete Gaussian random distribution. 
113        If this happens, rerun the tests several times and check whether this issue comes up again.");
114
115        // Check that the sampled occurrences roughly look
116        // like a discrete Gaussian distribution
117        assert!(counts[10] > 70, "{expl_text}");
118        assert!(counts[10] < 130, "{expl_text}");
119        assert!(counts[9] > 20, "{expl_text}");
120        assert!(counts[9] < 70, "{expl_text}");
121        assert!(counts[11] > 20, "{expl_text}");
122        assert!(counts[11] < 70, "{expl_text}");
123        assert!(counts[8] < 20, "{expl_text}");
124        assert!(counts[12] < 20, "{expl_text}");
125        for count in counts.iter().take(8) {
126            assert!(count < &10, "{expl_text}");
127        }
128        for count in counts.iter().skip(13) {
129            assert!(count < &10, "{expl_text}");
130        }
131    }
132}
qfall_math/integer/z/sample/discrete_gauss.rs

qfall_math/integer/z/sample/
discrete_gauss.rs
