phantom-zone/src/rgsw/mod.rs
src/rgsw/mod.rsRaw
1use itertools::{izip, Itertools};
2use num_traits::{PrimInt, Signed, ToPrimitive, Zero};
3use std::{
4 clone,
5 fmt::Debug,
6 iter,
7 marker::PhantomData,
8 ops::{Div, Neg, Sub},
9};
10
11use crate::{
12 backend::{ArithmeticOps, GetModulus, Modulus, VectorOps},
13 decomposer::{self, Decomposer, RlweDecomposer},
14 ntt::{self, Ntt, NttInit},
15 random::{
16 DefaultSecureRng, NewWithSeed, RandomElementInModulus, RandomFill,
17 RandomFillGaussianInModulus, RandomFillUniformInModulus,
18 },
19 utils::{fill_random_ternary_secret_with_hamming_weight, ToShoup, TryConvertFrom1, WithLocal},
20 Matrix, MatrixEntity, MatrixMut, Row, RowEntity, RowMut, Secret,
21};
22
23mod keygen;
24mod runtime;
25
26pub(crate) use keygen::*;
27pub(crate) use runtime::*;
28
29pub struct SeededAutoKey<M, S, Mod>
30where
31 M: Matrix,
32{
33 data: M,
34 seed: S,
35 modulus: Mod,
36}
37
38impl<M: Matrix + MatrixEntity, S, Mod: Modulus<Element = M::MatElement>> SeededAutoKey<M, S, Mod> {
39 fn empty<D: Decomposer>(ring_size: usize, auto_decomposer: &D, seed: S, modulus: Mod) -> Self {
40 SeededAutoKey {
41 data: M::zeros(auto_decomposer.decomposition_count(), ring_size),
42 seed,
43 modulus,
44 }
45 }
46}
47
48pub struct AutoKeyEvaluationDomain<M: Matrix, Mod, R, N> {
49 data: M,
50 _phantom: PhantomData<(R, N)>,
51 modulus: Mod,
52}
53
54impl<
55 M: MatrixMut + MatrixEntity,
56 Mod: Modulus<Element = M::MatElement> + Clone,
57 R: RandomFillUniformInModulus<[M::MatElement], Mod> + NewWithSeed,
58 N: NttInit<Mod> + Ntt<Element = M::MatElement>,
59 > From<&SeededAutoKey<M, R::Seed, Mod>> for AutoKeyEvaluationDomain<M, Mod, R, N>
60where
61 <M as Matrix>::R: RowMut,
62 M::MatElement: Copy,
63
64 R::Seed: Clone,
65{
66 fn from(value: &SeededAutoKey<M, R::Seed, Mod>) -> Self {
67 let (d, ring_size) = value.data.dimension();
68 let mut data = M::zeros(2 * d, ring_size);
69
70 // sample RLWE'_A(-s(X^k))
71 let mut p_rng = R::new_with_seed(value.seed.clone());
72 data.iter_rows_mut().take(d).for_each(|r| {
73 RandomFillUniformInModulus::random_fill(&mut p_rng, &value.modulus, r.as_mut());
74 });
75
76 // copy over RLWE'_B(-s(X^k))
77 izip!(data.iter_rows_mut().skip(d), value.data.iter_rows()).for_each(|(to_r, from_r)| {
78 to_r.as_mut().copy_from_slice(from_r.as_ref());
79 });
80
81 // send RLWE'(-s(X^k)) polynomials to evaluation domain
82 let ntt_op = N::new(&value.modulus, ring_size);
83 data.iter_rows_mut()
84 .for_each(|r| ntt_op.forward(r.as_mut()));
85
86 AutoKeyEvaluationDomain {
87 data,
88 _phantom: PhantomData,
89 modulus: value.modulus.clone(),
90 }
91 }
92}
93
94pub struct ShoupAutoKeyEvaluationDomain<M> {
95 data: M,
96}
97
98impl<M: Matrix + ToShoup<Modulus = M::MatElement>, Mod: Modulus<Element = M::MatElement>, R, N>
99 From<&AutoKeyEvaluationDomain<M, Mod, R, N>> for ShoupAutoKeyEvaluationDomain<M>
100{
101 fn from(value: &AutoKeyEvaluationDomain<M, Mod, R, N>) -> Self {
102 Self {
103 data: M::to_shoup(&value.data, value.modulus.q().unwrap()),
104 }
105 }
106}
107
108pub struct RgswCiphertext<M: Matrix, Mod> {
109 /// Rgsw ciphertext polynomials
110 pub(crate) data: M,
111 modulus: Mod,
112 /// Decomposition for RLWE part A
113 d_a: usize,
114 /// Decomposition for RLWE part B
115 d_b: usize,
116}
117
118impl<M: MatrixEntity, Mod: Modulus<Element = M::MatElement>> RgswCiphertext<M, Mod> {
119 pub(crate) fn empty<D: RlweDecomposer>(
120 ring_size: usize,
121 decomposer: &D,
122 modulus: Mod,
123 ) -> RgswCiphertext<M, Mod> {
124 RgswCiphertext {
125 data: M::zeros(
126 decomposer.a().decomposition_count() * 2 + decomposer.b().decomposition_count() * 2,
127 ring_size,
128 ),
129 d_a: decomposer.a().decomposition_count(),
130 d_b: decomposer.b().decomposition_count(),
131 modulus,
132 }
133 }
134}
135
136pub struct SeededRgswCiphertext<M, S, Mod>
137where
138 M: Matrix,
139{
140 pub(crate) data: M,
141 seed: S,
142 modulus: Mod,
143 /// Decomposition for RLWE part A
144 d_a: usize,
145 /// Decomposition for RLWE part B
146 d_b: usize,
147}
148
149impl<M: Matrix + MatrixEntity, S, Mod> SeededRgswCiphertext<M, S, Mod> {
150 pub(crate) fn empty<D: RlweDecomposer>(
151 ring_size: usize,
152 decomposer: &D,
153 seed: S,
154 modulus: Mod,
155 ) -> SeededRgswCiphertext<M, S, Mod> {
156 SeededRgswCiphertext {
157 data: M::zeros(
158 decomposer.a().decomposition_count() * 2 + decomposer.b().decomposition_count(),
159 ring_size,
160 ),
161 seed,
162 modulus,
