fhe-study/arithmetic/src/ringq.rs
arithmetic/src/ringq.rsRaw
1//! Polynomial ring Z_q[X]/(X^N+1)
2//!
3
4use rand::{distributions::Distribution, Rng};
5use std::array;
6use std::fmt;
7use std::ops;
8
9use crate::ntt::NTT;
10use crate::zq::{modulus_u64, Zq};
11use anyhow::{anyhow, Result};
12
13/// PolynomialRing element, where the PolynomialRing is R = Z_q[X]/(X^n +1)
14/// The implementation assumes that q is prime.
15#[derive(Clone, Copy)]
16pub struct Rq<const Q: u64, const N: usize> {
17 pub(crate) coeffs: [Zq<Q>; N],
18
19 // evals are set when doig a PRxPR multiplication, so it can be reused in future
20 // multiplications avoiding recomputing it
21 pub(crate) evals: Option<[Zq<Q>; N]>,
22}
23
24// TODO define a trait "PolynomialRingTrait" or similar, so that when other structs use it can just
25// use the trait and not need to add '<Q, N>' to their params
26
27impl<const Q: u64, const N: usize> From<crate::ring::R<N>> for Rq<Q, N> {
28 fn from(r: crate::ring::R<N>) -> Self {
29 Self::from_vec(
30 r.coeffs()
31 .iter()
32 .map(|e| Zq::<Q>::from_f64(*e as f64))
33 .collect(),
34 )
35 }
36}
37
38// apply mod (X^N+1)
39pub fn modulus<const Q: u64, const N: usize>(p: &mut Vec<Zq<Q>>) {
40 if p.len() < N {
41 return;
42 }
43 for i in N..p.len() {
44 p[i - N] = p[i - N].clone() - p[i].clone();
45 p[i] = Zq(0);
46 }
47 p.truncate(N);
48}
49
50// PR stands for PolynomialRing
51impl<const Q: u64, const N: usize> Rq<Q, N> {
52 pub fn coeffs(&self) -> [Zq<Q>; N] {
53 self.coeffs
54 }
55 pub fn to_r(self) -> crate::R<N> {
56 crate::R::<N>::from(self)
57 }
58
59 pub fn from_vec(coeffs: Vec<Zq<Q>>) -> Self {
60 let mut p = coeffs;
61 modulus::<Q, N>(&mut p);
62 let coeffs = array::from_fn(|i| p[i]);
63 Self {
64 coeffs,
65 evals: None,
66 }
67 }
68 // this method is mostly for tests
69 pub fn from_vec_u64(coeffs: Vec<u64>) -> Self {
70 let coeffs_mod_q = coeffs.iter().map(|c| Zq::from_u64(*c)).collect();
71 Self::from_vec(coeffs_mod_q)
72 }
73 pub fn from_vec_f64(coeffs: Vec<f64>) -> Self {
74 let coeffs_mod_q = coeffs.iter().map(|c| Zq::from_f64(*c)).collect();
75 Self::from_vec(coeffs_mod_q)
76 }
77 pub fn from_vec_i64(coeffs: Vec<i64>) -> Self {
78 let coeffs_mod_q = coeffs.iter().map(|c| Zq::from_f64(*c as f64)).collect();
79 Self::from_vec(coeffs_mod_q)
80 }
81 pub fn new(coeffs: [Zq<Q>; N], evals: Option<[Zq<Q>; N]>) -> Self {
82 Self { coeffs, evals }
83 }
84
85 pub fn rand_abs(mut rng: impl Rng, dist: impl Distribution<f64>) -> Result<Self> {
86 let coeffs: [Zq<Q>; N] = array::from_fn(|_| Zq::from_f64(dist.sample(&mut rng).abs()));
87 Ok(Self {
88 coeffs,
89 evals: None,
90 })
91 }
92 pub fn rand_f64_abs(mut rng: impl Rng, dist: impl Distribution<f64>) -> Result<Self> {
93 let coeffs: [Zq<Q>; N] = array::from_fn(|_| Zq::from_f64(dist.sample(&mut rng).abs()));
94 Ok(Self {
95 coeffs,
96 evals: None,
97 })
98 }
