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: MatrixMut + MatrixEntity, Mod: Modulus<Element = M::MatElement>, R, N>
99 From<&AutoKeyEvaluationDomain<M, Mod, R, N>> for ShoupAutoKeyEvaluationDomain<M>
100where
101 M::R: RowMut,
102 M::MatElement: ToShoup + Copy,
103{
104 fn from(value: &AutoKeyEvaluationDomain<M, Mod, R, N>) -> Self {
105 let (row, col) = value.data.dimension();
106 let mut shoup_data = M::zeros(row, col);
107
108 izip!(shoup_data.iter_rows_mut(), value.data.iter_rows()).for_each(|(shoup_r, r)| {
109 izip!(shoup_r.as_mut().iter_mut(), r.as_ref().iter()).for_each(|(s, e)| {
110 *s = M::MatElement::to_shoup(*e, value.modulus.q().unwrap());
111 });
112 });
113
114 Self { data: shoup_data }
115 }
116}
117
118pub struct RgswCiphertext<M: Matrix, Mod> {
119 /// Rgsw ciphertext polynomials
120 pub(crate) data: M,
121 modulus: Mod,
122 /// Decomposition for RLWE part A
123 d_a: usize,
124 /// Decomposition for RLWE part B
125 d_b: usize,
126}
127
128impl<M: MatrixEntity, Mod: Modulus<Element = M::MatElement>> RgswCiphertext<M, Mod> {
129 pub(crate) fn empty<D: RlweDecomposer>(
130 ring_size: usize,
131 decomposer: &D,
132 modulus: Mod,
133 ) -> RgswCiphertext<M, Mod> {
134 RgswCiphertext {
135 data: M::zeros(
136 decomposer.a().decomposition_count() * 2 + decomposer.b().decomposition_count() * 2,
137 ring_size,
138 ),
139 d_a: decomposer.a().decomposition_count(),
140 d_b: decomposer.b().decomposition_count(),
141 modulus,
142 }
143 }
144}
145
146pub struct SeededRgswCiphertext<M, S, Mod>
147where
148 M: Matrix,
149{
150 pub(crate) data: M,
151 seed: S,
152 modulus: Mod,
153 /// Decomposition for RLWE part A
154 d_a: usize,
155 /// Decomposition for RLWE part B
156 d_b: usize,
157}
158
159impl<M: Matrix + MatrixEntity, S, Mod> SeededRgswCiphertext<M, S, Mod> {
160 pub(crate) fn empty<D: RlweDecomposer>(
161 ring_size: usize,
162 decomposer: &D,
163 seed: S,
164 modulus: Mod,
165 ) -> SeededRgswCiphertext<M, S, Mod> {
166 SeededRgswCiphertext {
167 data: M::zeros(
168 decomposer.a().decomposition_count() * 2 + decomposer.b().decomposition_count(),
169 ring_size,
170 ),
171 seed,
172 modulus,
173 d_a: decomposer.a().decomposition_count(),
174 d_b: decomposer.b().decomposition_count(),
175 }
176 }
177}
178
179impl<M: Debug + Matrix, S: Debug, Mod: Debug> Debug for SeededRgswCiphertext<M, S, Mod>
180where
181 M::MatElement: Debug,
182{
183 fn fmt(&self, f: &mut std::fmt::Formatter<'_>) -> std::fmt::Result {
184 f.debug_struct("SeededRgswCiphertext")
185 .field("data", &self.data)
186 .field("seed", &self.seed)
187 .field("modulus", &self.modulus)
188 .finish()
189 }
190}
191
192pub struct RgswCiphertextEvaluationDomain<M, Mod, R, N> {
193 pub(crate) data: M,
194 modulus: Mod,
195 _phantom: PhantomData<(R, N)>,
196}
197
198impl<
199 M: MatrixMut + MatrixEntity,
200 Mod: Modulus<Element = M::MatElement> + Clone,
201 R: NewWithSeed + RandomFillUniformInModulus<[M::MatElement], Mod>,
202 N: NttInit<Mod> + Ntt<Element = M::MatElement> + Debug,
203 > From<&SeededRgswCiphertext<M, R::Seed, Mod>> for RgswCiphertextEvaluationDomain<M, Mod, R, N>
204where
205 <M as Matrix>::R: RowMut,
206 M::MatElement: Copy,
207 R::Seed: Clone,
208 M: Debug,
209{
210 fn from(value: &SeededRgswCiphertext<M, R::Seed, Mod>) -> Self {
211 let mut data = M::zeros(value.d_a * 2 + value.d_b * 2, value.data.dimension().1);
212
213 // copy RLWE'(-sm)
214 izip!(
215 data.iter_rows_mut().take(value.d_a * 2),
216 value.data.iter_rows().take(value.d_a * 2)
217 )
218 .for_each(|(to_ri, from_ri)| {
219 to_ri.as_mut().copy_from_slice(from_ri.as_ref());
220 });
221
222 // sample A polynomials of RLWE'(m) - RLWE'A(m)
223 // TODO(Jay): Do we want to be generic over RandomGenerator used here? I think
224 // not.