163 d_a: decomposer.a().decomposition_count(),
164 d_b: decomposer.b().decomposition_count(),
165 }
166 }
167}
168
169impl<M: Debug + Matrix, S: Debug, Mod: Debug> Debug for SeededRgswCiphertext<M, S, Mod>
170where
171 M::MatElement: Debug,
172{
173 fn fmt(&self, f: &mut std::fmt::Formatter<'_>) -> std::fmt::Result {
174 f.debug_struct("SeededRgswCiphertext")
175 .field("data", &self.data)
176 .field("seed", &self.seed)
177 .field("modulus", &self.modulus)
178 .finish()
179 }
180}
181
182pub struct RgswCiphertextEvaluationDomain<M, Mod, R, N> {
183 pub(crate) data: M,
184 modulus: Mod,
185 _phantom: PhantomData<(R, N)>,
186}
187
188impl<
189 M: MatrixMut + MatrixEntity,
190 Mod: Modulus<Element = M::MatElement> + Clone,
191 R: NewWithSeed + RandomFillUniformInModulus<[M::MatElement], Mod>,
192 N: NttInit<Mod> + Ntt<Element = M::MatElement> + Debug,
193 > From<&SeededRgswCiphertext<M, R::Seed, Mod>> for RgswCiphertextEvaluationDomain<M, Mod, R, N>
194where
195 <M as Matrix>::R: RowMut,
196 M::MatElement: Copy,
197 R::Seed: Clone,
198 M: Debug,
199{
200 fn from(value: &SeededRgswCiphertext<M, R::Seed, Mod>) -> Self {
201 let mut data = M::zeros(value.d_a * 2 + value.d_b * 2, value.data.dimension().1);
202
203 // copy RLWE'(-sm)
204 izip!(
205 data.iter_rows_mut().take(value.d_a * 2),
206 value.data.iter_rows().take(value.d_a * 2)
207 )
208 .for_each(|(to_ri, from_ri)| {
209 to_ri.as_mut().copy_from_slice(from_ri.as_ref());
210 });
211
212 // sample A polynomials of RLWE'(m) - RLWE'A(m)
213 // TODO(Jay): Do we want to be generic over RandomGenerator used here? I think
214 // not.
215 let mut p_rng = R::new_with_seed(value.seed.clone());
216 izip!(data.iter_rows_mut().skip(value.d_a * 2).take(value.d_b * 1))
217 .for_each(|ri| p_rng.random_fill(&value.modulus, ri.as_mut()));
218
219 // RLWE'_B(m)
220 izip!(
221 data.iter_rows_mut().skip(value.d_a * 2 + value.d_b),
222 value.data.iter_rows().skip(value.d_a * 2)
223 )
224 .for_each(|(to_ri, from_ri)| {
225 to_ri.as_mut().copy_from_slice(from_ri.as_ref());
226 });
227
228 // Send polynomials to evaluation domain
229 let ring_size = data.dimension().1;
230 let nttop = N::new(&value.modulus, ring_size);
231 data.iter_rows_mut()
232 .for_each(|ri| nttop.forward(ri.as_mut()));
233
234 Self {
235 data: data,
236 modulus: value.modulus.clone(),
237 _phantom: PhantomData,
238 }
239 }
240}
241
242impl<
243 M: MatrixMut + MatrixEntity,
244 Mod: Modulus<Element = M::MatElement> + Clone,
245 R,
246 N: NttInit<Mod> + Ntt<Element = M::MatElement>,
247 > From<&RgswCiphertext<M, Mod>> for RgswCiphertextEvaluationDomain<M, Mod, R, N>
248where
249 <M as Matrix>::R: RowMut,
250 M::MatElement: Copy,
251 M: Debug,
252{
253 fn from(value: &RgswCiphertext<M, Mod>) -> Self {
254 let mut data = M::zeros(value.d_a * 2 + value.d_b * 2, value.data.dimension().1);
255
256 // copy RLWE'(-sm)
257 izip!(
258 data.iter_rows_mut().take(value.d_a * 2),
259 value.data.iter_rows().take(value.d_a * 2)
260 )
261 .for_each(|(to_ri, from_ri)| {
262 to_ri.as_mut().copy_from_slice(from_ri.as_ref());
263 });
264
265 // copy RLWE'(m)
266 izip!(
267 data.iter_rows_mut().skip(value.d_a * 2),
268 value.data.iter_rows().skip(value.d_a * 2)
269 )
270 .for_each(|(to_ri, from_ri)| {
271 to_ri.as_mut().copy_from_slice(from_ri.as_ref());
272 });
273
274 // Send polynomials to evaluation domain
275 let ring_size = data.dimension().1;
276 let nttop = N::new(&value.modulus, ring_size);
277 data.iter_rows_mut()
278 .for_each(|ri| nttop.forward(ri.as_mut()));
279
280 Self {
281 data: data,
282 modulus: value.modulus.clone(),
283 _phantom: PhantomData,
284 }
285 }
286}
287
288impl<M: Debug, Mod: Debug, R, N> Debug for RgswCiphertextEvaluationDomain<M, Mod, R, N> {
289 fn fmt(&self, f: &mut std::fmt::Formatter<'_>) -> std::fmt::Result {
290 f.debug_struct("RgswCiphertextEvaluationDomain")
291 .field("data", &self.data)
292 .field("modulus", &self.modulus)
293 .field("_phantom", &self._phantom)
294 .finish()
295 }
296}
297
298impl<M: Matrix, Mod, R, N> Matrix for RgswCiphertextEvaluationDomain<M, Mod, R, N> {
299 type MatElement = M::MatElement;
300 type R = M::R;
301
302 fn dimension(&self) -> (usize, usize) {
303 self.data.dimension()
304 }
305
306 fn fits(&self, row: usize, col: usize) -> bool {
307 self.data.fits(row, col)
308 }
309}
310
311impl<M: Matrix, Mod, R, N> AsRef<[M::R]> for RgswCiphertextEvaluationDomain<M, Mod, R, N> {
312 fn as_ref(&self) -> &[M::R] {
313 self.data.as_ref()
314 }
315}
316
317pub struct ShoupRgswCiphertextEvaluationDomain<M> {