99 pub fn rand_f64(mut rng: impl Rng, dist: impl Distribution<f64>) -> Result<Self> {
100 let coeffs: [Zq<Q>; N] = array::from_fn(|_| Zq::from_f64(dist.sample(&mut rng)));
101 Ok(Self {
102 coeffs,
103 evals: None,
104 })
105 }
106 pub fn rand_u64(mut rng: impl Rng, dist: impl Distribution<u64>) -> Result<Self> {
107 let coeffs: [Zq<Q>; N] = array::from_fn(|_| Zq::from_u64(dist.sample(&mut rng)));
108 Ok(Self {
109 coeffs,
110 evals: None,
111 })
112 }
113 // WIP. returns random v \in {0,1}. // TODO {-1, 0, 1}
114 pub fn rand_bin(mut rng: impl Rng, dist: impl Distribution<bool>) -> Result<Self> {
115 let coeffs: [Zq<Q>; N] = array::from_fn(|_| Zq::from_bool(dist.sample(&mut rng)));
116 Ok(Rq {
117 coeffs,
118 evals: None,
119 })
120 }
121 // Warning: this method will behave differently depending on the values P and Q:
122 // if Q<P, it just 'renames' the modulus parameter to P
123 // if Q>=P, it crops to mod P
124 pub fn remodule<const P: u64>(&self) -> Rq<P, N> {
125 Rq::<P, N>::from_vec_u64(self.coeffs().iter().map(|m_i| m_i.0).collect())
126 }
127 // applies mod(T) to all coefficients of self
128 pub fn coeffs_mod<const T: u64>(&self) -> Self {
129 Rq::<Q, N>::from_vec_u64(
130 self.coeffs()
131 .iter()
132 .map(|m_i| modulus_u64::<T>(m_i.0))
133 .collect(),
134 )
135 }
136
137 // TODO review if needed, or if with this interface
138 pub fn mul_by_matrix(&self, m: &Vec<Vec<Zq<Q>>>) -> Result<Vec<Zq<Q>>> {
139 matrix_vec_product(m, &self.coeffs.to_vec())
140 }
141 pub fn mul_by_zq(&self, s: &Zq<Q>) -> Self {
142 Self {
143 coeffs: array::from_fn(|i| self.coeffs[i] * *s),
144 evals: None,
145 }
146 }
147 pub fn mul_by_u64(&self, s: u64) -> Self {
148 let s = Zq::from_u64(s);
149 Self {
150 coeffs: array::from_fn(|i| self.coeffs[i] * s),
151 // coeffs: self.coeffs.iter().map(|&e| e * s).collect(),
152 evals: None,
153 }
154 }
155 pub fn mul_by_f64(&self, s: f64) -> Self {
156 Self {
157 coeffs: array::from_fn(|i| Zq::from_f64(self.coeffs[i].0 as f64 * s)),
158 evals: None,
159 }
160 }
161
162 pub fn mul(&mut self, rhs: &mut Self) -> Self {
163 mul_mut(self, rhs)
164 }
165 // divides by the given scalar 's' and rounds, returning a Rq<Q,N>
166 // TODO rm
167 pub fn div_round(&self, s: u64) -> Self {
168 let r: Vec<f64> = self
169 .coeffs()
170 .iter()
171 .map(|e| (e.0 as f64 / s as f64).round())
172 .collect();
173 Rq::<Q, N>::from_vec_f64(r)
174 }
175 // returns [ [(num/den) * self].round() ] mod q
176 // ie. performs the multiplication and division over f64, and then it rounds the
177 // result, only applying the mod Q at the end
178 pub fn mul_div_round(&self, num: u64, den: u64) -> Self {
179 let r: Vec<f64> = self
180 .coeffs()
181 .iter()
182 .map(|e| ((num as f64 * e.0 as f64) / den as f64).round())
183 .collect();
184 Rq::<Q, N>::from_vec_f64(r)
185 }
186
187 fn fmt(&self, f: &mut fmt::Formatter) -> fmt::Result {
188 // TODO simplify
189 let mut str = "";