225 let mut p_rng = R::new_with_seed(value.seed.clone());
226 izip!(data.iter_rows_mut().skip(value.d_a * 2).take(value.d_b * 1))
227 .for_each(|ri| p_rng.random_fill(&value.modulus, ri.as_mut()));
228
229 // RLWE'_B(m)
230 izip!(
231 data.iter_rows_mut().skip(value.d_a * 2 + value.d_b),
232 value.data.iter_rows().skip(value.d_a * 2)
233 )
234 .for_each(|(to_ri, from_ri)| {
235 to_ri.as_mut().copy_from_slice(from_ri.as_ref());
236 });
237
238 // Send polynomials to evaluation domain
239 let ring_size = data.dimension().1;
240 let nttop = N::new(&value.modulus, ring_size);
241 data.iter_rows_mut()
242 .for_each(|ri| nttop.forward(ri.as_mut()));
243
244 Self {
245 data: data,
246 modulus: value.modulus.clone(),
247 _phantom: PhantomData,
248 }
249 }
250}
251
252impl<
253 M: MatrixMut + MatrixEntity,
254 Mod: Modulus<Element = M::MatElement> + Clone,
255 R,
256 N: NttInit<Mod> + Ntt<Element = M::MatElement>,
257 > From<&RgswCiphertext<M, Mod>> for RgswCiphertextEvaluationDomain<M, Mod, R, N>
258where
259 <M as Matrix>::R: RowMut,
260 M::MatElement: Copy,
261 M: Debug,
262{
263 fn from(value: &RgswCiphertext<M, Mod>) -> Self {
264 let mut data = M::zeros(value.d_a * 2 + value.d_b * 2, value.data.dimension().1);
265
266 // copy RLWE'(-sm)
267 izip!(
268 data.iter_rows_mut().take(value.d_a * 2),
269 value.data.iter_rows().take(value.d_a * 2)
270 )
271 .for_each(|(to_ri, from_ri)| {
272 to_ri.as_mut().copy_from_slice(from_ri.as_ref());
273 });
274
275 // copy RLWE'(m)
276 izip!(
277 data.iter_rows_mut().skip(value.d_a * 2),
278 value.data.iter_rows().skip(value.d_a * 2)
279 )
280 .for_each(|(to_ri, from_ri)| {
281 to_ri.as_mut().copy_from_slice(from_ri.as_ref());
282 });
283
284 // Send polynomials to evaluation domain
285 let ring_size = data.dimension().1;
286 let nttop = N::new(&value.modulus, ring_size);
287 data.iter_rows_mut()
288 .for_each(|ri| nttop.forward(ri.as_mut()));
289
290 Self {
291 data: data,
292 modulus: value.modulus.clone(),
293 _phantom: PhantomData,
294 }
295 }
296}
297
298impl<M: Debug, Mod: Debug, R, N> Debug for RgswCiphertextEvaluationDomain<M, Mod, R, N> {
299 fn fmt(&self, f: &mut std::fmt::Formatter<'_>) -> std::fmt::Result {
300 f.debug_struct("RgswCiphertextEvaluationDomain")
301 .field("data", &self.data)
302 .field("modulus", &self.modulus)
303 .field("_phantom", &self._phantom)
304 .finish()
305 }
306}
307
308impl<M: Matrix, Mod, R, N> Matrix for RgswCiphertextEvaluationDomain<M, Mod, R, N> {
309 type MatElement = M::MatElement;
310 type R = M::R;
311
312 fn dimension(&self) -> (usize, usize) {
313 self.data.dimension()
314 }
315
316 fn fits(&self, row: usize, col: usize) -> bool {
317 self.data.fits(row, col)
318 }
319}
320
321impl<M: Matrix, Mod, R, N> AsRef<[M::R]> for RgswCiphertextEvaluationDomain<M, Mod, R, N> {