318 pub(crate) data: M,
319}
320
321impl<M: Matrix + ToShoup<Modulus = M::MatElement>, Mod: Modulus<Element = M::MatElement>, R, N>
322 From<&RgswCiphertextEvaluationDomain<M, Mod, R, N>> for ShoupRgswCiphertextEvaluationDomain<M>
323{
324 fn from(value: &RgswCiphertextEvaluationDomain<M, Mod, R, N>) -> Self {
325 Self {
326 data: M::to_shoup(&value.data, value.modulus.q().unwrap()),
327 }
328 }
329}
330
331pub struct SeededRlweCiphertext<R, S, Mod> {
332 pub(crate) data: R,
333 pub(crate) seed: S,
334 pub(crate) modulus: Mod,
335}
336
337impl<R: RowEntity, S, Mod> SeededRlweCiphertext<R, S, Mod> {
338 pub(crate) fn empty(ring_size: usize, seed: S, modulus: Mod) -> Self {
339 SeededRlweCiphertext {
340 data: R::zeros(ring_size),
341 seed,
342 modulus,
343 }
344 }
345}
346
347pub struct RlweCiphertext<M, Rng> {
348 pub(crate) data: M,
349 pub(crate) is_trivial: bool,
350 pub(crate) _phatom: PhantomData<Rng>,
351}
352
353impl<M, Rng> RlweCiphertext<M, Rng> {
354 pub(crate) fn new_trivial(data: M) -> Self {
355 RlweCiphertext {
356 data,
357 is_trivial: true,
358 _phatom: PhantomData,
359 }
360 }
361}
362
363impl<M: Matrix, Rng> Matrix for RlweCiphertext<M, Rng> {
364 type MatElement = M::MatElement;
365 type R = M::R;
366
367 fn dimension(&self) -> (usize, usize) {
368 self.data.dimension()
369 }
370
371 fn fits(&self, row: usize, col: usize) -> bool {
372 self.data.fits(row, col)
373 }
374}
375
376impl<M: MatrixMut, Rng> MatrixMut for RlweCiphertext<M, Rng> where <M as Matrix>::R: RowMut {}
377
378impl<M: Matrix, Rng> AsRef<[<M as Matrix>::R]> for RlweCiphertext<M, Rng> {
379 fn as_ref(&self) -> &[<M as Matrix>::R] {
380 self.data.as_ref()
381 }
382}
383
384impl<M: MatrixMut, Rng> AsMut<[<M as Matrix>::R]> for RlweCiphertext<M, Rng>
385where
386 <M as Matrix>::R: RowMut,
387{
388 fn as_mut(&mut self) -> &mut [<M as Matrix>::R] {
389 self.data.as_mut()
390 }
391}
392
393impl<M, Rng> IsTrivial for RlweCiphertext<M, Rng> {
394 fn is_trivial(&self) -> bool {
395 self.is_trivial
396 }
397 fn set_not_trivial(&mut self) {
398 self.is_trivial = false;
399 }
400}
401
402impl<
403 R: Row,
404 M: MatrixEntity<R = R, MatElement = R::Element> + MatrixMut,
405 Rng: NewWithSeed + RandomFillUniformInModulus<[M::MatElement], Mod>,
406 Mod: Modulus<Element = R::Element>,
407 > From<&SeededRlweCiphertext<R, Rng::Seed, Mod>> for RlweCiphertext<M, Rng>
408where
409 Rng::Seed: Clone,
410 <M as Matrix>::R: RowMut,
411 R::Element: Copy,
412{
413 fn from(value: &SeededRlweCiphertext<R, Rng::Seed, Mod>) -> Self {
414 let mut data = M::zeros(2, value.data.as_ref().len());
415
416 // sample a
417 let mut p_rng = Rng::new_with_seed(value.seed.clone());
418 RandomFillUniformInModulus::random_fill(&mut p_rng, &value.modulus, data.get_row_mut(0));
419
420 data.get_row_mut(1).copy_from_slice(value.data.as_ref());
421
422 RlweCiphertext {
423 data,
424 is_trivial: false,
425 _phatom: PhantomData,
426 }
427 }
428}
429
430pub trait IsTrivial {
431 fn is_trivial(&self) -> bool;
432 fn set_not_trivial(&mut self);
433}
434
435pub struct SeededRlwePublicKey<Ro: Row, S> {
436 data: Ro,
437 seed: S,
438 modulus: Ro::Element,
439}
440
441impl<Ro: RowEntity, S> SeededRlwePublicKey<Ro, S> {
442 pub(crate) fn empty(ring_size: usize, seed: S, modulus: Ro::Element) -> Self {
443 Self {
444 data: Ro::zeros(ring_size),
445 seed,
446 modulus,
447 }
448 }
449}
450
451pub struct RlwePublicKey<M, R> {
452 data: M,
453 _phantom: PhantomData<R>,
454}
455
456impl<
457 M: MatrixMut + MatrixEntity,
458 Rng: NewWithSeed + RandomFillUniformInModulus<[M::MatElement], M::MatElement>,
459 > From<&SeededRlwePublicKey<M::R, Rng::Seed>> for RlwePublicKey<M, Rng>
460where
461 <M as Matrix>::R: RowMut,
462 M::MatElement: Copy,
463 Rng::Seed: Copy,
464{
465 fn from(value: &SeededRlwePublicKey<M::R, Rng::Seed>) -> Self {
466 let mut data = M::zeros(2, value.data.as_ref().len());
467
468 // sample a
469 let mut p_rng = Rng::new_with_seed(value.seed);
470 RandomFillUniformInModulus::random_fill(&mut p_rng, &value.modulus, data.get_row_mut(0));
471
472 // copy over b
473 data.get_row_mut(1).copy_from_slice(value.data.as_ref());
474
475 Self {
476 data,
477 _phantom: PhantomData,
478 }
479 }
480}
481
482#[derive(Clone)]
483pub struct RlweSecret {
484 pub(crate) values: Vec<i32>,
485}
486
487impl Secret for RlweSecret {
488 type Element = i32;
489 fn values(&self) -> &[Self::Element] {
490 &self.values
491 }
492}
493
494impl RlweSecret {