190 let mut zero = true;
191 for (i, coeff) in self.coeffs.iter().enumerate().rev() {
192 if coeff.0 == 0 {
193 continue;
194 }
195 zero = false;
196 f.write_str(str)?;
197 if coeff.0 != 1 {
198 f.write_str(coeff.0.to_string().as_str())?;
199 if i > 0 {
200 f.write_str("*")?;
201 }
202 }
203 if coeff.0 == 1 && i == 0 {
204 f.write_str(coeff.0.to_string().as_str())?;
205 }
206 if i == 1 {
207 f.write_str("x")?;
208 } else if i > 1 {
209 f.write_str("x^")?;
210 f.write_str(i.to_string().as_str())?;
211 }
212 str = " + ";
213 }
214 if zero {
215 f.write_str("0")?;
216 }
217
218 f.write_str(" mod Z_")?;
219 f.write_str(Q.to_string().as_str())?;
220 f.write_str("/(X^")?;
221 f.write_str(N.to_string().as_str())?;
222 f.write_str("+1)")?;
223 Ok(())
224 }
225
226 pub fn infinity_norm(&self) -> u64 {
227 self.coeffs().iter().map(|x| x.0).fold(0, |a, b| a.max(b))
228 }
229}
230pub fn matrix_vec_product<const Q: u64>(m: &Vec<Vec<Zq<Q>>>, v: &Vec<Zq<Q>>) -> Result<Vec<Zq<Q>>> {
231 // assert_eq!(m.len(), m[0].len()); // TODO change to returning err
232 // assert_eq!(m.len(), v.len());
233 if m.len() != m[0].len() {
234 return Err(anyhow!("expected 'm' to be a square matrix"));
235 }
236 if m.len() != v.len() {
237 return Err(anyhow!(
238 "m.len: {} should be equal to v.len(): {}",
239 m.len(),
240 v.len(),
241 ));
242 }
243
244 Ok(m.iter()
245 .map(|row| {
246 row.iter()
247 .zip(v.iter())
248 .map(|(&row_i, &v_i)| row_i * v_i)
249 .sum()
250 })
251 .collect::<Vec<Zq<Q>>>())
252}
253pub fn transpose<const Q: u64>(m: &[Vec<Zq<Q>>]) -> Vec<Vec<Zq<Q>>> {
254 // TODO case when m[0].len()=0
255 // TODO non square matrix
256 let mut r: Vec<Vec<Zq<Q>>> = vec![vec![Zq(0); m[0].len()]; m.len()];
257 for (i, m_row) in m.iter().enumerate() {
258 for (j, m_ij) in m_row.iter().enumerate() {
259 r[j][i] = *m_ij;
260 }
261 }
262 r
263}
264
265impl<const Q: u64, const N: usize> PartialEq for Rq<Q, N> {
266 fn eq(&self, other: &Self) -> bool {
267 self.coeffs == other.coeffs
268 }
269}
270impl<const Q: u64, const N: usize> ops::Add<Rq<Q, N>> for Rq<Q, N> {
271 type Output = Self;
272
273 fn add(self, rhs: Self) -> Self {
274 Self {
275 coeffs: array::from_fn(|i| self.coeffs[i] + rhs.coeffs[i]),
276 evals: None,
277 }
278 // Self {
279 // coeffs: self
280 // .coeffs
281 // .iter()
282 // .zip(rhs.coeffs)
283 // .map(|(a, b)| *a + b)
284 // .collect(),
285 // evals: None,
286 // }
287 // Self(r.iter_mut().map(|e| e.r#mod()).collect()) // TODO mod should happen auto in +
288 }
289}
290impl<const Q: u64, const N: usize> ops::Add<&Rq<Q, N>> for &Rq<Q, N> {
291 type Output = Rq<Q, N>;
292
293 fn add(self, rhs: &Rq<Q, N>) -> Self::Output {
294 Rq {
295 coeffs: array::from_fn(|i| self.coeffs[i] + rhs.coeffs[i]),
296 evals: None,
297 }
298 }
299}
300impl<const Q: u64, const N: usize> ops::Sub<Rq<Q, N>> for Rq<Q, N> {
301 type Output = Self;
302
303 fn sub(self, rhs: Self) -> Self {