322 fn as_ref(&self) -> &[M::R] {
323 self.data.as_ref()
324 }
325}
326
327pub struct ShoupRgswCiphertextEvaluationDomain<M> {
328 pub(crate) data: M,
329}
330
331impl<M: MatrixMut + MatrixEntity, Mod: Modulus<Element = M::MatElement>, R, N>
332 From<&RgswCiphertextEvaluationDomain<M, Mod, R, N>> for ShoupRgswCiphertextEvaluationDomain<M>
333where
334 M::R: RowMut,
335 M::MatElement: ToShoup + Copy,
336{
337 fn from(value: &RgswCiphertextEvaluationDomain<M, Mod, R, N>) -> Self {
338 let (row, col) = value.data.dimension();
339 let mut shoup_data = M::zeros(row, col);
340
341 izip!(shoup_data.iter_rows_mut(), value.data.iter_rows()).for_each(|(shoup_r, r)| {
342 izip!(shoup_r.as_mut().iter_mut(), r.as_ref().iter()).for_each(|(s, e)| {
343 *s = M::MatElement::to_shoup(*e, value.modulus.q().unwrap());
344 });
345 });
346
347 Self { data: shoup_data }
348 }
349}
350
351pub struct SeededRlweCiphertext<R, S, Mod> {
352 pub(crate) data: R,
353 pub(crate) seed: S,
354 pub(crate) modulus: Mod,
355}
356
357impl<R: RowEntity, S, Mod> SeededRlweCiphertext<R, S, Mod> {
358 pub(crate) fn empty(ring_size: usize, seed: S, modulus: Mod) -> Self {
359 SeededRlweCiphertext {
360 data: R::zeros(ring_size),
361 seed,
362 modulus,
363 }
364 }
365}
366
367pub struct RlweCiphertext<M, Rng> {
368 pub(crate) data: M,
369 pub(crate) is_trivial: bool,
370 pub(crate) _phatom: PhantomData<Rng>,
371}
372
373impl<M, Rng> RlweCiphertext<M, Rng> {
374 pub(crate) fn new_trivial(data: M) -> Self {
375 RlweCiphertext {
376 data,
377 is_trivial: true,
378 _phatom: PhantomData,
379 }
380 }
381}
382
383impl<M: Matrix, Rng> Matrix for RlweCiphertext<M, Rng> {
384 type MatElement = M::MatElement;
385 type R = M::R;
386
387 fn dimension(&self) -> (usize, usize) {
388 self.data.dimension()
389 }
390
391 fn fits(&self, row: usize, col: usize) -> bool {
392 self.data.fits(row, col)
393 }
394}
395
396impl<M: MatrixMut, Rng> MatrixMut for RlweCiphertext<M, Rng> where <M as Matrix>::R: RowMut {}
397
398impl<M: Matrix, Rng> AsRef<[<M as Matrix>::R]> for RlweCiphertext<M, Rng> {
399 fn as_ref(&self) -> &[<M as Matrix>::R] {
400 self.data.as_ref()
401 }
402}
403
404impl<M: MatrixMut, Rng> AsMut<[<M as Matrix>::R]> for RlweCiphertext<M, Rng>
405where
406 <M as Matrix>::R: RowMut,
407{
408 fn as_mut(&mut self) -> &mut [<M as Matrix>::R] {
409 self.data.as_mut()
410 }
411}
412
413impl<M, Rng> IsTrivial for RlweCiphertext<M, Rng> {
414 fn is_trivial(&self) -> bool {
415 self.is_trivial
416 }
417 fn set_not_trivial(&mut self) {
418 self.is_trivial = false;
419 }
420}
421
422impl<
423 R: Row,
424 M: MatrixEntity<R = R, MatElement = R::Element> + MatrixMut,
425 Rng: NewWithSeed + RandomFillUniformInModulus<[M::MatElement], Mod>,
426 Mod: Modulus<Element = R::Element>,
427 > From<&SeededRlweCiphertext<R, Rng::Seed, Mod>> for RlweCiphertext<M, Rng>