495 pub fn random(hw: usize, n: usize) -> RlweSecret {
496 DefaultSecureRng::with_local_mut(|rng| {
497 let mut out = vec![0i32; n];
498 fill_random_ternary_secret_with_hamming_weight(&mut out, hw, rng);
499
500 RlweSecret { values: out }
501 })
502 }
503}
504
505#[cfg(test)]
506pub(crate) mod tests {
507 use std::{marker::PhantomData, ops::Mul, vec};
508
509 use itertools::{izip, Itertools};
510 use rand::{thread_rng, Rng};
511
512 use crate::{
513 backend::{GetModulus, ModInit, ModularOpsU64, Modulus, VectorOps},
514 decomposer::{Decomposer, DefaultDecomposer, RlweDecomposer},
515 ntt::{self, Ntt, NttBackendU64, NttInit},
516 random::{DefaultSecureRng, NewWithSeed, RandomFillUniformInModulus},
517 rgsw::{
518 galois_auto_shoup, rlwe_by_rgsw_shoup, ShoupAutoKeyEvaluationDomain,
519 ShoupRgswCiphertextEvaluationDomain,
520 },
521 utils::{generate_prime, negacyclic_mul, Stats, TryConvertFrom1},
522 Matrix, Secret,
523 };
524
525 use super::{
526 keygen::{
527 decrypt_rlwe, galois_key_gen, gen_rlwe_public_key, generate_auto_map, measure_noise,
528 public_key_encrypt_rgsw, secret_key_encrypt_rgsw, secret_key_encrypt_rlwe,
529 },
530 runtime::{galois_auto, rgsw_by_rgsw_inplace, rlwe_by_rgsw},
531 AutoKeyEvaluationDomain, RgswCiphertext, RgswCiphertextEvaluationDomain, RlweCiphertext,
532 RlwePublicKey, RlweSecret, SeededAutoKey, SeededRgswCiphertext, SeededRlweCiphertext,
533 SeededRlwePublicKey,
534 };
535
536 pub(crate) fn _sk_encrypt_rlwe<T: Modulus<Element = u64> + Clone>(
537 m: &[u64],
538 s: &[i32],
539 ntt_op: &NttBackendU64,
540 mod_op: &ModularOpsU64<T>,
541 ) -> RlweCiphertext<Vec<Vec<u64>>, DefaultSecureRng> {
542 let ring_size = m.len();
543 let q = mod_op.modulus();
544 assert!(s.len() == ring_size);
545
546 let mut rng = DefaultSecureRng::new();
547 let mut rlwe_seed = [0u8; 32];
548 rng.fill_bytes(&mut rlwe_seed);
549 let mut seeded_rlwe_ct =
550 SeededRlweCiphertext::<_, [u8; 32], _>::empty(ring_size as usize, rlwe_seed, q.clone());
551 let mut p_rng = DefaultSecureRng::new_seeded(rlwe_seed);
552 secret_key_encrypt_rlwe(
553 &m,
554 &mut seeded_rlwe_ct.data,
555 s,
556 mod_op,
557 ntt_op,
558 &mut p_rng,
559 &mut rng,
560 );
561
562 RlweCiphertext::<Vec<Vec<u64>>, DefaultSecureRng>::from(&seeded_rlwe_ct)
563 }
564
565 // Encrypt m as RGSW ciphertext RGSW(m) using supplied public key
566 pub(crate) fn _pk_encrypt_rgsw<T: Modulus<Element = u64> + Clone>(
567 m: &[u64],
568 public_key: &RlwePublicKey<Vec<Vec<u64>>, DefaultSecureRng>,
569 decomposer: &(DefaultDecomposer<u64>, DefaultDecomposer<u64>),
570 mod_op: &ModularOpsU64<T>,
571 ntt_op: &NttBackendU64,
572 ) -> RgswCiphertext<Vec<Vec<u64>>, T> {
573 let (_, ring_size) = Matrix::dimension(&public_key.data);
574 let gadget_vector_a = decomposer.a().gadget_vector();
575 let gadget_vector_b = decomposer.b().gadget_vector();
576
577 let mut rng = DefaultSecureRng::new();
578
579 assert!(m.len() == ring_size);
580
581 // public key encrypt RGSW(m1)
582 let mut rgsw_ct = RgswCiphertext::empty(ring_size, decomposer, mod_op.modulus().clone());
583 public_key_encrypt_rgsw(
584 &mut rgsw_ct.data,
585 m,
586 &public_key.data,
587 &gadget_vector_a,
588 &gadget_vector_b,
589 mod_op,
590 ntt_op,
591 &mut rng,
592 );
593
594 rgsw_ct
595 }
596
597 /// Encrypts m as RGSW ciphertext RGSW(m) using supplied secret key. Returns
598 /// unseeded RGSW ciphertext in coefficient domain
599 pub(crate) fn _sk_encrypt_rgsw<T: Modulus<Element = u64> + Clone>(
600 m: &[u64],
601 s: &[i32],
602 decomposer: &(DefaultDecomposer<u64>, DefaultDecomposer<u64>),
603 mod_op: &ModularOpsU64<T>,
604 ntt_op: &NttBackendU64,
605 ) -> SeededRgswCiphertext<Vec<Vec<u64>>, [u8; 32], T> {
606 let ring_size = s.len();
607 assert!(m.len() == s.len());
608
609 let q = mod_op.modulus();
610
611 let gadget_vector_a = decomposer.a().gadget_vector();
612 let gadget_vector_b = decomposer.b().gadget_vector();
613
614 let mut rng = DefaultSecureRng::new();
615 let mut rgsw_seed = [0u8; 32];
616 rng.fill_bytes(&mut rgsw_seed);
617 let mut seeded_rgsw_ct = SeededRgswCiphertext::<Vec<Vec<u64>>, [u8; 32], T>::empty(
618 ring_size as usize,
619 decomposer,
620 rgsw_seed,
621 q.clone(),
622 );
623 let mut p_rng = DefaultSecureRng::new_seeded(rgsw_seed);
624 secret_key_encrypt_rgsw(
625 &mut seeded_rgsw_ct.data,
626 m,
627 &gadget_vector_a,
628 &gadget_vector_b,
629 s,
630 mod_op,
631 ntt_op,
632 &mut p_rng,
633 &mut rng,
634 );
635 seeded_rgsw_ct
636 }
637
638 /// Prints noise in RGSW ciphertext RGSW(m).