304 Self {
305 coeffs: array::from_fn(|i| self.coeffs[i] - rhs.coeffs[i]),
306 evals: None,
307 }
308 }
309}
310impl<const Q: u64, const N: usize> ops::Sub<&Rq<Q, N>> for &Rq<Q, N> {
311 type Output = Rq<Q, N>;
312
313 fn sub(self, rhs: &Rq<Q, N>) -> Self::Output {
314 Rq {
315 coeffs: array::from_fn(|i| self.coeffs[i] - rhs.coeffs[i]),
316 evals: None,
317 }
318 }
319}
320impl<const Q: u64, const N: usize> ops::Mul<Rq<Q, N>> for Rq<Q, N> {
321 type Output = Self;
322
323 fn mul(self, rhs: Self) -> Self {
324 mul(&self, &rhs)
325 }
326}
327impl<const Q: u64, const N: usize> ops::Mul<&Rq<Q, N>> for &Rq<Q, N> {
328 type Output = Rq<Q, N>;
329
330 fn mul(self, rhs: &Rq<Q, N>) -> Self::Output {
331 mul(self, rhs)
332 }
333}
334
335// mul by Zq element
336impl<const Q: u64, const N: usize> ops::Mul<Zq<Q>> for Rq<Q, N> {
337 type Output = Self;
338
339 fn mul(self, s: Zq<Q>) -> Self {
340 self.mul_by_zq(&s)
341 }
342}
343impl<const Q: u64, const N: usize> ops::Mul<&Zq<Q>> for &Rq<Q, N> {
344 type Output = Rq<Q, N>;
345
346 fn mul(self, s: &Zq<Q>) -> Self::Output {
347 self.mul_by_zq(s)
348 }
349}
350// mul by u64
351impl<const Q: u64, const N: usize> ops::Mul<u64> for Rq<Q, N> {
352 type Output = Self;
353
354 fn mul(self, s: u64) -> Self {
355 self.mul_by_u64(s)
356 }
357}
358impl<const Q: u64, const N: usize> ops::Mul<&u64> for &Rq<Q, N> {
359 type Output = Rq<Q, N>;
360
361 fn mul(self, s: &u64) -> Self::Output {
362 self.mul_by_u64(*s)
363 }
364}
365
366impl<const Q: u64, const N: usize> ops::Neg for Rq<Q, N> {
367 type Output = Self;
368
369 fn neg(self) -> Self::Output {
370 Self {
371 coeffs: array::from_fn(|i| -self.coeffs[i]),
372 evals: None,
373 }
374 }
375}
376
377fn mul_mut<const Q: u64, const N: usize>(lhs: &mut Rq<Q, N>, rhs: &mut Rq<Q, N>) -> Rq<Q, N> {
378 // reuse evaluations if already computed
379 if !lhs.evals.is_some() {
380 lhs.evals = Some(NTT::<Q, N>::ntt(lhs.coeffs));
381 };
382 if !rhs.evals.is_some() {
383 rhs.evals = Some(NTT::<Q, N>::ntt(rhs.coeffs));
384 };
385 let lhs_evals = lhs.evals.unwrap();
386 let rhs_evals = rhs.evals.unwrap();
387
388 let c_ntt: [Zq<Q>; N] = array::from_fn(|i| lhs_evals[i] * rhs_evals[i]);
389 let c = NTT::<Q, { N }>::intt(c_ntt);
390 Rq::new(c, Some(c_ntt))
391}
392fn mul<const Q: u64, const N: usize>(lhs: &Rq<Q, N>, rhs: &Rq<Q, N>) -> Rq<Q, N> {
393 // reuse evaluations if already computed
394 let lhs_evals = if lhs.evals.is_some() {
395 lhs.evals.unwrap()
396 } else {
397 NTT::<Q, N>::ntt(lhs.coeffs)
398 };
399 let rhs_evals = if rhs.evals.is_some() {
400 rhs.evals.unwrap()
401 } else {
402 NTT::<Q, N>::ntt(rhs.coeffs)
403 };
404
405 let c_ntt: [Zq<Q>; N] = array::from_fn(|i| lhs_evals[i] * rhs_evals[i]);
406 let c = NTT::<Q, { N }>::intt(c_ntt);
407 Rq::new(c, Some(c_ntt))
408}
409
410impl<const Q: u64, const N: usize> fmt::Display for Rq<Q, N> {
411 fn fmt(&self, f: &mut fmt::Formatter) -> fmt::Result {