428where
429 Rng::Seed: Clone,
430 <M as Matrix>::R: RowMut,
431 R::Element: Copy,
432{
433 fn from(value: &SeededRlweCiphertext<R, Rng::Seed, Mod>) -> Self {
434 let mut data = M::zeros(2, value.data.as_ref().len());
435
436 // sample a
437 let mut p_rng = Rng::new_with_seed(value.seed.clone());
438 RandomFillUniformInModulus::random_fill(&mut p_rng, &value.modulus, data.get_row_mut(0));
439
440 data.get_row_mut(1).copy_from_slice(value.data.as_ref());
441
442 RlweCiphertext {
443 data,
444 is_trivial: false,
445 _phatom: PhantomData,
446 }
447 }
448}
449
450pub trait IsTrivial {
451 fn is_trivial(&self) -> bool;
452 fn set_not_trivial(&mut self);
453}
454
455pub struct SeededRlwePublicKey<Ro: Row, S> {
456 data: Ro,
457 seed: S,
458 modulus: Ro::Element,
459}
460
461impl<Ro: RowEntity, S> SeededRlwePublicKey<Ro, S> {
462 pub(crate) fn empty(ring_size: usize, seed: S, modulus: Ro::Element) -> Self {
463 Self {
464 data: Ro::zeros(ring_size),
465 seed,
466 modulus,
467 }
468 }
469}
470
471pub struct RlwePublicKey<M, R> {
472 data: M,
473 _phantom: PhantomData<R>,
474}
475
476impl<
477 M: MatrixMut + MatrixEntity,
478 Rng: NewWithSeed + RandomFillUniformInModulus<[M::MatElement], M::MatElement>,
479 > From<&SeededRlwePublicKey<M::R, Rng::Seed>> for RlwePublicKey<M, Rng>
480where
481 <M as Matrix>::R: RowMut,
482 M::MatElement: Copy,
483 Rng::Seed: Copy,
484{
485 fn from(value: &SeededRlwePublicKey<M::R, Rng::Seed>) -> Self {
486 let mut data = M::zeros(2, value.data.as_ref().len());
487
488 // sample a
489 let mut p_rng = Rng::new_with_seed(value.seed);
490 RandomFillUniformInModulus::random_fill(&mut p_rng, &value.modulus, data.get_row_mut(0));
491
492 // copy over b
493 data.get_row_mut(1).copy_from_slice(value.data.as_ref());
494
495 Self {
496 data,
497 _phantom: PhantomData,
498 }
499 }
500}
501
502#[derive(Clone)]
503pub struct RlweSecret {
504 pub(crate) values: Vec<i32>,
505}
506
507impl Secret for RlweSecret {
508 type Element = i32;
509 fn values(&self) -> &[Self::Element] {
510 &self.values
511 }
512}
513
514impl RlweSecret {
515 pub fn random(hw: usize, n: usize) -> RlweSecret {
516 DefaultSecureRng::with_local_mut(|rng| {
517 let mut out = vec![0i32; n];
518 fill_random_ternary_secret_with_hamming_weight(&mut out, hw, rng);
519
520 RlweSecret { values: out }
521 })
522 }
523}
524
525#[cfg(test)]
526pub(crate) mod tests {
527 use std::{marker::PhantomData, ops::Mul, vec};
528
529 use itertools::{izip, Itertools};
530 use rand::{thread_rng, Rng};
531
532 use crate::{
533 backend::{GetModulus, ModInit, ModularOpsU64, Modulus, VectorOps},
534 decomposer::{Decomposer, DefaultDecomposer, RlweDecomposer},
535 ntt::{self, Ntt, NttBackendU64, NttInit},
536 random::{DefaultSecureRng, NewWithSeed, RandomFillUniformInModulus},