639 ///
640 /// - rgsw_ct: RGSW ciphertext in coefficient domain
641 pub(crate) fn _measure_noise_rgsw<T: Modulus<Element = u64> + Clone>(
642 rgsw_ct: &[Vec<u64>],
643 m: &[u64],
644 s: &[i32],
645 decomposer: &(DefaultDecomposer<u64>, DefaultDecomposer<u64>),
646 q: &T,
647 ) {
648 let gadget_vector_a = decomposer.a().gadget_vector();
649 let gadget_vector_b = decomposer.b().gadget_vector();
650 let d_a = gadget_vector_a.len();
651 let d_b = gadget_vector_b.len();
652 let ring_size = s.len();
653 assert!(Matrix::dimension(&rgsw_ct) == (d_a * 2 + d_b * 2, ring_size));
654 assert!(m.len() == ring_size);
655
656 let mod_op = ModularOpsU64::new(q.clone());
657 let ntt_op = NttBackendU64::new(q, ring_size);
658
659 let mul_mod =
660 |a: &u64, b: &u64| ((*a as u128 * *b as u128) % q.q().unwrap() as u128) as u64;
661 let s_poly = Vec::<u64>::try_convert_from(s, q);
662 let mut neg_s = s_poly.clone();
663 mod_op.elwise_neg_mut(neg_s.as_mut());
664 let neg_sm0m1 = negacyclic_mul(&neg_s, &m, mul_mod, q.q().unwrap());
665
666 // RLWE(\beta^j -s * m)
667 for j in 0..d_a {
668 let ideal_m = {
669 // RLWE(\beta^j -s * m)
670 let mut beta_neg_sm0m1 = vec![0u64; ring_size as usize];
671 mod_op.elwise_scalar_mul(beta_neg_sm0m1.as_mut(), &neg_sm0m1, &gadget_vector_a[j]);
672 beta_neg_sm0m1
673 };
674
675 let mut rlwe = vec![vec![0u64; ring_size as usize]; 2];
676 rlwe[0].copy_from_slice(rgsw_ct.get_row_slice(j));
677 rlwe[1].copy_from_slice(rgsw_ct.get_row_slice(d_a + j));
678 let noise = measure_noise(&rlwe, &ideal_m, &ntt_op, &mod_op, s);
679
680 println!(r"Noise RLWE(\beta^{j} -sm0m1): {noise}");
681 }
682
683 // RLWE(\beta^j m)
684 for j in 0..d_b {
685 let ideal_m = {
686 // RLWE(\beta^j m)
687 let mut beta_m0m1 = vec![0u64; ring_size as usize];
688 mod_op.elwise_scalar_mul(beta_m0m1.as_mut(), &m, &gadget_vector_b[j]);
689 beta_m0m1
690 };
691
692 let mut rlwe = vec![vec![0u64; ring_size as usize]; 2];
693 rlwe[0].copy_from_slice(rgsw_ct.get_row_slice(d_a * 2 + j));
694 rlwe[1].copy_from_slice(rgsw_ct.get_row_slice(d_a * 2 + d_b + j));
695 let noise = measure_noise(&rlwe, &ideal_m, &ntt_op, &mod_op, s);
696
697 println!(r"Noise RLWE(\beta^{j} m0m1): {noise}");
698 }
699 }
700
701 #[test]
702 fn rlwe_encrypt_decryption() {
703 let logq = 50;
704 let logp = 2;
705 let ring_size = 1 << 4;
706 let q = generate_prime(logq, ring_size, 1u64 << logq).unwrap();
707 let p = 1u64 << logp;
708
709 let mut rng = DefaultSecureRng::new();
710
711 let s = RlweSecret::random((ring_size >> 1) as usize, ring_size as usize);
712
713 // sample m0
714 let mut m0 = vec![0u64; ring_size as usize];
715 RandomFillUniformInModulus::<[u64], u64>::random_fill(
716 &mut rng,
717 &(1u64 << logp),
718 m0.as_mut_slice(),
719 );
720
721 let ntt_op = NttBackendU64::new(&q, ring_size as usize);
722 let mod_op = ModularOpsU64::new(q);
723
724 // encrypt m0
725 let encoded_m = m0
726 .iter()
727 .map(|v| (((*v as f64) * q as f64) / (p as f64)).round() as u64)
728 .collect_vec();
729 let rlwe_in_ct = _sk_encrypt_rlwe(&encoded_m, s.values(), &ntt_op, &mod_op);
730
731 let mut encoded_m_back = vec![0u64; ring_size as usize];
732 decrypt_rlwe(
733 &rlwe_in_ct,
734 s.values(),
735 &mut encoded_m_back,
736 &ntt_op,
737 &mod_op,
738 );
739 let m_back = encoded_m_back
740 .iter()
741 .map(|v| (((*v as f64 * p as f64) / q as f64).round() as u64) % p)
742 .collect_vec();
743 assert_eq!(m0, m_back);
744
745 // let noise = measure_noise(&rlwe_in_ct, &encoded_m, &ntt_op, &mod_op,
746 // s.values()); println!("Noise: {noise}");
747 }
748
749 #[test]
750 fn rlwe_by_rgsw_works() {
751 let logq = 50;
752 let logp = 2;
753 let ring_size = 1 << 9;
754 let q = generate_prime(logq, ring_size, 1u64 << logq).unwrap();
755 let p: u64 = 1u64 << logp;
756
757 let mut rng = DefaultSecureRng::new_seeded([0u8; 32]);
758
759 let s = RlweSecret::random((ring_size >> 1) as usize, ring_size as usize);
760
761 let mut m0 = vec![0u64; ring_size as usize];
762 RandomFillUniformInModulus::<[u64], _>::random_fill(
763 &mut rng,
764 &(1u64 << logp),
765 m0.as_mut_slice(),
766 );
767 let mut m1 = vec![0u64; ring_size as usize];
768 m1[thread_rng().gen_range(0..ring_size) as usize] = 1;
769
770 let ntt_op = NttBackendU64::new(&q, ring_size as usize);
771 let mod_op = ModularOpsU64::new(q);
772 let d_rgsw = 10;
773 let logb = 5;
774 let decomposer = (
775 DefaultDecomposer::new(q, logb, d_rgsw),
776 DefaultDecomposer::new(q, logb, d_rgsw),
777 );
778
779 // create public key
780 let mut pk_seed = [0u8; 32];
781 rng.fill_bytes(&mut pk_seed);
782 let mut pk_prng = DefaultSecureRng::new_seeded(pk_seed);
783 let mut seeded_pk =