412 self.fmt(f)?;
413 Ok(())
414 }
415}
416impl<const Q: u64, const N: usize> fmt::Debug for Rq<Q, N> {
417 fn fmt(&self, f: &mut fmt::Formatter) -> fmt::Result {
418 self.fmt(f)?;
419 Ok(())
420 }
421}
422
423#[cfg(test)]
424mod tests {
425 use super::*;
426
427 #[test]
428 fn poly_ring() {
429 // the test values used are generated with SageMath
430 const Q: u64 = 7;
431 const N: usize = 3;
432
433 // p = 1x + 2x^2 + 3x^3 + 4 x^4 + 5 x^5 in R=Z_q[X]/(X^n +1)
434 let p = Rq::<Q, N>::from_vec_u64(vec![0u64, 1, 2, 3, 4, 5]);
435 assert_eq!(p.to_string(), "4*x^2 + 4*x + 4 mod Z_7/(X^3+1)");
436
437 // try with coefficients bigger than Q
438 let p = Rq::<Q, N>::from_vec_u64(vec![0u64, 1, Q + 2, 3, 4, 5]);
439 assert_eq!(p.to_string(), "4*x^2 + 4*x + 4 mod Z_7/(X^3+1)");
440
441 // try with other ring
442 let p = Rq::<7, 4>::from_vec_u64(vec![0u64, 1, 2, 3, 4, 5]);
443 assert_eq!(p.to_string(), "3*x^3 + 2*x^2 + 3*x + 3 mod Z_7/(X^4+1)");
444
445 let p = Rq::<Q, N>::from_vec_u64(vec![0u64, 0, 0, 0, 4, 5]);
446 assert_eq!(p.to_string(), "2*x^2 + 3*x mod Z_7/(X^3+1)");
447
448 let p = Rq::<Q, N>::from_vec_u64(vec![5u64, 4, 5, 2, 1, 0]);
449 assert_eq!(p.to_string(), "5*x^2 + 3*x + 3 mod Z_7/(X^3+1)");
450
451 let a = Rq::<Q, N>::from_vec_u64(vec![0u64, 1, 2, 3, 4, 5]);
452 assert_eq!(a.to_string(), "4*x^2 + 4*x + 4 mod Z_7/(X^3+1)");
453
454 let b = Rq::<Q, N>::from_vec_u64(vec![5u64, 4, 3, 2, 1, 0]);
455 assert_eq!(b.to_string(), "3*x^2 + 3*x + 3 mod Z_7/(X^3+1)");
456
457 // add
458 assert_eq!((a.clone() + b.clone()).to_string(), "0 mod Z_7/(X^3+1)");
459 assert_eq!((&a + &b).to_string(), "0 mod Z_7/(X^3+1)");
460 // assert_eq!((a.0.clone() + b.0.clone()).to_string(), "[0, 0, 0]"); // TODO
461
462 // sub
463 assert_eq!(
464 (a.clone() - b.clone()).to_string(),
465 "x^2 + x + 1 mod Z_7/(X^3+1)"
466 );
467 }
468
469 fn test_mul_opt<const Q: u64, const N: usize>(
470 a: [u64; N],
471 b: [u64; N],
472 expected_c: [u64; N],
473 ) -> Result<()> {
474 let a: [Zq<Q>; N] = array::from_fn(|i| Zq::from_u64(a[i]));
475 let mut a = Rq::new(a, None);
476 let b: [Zq<Q>; N] = array::from_fn(|i| Zq::from_u64(b[i]));
477 let mut b = Rq::new(b, None);
478 let expected_c: [Zq<Q>; N] = array::from_fn(|i| Zq::from_u64(expected_c[i]));
479 let expected_c = Rq::new(expected_c, None);
480
481 let c = mul_mut(&mut a, &mut b);
482 assert_eq!(c, expected_c);
483 Ok(())
484 }
485 #[test]
486 fn test_mul() -> Result<()> {
487 const Q: u64 = 2u64.pow(16) + 1;
488 const N: usize = 4;
489
490 let a: [u64; N] = [1u64, 2, 3, 4];
491 let b: [u64; N] = [1u64, 2, 3, 4];
492 let c: [u64; N] = [65513, 65517, 65531, 20];
493 test_mul_opt::<Q, N>(a, b, c)?;
494
495 let a: [u64; N] = [0u64, 0, 0, 2];
496 let b: [u64; N] = [0u64, 0, 0, 2];
497 let c: [u64; N] = [0u64, 0, 65533, 0];
498 test_mul_opt::<Q, N>(a, b, c)?;
499
500 // TODO more testvectors
501
502 Ok(())
503 }
504}