537 rgsw::{
538 galois_auto_shoup, rlwe_by_rgsw_shoup, ShoupAutoKeyEvaluationDomain,
539 ShoupRgswCiphertextEvaluationDomain,
540 },
541 utils::{generate_prime, negacyclic_mul, Stats, TryConvertFrom1},
542 Matrix, Secret,
543 };
544
545 use super::{
546 keygen::{
547 decrypt_rlwe, galois_key_gen, gen_rlwe_public_key, generate_auto_map, measure_noise,
548 public_key_encrypt_rgsw, secret_key_encrypt_rgsw, secret_key_encrypt_rlwe,
549 },
550 runtime::{galois_auto, rgsw_by_rgsw_inplace, rlwe_by_rgsw},
551 AutoKeyEvaluationDomain, RgswCiphertext, RgswCiphertextEvaluationDomain, RlweCiphertext,
552 RlwePublicKey, RlweSecret, SeededAutoKey, SeededRgswCiphertext, SeededRlweCiphertext,
553 SeededRlwePublicKey,
554 };
555
556 pub(crate) fn _sk_encrypt_rlwe<T: Modulus<Element = u64> + Clone>(
557 m: &[u64],
558 s: &[i32],
559 ntt_op: &NttBackendU64,
560 mod_op: &ModularOpsU64<T>,
561 ) -> RlweCiphertext<Vec<Vec<u64>>, DefaultSecureRng> {
562 let ring_size = m.len();
563 let q = mod_op.modulus();
564 assert!(s.len() == ring_size);
565
566 let mut rng = DefaultSecureRng::new();
567 let mut rlwe_seed = [0u8; 32];
568 rng.fill_bytes(&mut rlwe_seed);
569 let mut seeded_rlwe_ct =
570 SeededRlweCiphertext::<_, [u8; 32], _>::empty(ring_size as usize, rlwe_seed, q.clone());
571 let mut p_rng = DefaultSecureRng::new_seeded(rlwe_seed);
572 secret_key_encrypt_rlwe(
573 &m,
574 &mut seeded_rlwe_ct.data,
575 s,
576 mod_op,
577 ntt_op,
578 &mut p_rng,
579 &mut rng,
580 );
581
582 RlweCiphertext::<Vec<Vec<u64>>, DefaultSecureRng>::from(&seeded_rlwe_ct)
583 }
584
585 // Encrypt m as RGSW ciphertext RGSW(m) using supplied public key
586 pub(crate) fn _pk_encrypt_rgsw<T: Modulus<Element = u64> + Clone>(
587 m: &[u64],
588 public_key: &RlwePublicKey<Vec<Vec<u64>>, DefaultSecureRng>,
589 decomposer: &(DefaultDecomposer<u64>, DefaultDecomposer<u64>),
590 mod_op: &ModularOpsU64<T>,
591 ntt_op: &NttBackendU64,
592 ) -> RgswCiphertext<Vec<Vec<u64>>, T> {
593 let (_, ring_size) = Matrix::dimension(&public_key.data);
594 let gadget_vector_a = decomposer.a().gadget_vector();
595 let gadget_vector_b = decomposer.b().gadget_vector();
596
597 let mut rng = DefaultSecureRng::new();
598
599 assert!(m.len() == ring_size);
600
601 // public key encrypt RGSW(m1)
602 let mut rgsw_ct = RgswCiphertext::empty(ring_size, decomposer, mod_op.modulus().clone());
603 public_key_encrypt_rgsw(
604 &mut rgsw_ct.data,
605 m,
606 &public_key.data,
607 &gadget_vector_a,
608 &gadget_vector_b,
609 mod_op,
610 ntt_op,
611 &mut rng,
612 );
613
614 rgsw_ct
615 }
616
617 /// Encrypts m as RGSW ciphertext RGSW(m) using supplied secret key. Returns
618 /// unseeded RGSW ciphertext in coefficient domain
619 pub(crate) fn _sk_encrypt_rgsw<T: Modulus<Element = u64> + Clone>(
620 m: &[u64],
621 s: &[i32],