784 SeededRlwePublicKey::<Vec<u64>, _>::empty(ring_size as usize, pk_seed, q);
785 gen_rlwe_public_key(
786 &mut seeded_pk.data,
787 s.values(),
788 &ntt_op,
789 &mod_op,
790 &mut pk_prng,
791 &mut rng,
792 );
793 let pk = RlwePublicKey::<Vec<Vec<u64>>, DefaultSecureRng>::from(&seeded_pk);
794
795 // Encrypt m1 as RGSW(m1)
796 let rgsw_ct = {
797 //TODO(Jay): Figure out better way to test secret key and public key variant of
798 // RGSW ciphertext encryption within the same test
799
800 if true {
801 // Encryption m1 as RGSW(m1) using secret key
802 let seeded_rgsw_ct =
803 _sk_encrypt_rgsw(&m1, s.values(), &decomposer, &mod_op, &ntt_op);
804 RgswCiphertextEvaluationDomain::<Vec<Vec<u64>>, _,DefaultSecureRng, NttBackendU64>::from(&seeded_rgsw_ct)
805 } else {
806 // Encrypt m1 as RGSW(m1) using public key
807 let rgsw_ct = _pk_encrypt_rgsw(&m1, &pk, &decomposer, &mod_op, &ntt_op);
808 RgswCiphertextEvaluationDomain::<_, _, DefaultSecureRng, NttBackendU64>::from(
809 &rgsw_ct,
810 )
811 }
812 };
813
814 // Encrypt m0 as RLWE(m0)
815 let mut rlwe_in_ct = {
816 let encoded_m = m0
817 .iter()
818 .map(|v| (((*v as f64) * q as f64) / (p as f64)).round() as u64)
819 .collect_vec();
820
821 _sk_encrypt_rlwe(&encoded_m, s.values(), &ntt_op, &mod_op)
822 };
823
824 // RLWE(m0m1) = RLWE(m0) x RGSW(m1)
825 let mut scratch_space = vec![
826 vec![0u64; ring_size as usize];
827 std::cmp::max(
828 decomposer.a().decomposition_count(),
829 decomposer.b().decomposition_count()
830 ) + 2
831 ];
832
833 // rlwe x rgsw with additional RGSW ciphertexts in shoup repr
834 let rlwe_in_ct_shoup = {
835 let mut rlwe_in_ct_shoup = RlweCiphertext::<_, DefaultSecureRng> {
836 data: rlwe_in_ct.data.clone(),
837 is_trivial: rlwe_in_ct.is_trivial,
838 _phatom: PhantomData::default(),
839 };
840
841 let rgsw_ct_shoup = ShoupRgswCiphertextEvaluationDomain::from(&rgsw_ct);
842
843 rlwe_by_rgsw_shoup(
844 &mut rlwe_in_ct_shoup,
845 &rgsw_ct.data,
846 &rgsw_ct_shoup.data,
847 &mut scratch_space,
848 &decomposer,
849 &ntt_op,
850 &mod_op,
851 );
852
853 rlwe_in_ct_shoup
854 };
855
856 // rlwe x rgsw normal
857 {
858 rlwe_by_rgsw(
859 &mut rlwe_in_ct,
860 &rgsw_ct.data,
861 &mut scratch_space,
862 &decomposer,
863 &ntt_op,
864 &mod_op,
865 );
866 }
867
868 // output from both functions must be equal
869 {
870 assert_eq!(rlwe_in_ct.data, rlwe_in_ct_shoup.data);
871 }
872
873 // Decrypt RLWE(m0m1)
874 let mut encoded_m0m1_back = vec![0u64; ring_size as usize];
875 decrypt_rlwe(
876 &rlwe_in_ct,
877 s.values(),
878 &mut encoded_m0m1_back,
879 &ntt_op,
880 &mod_op,
881 );
882 let m0m1_back = encoded_m0m1_back
883 .iter()
884 .map(|v| (((*v as f64 * p as f64) / (q as f64)).round() as u64) % p)
885 .collect_vec();
886
887 let mul_mod = |v0: &u64, v1: &u64| (v0 * v1) % p;
888 let m0m1 = negacyclic_mul(&m0, &m1, mul_mod, p);
889
890 // {
891 // // measure noise
892 // let encoded_m_ideal = m0m1
893 // .iter()
894 // .map(|v| (((*v as f64) * q as f64) / (p as f64)).round() as u64)
895 // .collect_vec();
896
897 // let noise = measure_noise(&rlwe_in_ct, &encoded_m_ideal, &ntt_op,
898 // &mod_op, s.values()); println!("Noise RLWE(m0m1)(=
899 // RLWE(m0)xRGSW(m1)) : {noise}"); }
900
901 assert!(
902 m0m1 == m0m1_back,
903 "Expected {:?} \n Got {:?}",
904 m0m1,
905 m0m1_back
906 );
907 }
908
909 #[test]
910 fn galois_auto_works() {
911 let logq = 55;
912 let ring_size = 1 << 11;
913 let q = generate_prime(logq, 2 * ring_size, 1u64 << logq).unwrap();
914 let logp = 3;
915 let p = 1u64 << logp;
916 let d_rgsw = 5;
917 let logb = 11;
918
919 let mut rng = DefaultSecureRng::new();
920 let s = RlweSecret::random((ring_size >> 1) as usize, ring_size as usize);
921
922 let mut m = vec![0u64; ring_size as usize];
923 RandomFillUniformInModulus::random_fill(&mut rng, &p, m.as_mut_slice());
924 let encoded_m = m
925 .iter()
926 .map(|v| (((*v as f64 * q as f64) / (p as f64)).round() as u64))
927 .collect_vec();
928
929 let ntt_op = NttBackendU64::new(&q, ring_size as usize);
930 let mod_op = ModularOpsU64::new(q);
931
932 // RLWE_{s}(m)
933 let mut seed_rlwe = [0u8; 32];
934 rng.fill_bytes(&mut seed_rlwe);
935 let mut seeded_rlwe_m = SeededRlweCiphertext::empty(ring_size as usize, seed_rlwe, q);
936 let mut p_rng = DefaultSecureRng::new_seeded(seed_rlwe);
937 secret_key_encrypt_rlwe(
938 &encoded_m,
939 &mut seeded_rlwe_m.data,
940 s.values(),
941 &mod_op,
942 &ntt_op,
943 &mut p_rng,
944 &mut rng,
945 );
946 let mut rlwe_m = RlweCiphertext::<Vec<Vec<u64>>, DefaultSecureRng>::from(&seeded_rlwe_m);
947
948 let auto_k = -125;
949
950 // Generate galois key to key switch from s^k to s
951 let decomposer = DefaultDecomposer::new(q, logb, d_rgsw);
952 let mut seed_auto = [0u8; 32];
953 rng.fill_bytes(&mut seed_auto);
954 let mut seeded_auto_key =
955 SeededAutoKey::empty(ring_size as usize, &decomposer, seed_auto, q);
956 let mut p_rng = DefaultSecureRng::new_seeded(seed_auto);
957 let gadget_vector = decomposer.gadget_vector();
958 galois_key_gen(
959 &mut seeded_auto_key.data,
960 s.values(),
961 auto_k,
962 &gadget_vector,
963 &mod_op,
964 &ntt_op,
965 &mut p_rng,
966 &mut rng,
967 );
968 let auto_key =
969 AutoKeyEvaluationDomain::<Vec<Vec<u64>>, _, DefaultSecureRng, NttBackendU64>::from(
970 &seeded_auto_key,
971 );
972
973 // Send RLWE_{s}(m) -> RLWE_{s}(m^k)
974 let mut scratch_space = vec![vec![0u64; ring_size as usize]; d_rgsw + 2];
975 let (auto_map_index, auto_map_sign) = generate_auto_map(ring_size as usize, auto_k);
976
977 // galois auto with additional auto key in shoup repr
978 let rlwe_m_shoup = {
979 let auto_key_shoup = ShoupAutoKeyEvaluationDomain::from(&auto_key);
980 let mut rlwe_m_shoup = RlweCiphertext::<_, DefaultSecureRng> {
981 data: rlwe_m.data.clone(),
982 is_trivial: rlwe_m.is_trivial,
983 _phatom: PhantomData::default(),
984 };
985 galois_auto_shoup(
986 &mut rlwe_m_shoup,
987 &auto_key.data,
988 &auto_key_shoup.data,
989 &mut scratch_space,
990 &auto_map_index,
991 &auto_map_sign,
992 &mod_op,
993 &ntt_op,
994 &decomposer,
995 );
996 rlwe_m_shoup
997 };
998
999 // normal galois auto
1000 {
1001 galois_auto(
1002 &mut rlwe_m,
1003 &auto_key.data,
1004 &mut scratch_space,
1005 &auto_map_index,
1006 &auto_map_sign,
1007 &mod_op,
1008 &ntt_op,
1009 &decomposer,
1010 );
1011 }
1012
1013 // rlwe out from both functions must be same
1014 assert_eq!(rlwe_m.data, rlwe_m_shoup.data);
1015
1016 let rlwe_m_k = rlwe_m;
1017
1018 // Decrypt RLWE_{s}(m^k) and check
1019 let mut encoded_m_k_back = vec![0u64; ring_size as usize];
1020 decrypt_rlwe(
1021 &rlwe_m_k,
1022 s.values(),
1023 &mut encoded_m_k_back,
1024 &ntt_op,
1025 &mod_op,
1026 );
1027 let m_k_back = encoded_m_k_back
1028 .iter()
1029 .map(|v| (((*v as f64 * p as f64) / q as f64).round() as u64) % p)
1030 .collect_vec();
1031
1032 let mut m_k = vec![0u64; ring_size as usize];
1033 // Send \delta m -> \delta m^k
1034 izip!(m.iter(), auto_map_index.iter(), auto_map_sign.iter()).for_each(
1035 |(v, to_index, sign)| {
1036 if !*sign {
1037 m_k[*to_index] = (p - *v) % p;
1038 } else {
1039 m_k[*to_index] = *v;
1040 }
1041 },
1042 );
1043
1044 {
1045 let encoded_m_k = m_k
1046 .iter()
1047 .map(|v| ((*v as f64 * q as f64) / p as f64).round() as u64)
1048 .collect_vec();
1049
1050 let noise = measure_noise(&rlwe_m_k, &encoded_m_k, &ntt_op, &mod_op, s.values());
1051 println!("Ksk noise: {noise}");
1052 }
1053
1054 assert_eq!(m_k_back, m_k);
1055 }
1056
1057 #[test]
1058 fn sk_rgsw_by_rgsw() {
1059 let logq = 60;
1060 let logp = 2;
1061 let ring_size = 1 << 11;
1062 let q = generate_prime(logq, ring_size, 1u64 << logq).unwrap();
1063 let p = 1u64 << logp;
1064 let d_rgsw = 12;
1065 let logb = 5;
1066
1067 let s = RlweSecret::random((ring_size >> 1) as usize, ring_size as usize);
1068
1069 let mut rng = DefaultSecureRng::new();
1070 let ntt_op = NttBackendU64::new(&q, ring_size as usize);
1071 let mod_op = ModularOpsU64::new(q);
1072 let decomposer = (
1073 DefaultDecomposer::new(q, logb, d_rgsw),
1074 DefaultDecomposer::new(q, logb, d_rgsw),
1075 );
1076
1077 let mul_mod = |a: &u64, b: &u64| ((*a as u128 * *b as u128) % q as u128) as u64;
1078
1079 let mut carry_m = vec![0u64; ring_size as usize];
1080 carry_m[thread_rng().gen_range(0..ring_size) as usize] = 1;
1081
1082 // RGSW(carry_m)
1083 let mut rgsw_carrym = {
1084 let seeded_rgsw = _sk_encrypt_rgsw(&carry_m, s.values(), &decomposer, &mod_op, &ntt_op);
1085 let mut rgsw_eval =
1086 RgswCiphertextEvaluationDomain::<_, _, DefaultSecureRng, NttBackendU64>::from(
1087 &seeded_rgsw,
1088 );
1089 rgsw_eval
1090 .data
1091 .iter_mut()
1092 .for_each(|ri| ntt_op.backward(ri.as_mut()));
1093 rgsw_eval.data
1094 };
1095
1096 let mut scratch_matrix = vec![
1097 vec![0u64; ring_size as usize];
1098 decomposer.a().decomposition_count() * 2
1099 + decomposer.b().decomposition_count() * 2
1100 + std::cmp::max(
1101 decomposer.a().decomposition_count(),
1102 decomposer.b().decomposition_count()
1103 )
1104 ];
1105
1106 _measure_noise_rgsw(&rgsw_carrym, &carry_m, s.values(), &decomposer, &q);
1107
1108 for i in 0..2 {
1109 let mut m = vec![0u64; ring_size as usize];
1110 m[thread_rng().gen_range(0..ring_size) as usize] = if (i & 1) == 1 { q - 1 } else { 1 };
1111 let rgsw_m =
1112 RgswCiphertextEvaluationDomain::<_, _, DefaultSecureRng, NttBackendU64>::from(
1113 &_sk_encrypt_rgsw(&m, s.values(), &decomposer, &mod_op, &ntt_op),
1114 );
1115 rgsw_by_rgsw_inplace(
1116 &mut rgsw_carrym,
1117 &rgsw_m.data,
1118 &decomposer,
1119 &mut scratch_matrix,
1120 &ntt_op,
1121 &mod_op,
1122 );
1123
1124 // measure noise
1125 carry_m = negacyclic_mul(&carry_m, &m, mul_mod, q);
1126 println!("########### Noise RGSW(carrym) in {i}^th loop ###########");
1127 _measure_noise_rgsw(&rgsw_carrym, &carry_m, s.values(), &decomposer, &q);
1128 }
1129 {
1130 // RLWE(m) x RGSW(carry_m)
1131 let mut m = vec![0u64; ring_size as usize];
1132 RandomFillUniformInModulus::random_fill(&mut rng, &q, m.as_mut_slice());
1133 let mut rlwe_ct = _sk_encrypt_rlwe(&m, s.values(), &ntt_op, &mod_op);
1134
1135 // send rgsw to evaluation domain
1136 rgsw_carrym
1137 .iter_mut()
1138 .for_each(|ri| ntt_op.forward(ri.as_mut_slice()));
1139
1140 rlwe_by_rgsw(
1141 &mut rlwe_ct,
1142 &rgsw_carrym,
1143 &mut scratch_matrix,
1144 &decomposer,
1145 &ntt_op,
1146 &mod_op,
1147 );
1148 let m_expected = negacyclic_mul(&carry_m, &m, mul_mod, q);
1149 let noise = measure_noise(&rlwe_ct, &m_expected, &ntt_op, &mod_op, s.values());
1150 println!("RLWE(m) x RGSW(carry_m): {noise}");
1151 }
1152 }
1153
1154 #[test]
1155 fn some_work() {
1156 let logq = 50;
1157 let ring_size = 1 << 11;
1158 let q = generate_prime(logq, ring_size, 1u64 << logq).unwrap();
1159 let d_rgsw = 10;
1160 let logb = 5;
1161 let decomposer = (
1162 DefaultDecomposer::new(q, logb, d_rgsw),
1163 DefaultDecomposer::new(q, logb, d_rgsw),
1164 );
1165
1166 let ntt_op = NttBackendU64::new(&q, ring_size as usize);
1167 let mod_op = ModularOpsU64::new(q);
1168 let mut rng = DefaultSecureRng::new_seeded([0u8; 32]);
1169
1170 let s = RlweSecret::random((ring_size >> 1) as usize, ring_size as usize);
1171
1172 let mut check = Stats { samples: vec![] };
1173
1174 for _ in 0..100 {
1175 let mut m0 = vec![0u64; ring_size as usize];
1176 m0[thread_rng().gen_range(0..ring_size) as usize] = 1;
1177 let mut m1 = vec![0u64; ring_size as usize];
1178 m1[thread_rng().gen_range(0..ring_size) as usize] = 1;
1179
1180 let mut rgsw_ct0 = {
1181 let seeded_rgsw_ct =
1182 _sk_encrypt_rgsw(&m0, s.values(), &decomposer, &mod_op, &ntt_op);
1183 RgswCiphertextEvaluationDomain::<Vec<Vec<u64>>, _,DefaultSecureRng, NttBackendU64>::from(&seeded_rgsw_ct)
1184 };
1185 let rgsw_ct1 = {
1186 let seeded_rgsw_ct =
1187 _sk_encrypt_rgsw(&m1, s.values(), &decomposer, &mod_op, &ntt_op);
1188 RgswCiphertextEvaluationDomain::<Vec<Vec<u64>>,_, DefaultSecureRng, NttBackendU64>::from(&seeded_rgsw_ct)
1189 };
1190
1191 // RGSW x RGSW
1192 // send RGSW(m0) to coefficient domain
1193 rgsw_ct0
1194 .data
1195 .iter_mut()
1196 .for_each(|r| ntt_op.backward(r.as_mut_slice()));
1197 let mut scratch_matrix = vec![
1198 vec![0u64; ring_size as usize];
1199 std::cmp::max(
1200 decomposer.a().decomposition_count(),
1201 decomposer.b().decomposition_count()
1202 ) + decomposer.a().decomposition_count() * 2
1203 + decomposer.b().decomposition_count() * 2
1204 ];
1205 rgsw_by_rgsw_inplace(
1206 &mut rgsw_ct0.data,
1207 &rgsw_ct1.data,
1208 &decomposer,
1209 &mut scratch_matrix,
1210 &ntt_op,
1211 &mod_op,
1212 );
1213 let mut rgsw_m0m1 = rgsw_ct0;
1214 // Back to Evaluation for RLWExRGSW
1215 rgsw_m0m1
1216 .data
1217 .iter_mut()
1218 .for_each(|r| ntt_op.forward(r.as_mut_slice()));
1219
1220 // Sample m2, encrypt it as RLWE(m2) and multiply RLWE(m2)xRGSW(m0m1)
1221 let mut m2 = vec![0u64; ring_size as usize];
1222 RandomFillUniformInModulus::random_fill(&mut rng, &q, m2.as_mut_slice());
1223 let mut rlwe_in_ct = { _sk_encrypt_rlwe(&m2, s.values(), &ntt_op, &mod_op) };
1224 let mut scratch_space = vec![
1225 vec![0u64; ring_size as usize];
1226 std::cmp::max(
1227 decomposer.a().decomposition_count(),
1228 decomposer.b().decomposition_count()
1229 ) + 2
1230 ];
1231 rlwe_by_rgsw(
1232 &mut rlwe_in_ct,
1233 &rgsw_m0m1.data,
1234 &mut scratch_space,
1235 &decomposer,
1236 &ntt_op,
1237 &mod_op,
1238 );
1239
1240 // Decrypt RLWE(m0m1m2)
1241 let mut m0m1m2_back = vec![0u64; ring_size as usize];
1242 decrypt_rlwe(&rlwe_in_ct, s.values(), &mut m0m1m2_back, &ntt_op, &mod_op);
1243
1244 // Calculate m0m1m2
1245 let mul_mod = |v0: &u64, v1: &u64| ((*v0 as u128 * *v1 as u128) % q as u128) as u64;
1246 let m0m1 = negacyclic_mul(&m0, &m1, mul_mod, q);
1247 let m0m1m2 = negacyclic_mul(&m2, &m0m1, mul_mod, q);
1248
1249 // diff
1250 mod_op.elwise_sub_mut(m0m1m2_back.as_mut_slice(), m0m1m2.as_ref());
1251
1252 check.add_more(&Vec::<i64>::try_convert_from(&m0m1m2_back, &q));
1253 }
1254
1255 println!("Std: {}", check.std_dev().abs().log2());
1256 }
1257}