622 decomposer: &(DefaultDecomposer<u64>, DefaultDecomposer<u64>),
623 mod_op: &ModularOpsU64<T>,
624 ntt_op: &NttBackendU64,
625 ) -> SeededRgswCiphertext<Vec<Vec<u64>>, [u8; 32], T> {
626 let ring_size = s.len();
627 assert!(m.len() == s.len());
628
629 let q = mod_op.modulus();
630
631 let gadget_vector_a = decomposer.a().gadget_vector();
632 let gadget_vector_b = decomposer.b().gadget_vector();
633
634 let mut rng = DefaultSecureRng::new();
635 let mut rgsw_seed = [0u8; 32];
636 rng.fill_bytes(&mut rgsw_seed);
637 let mut seeded_rgsw_ct = SeededRgswCiphertext::<Vec<Vec<u64>>, [u8; 32], T>::empty(
638 ring_size as usize,
639 decomposer,
640 rgsw_seed,
641 q.clone(),
642 );
643 let mut p_rng = DefaultSecureRng::new_seeded(rgsw_seed);
644 secret_key_encrypt_rgsw(
645 &mut seeded_rgsw_ct.data,
646 m,
647 &gadget_vector_a,
648 &gadget_vector_b,
649 s,
650 mod_op,
651 ntt_op,
652 &mut p_rng,
653 &mut rng,
654 );
655 seeded_rgsw_ct
656 }
657
658 /// Prints noise in RGSW ciphertext RGSW(m).
659 ///
660 /// - rgsw_ct: RGSW ciphertext in coefficient domain
661 pub(crate) fn _measure_noise_rgsw<T: Modulus<Element = u64> + Clone>(
662 rgsw_ct: &[Vec<u64>],
663 m: &[u64],
664 s: &[i32],
665 decomposer: &(DefaultDecomposer<u64>, DefaultDecomposer<u64>),
666 q: &T,
667 ) {
668 let gadget_vector_a = decomposer.a().gadget_vector();
669 let gadget_vector_b = decomposer.b().gadget_vector();
670 let d_a = gadget_vector_a.len();
671 let d_b = gadget_vector_b.len();
672 let ring_size = s.len();
673 assert!(Matrix::dimension(&rgsw_ct) == (d_a * 2 + d_b * 2, ring_size));
674 assert!(m.len() == ring_size);
675
676 let mod_op = ModularOpsU64::new(q.clone());
677 let ntt_op = NttBackendU64::new(q, ring_size);
678
679 let mul_mod =
680 |a: &u64, b: &u64| ((*a as u128 * *b as u128) % q.q().unwrap() as u128) as u64;
681 let s_poly = Vec::<u64>::try_convert_from(s, q);
682 let mut neg_s = s_poly.clone();
683 mod_op.elwise_neg_mut(neg_s.as_mut());
684 let neg_sm0m1 = negacyclic_mul(&neg_s, &m, mul_mod, q.q().unwrap());
685
686 // RLWE(\beta^j -s * m)
687 for j in 0..d_a {
688 let ideal_m = {
689 // RLWE(\beta^j -s * m)
690 let mut beta_neg_sm0m1 = vec![0u64; ring_size as usize];
691 mod_op.elwise_scalar_mul(beta_neg_sm0m1.as_mut(), &neg_sm0m1, &gadget_vector_a[j]);
692 beta_neg_sm0m1
693 };
694
695 let mut rlwe = vec![vec![0u64; ring_size as usize]; 2];
696 rlwe[0].copy_from_slice(rgsw_ct.get_row_slice(j));
697 rlwe[1].copy_from_slice(rgsw_ct.get_row_slice(d_a + j));
698 let noise = measure_noise(&rlwe, &ideal_m, &ntt_op, &mod_op, s);
699
700 println!(r"Noise RLWE(\beta^{j} -sm0m1): {noise}");
701 }
702
703 // RLWE(\beta^j m)
704 for j in 0..d_b {
705 let ideal_m = {
706 // RLWE(\beta^j m)
707 let mut beta_m0m1 = vec![0u64; ring_size as usize];
708 mod_op.elwise_scalar_mul(beta_m0m1.as_mut(), &m, &gadget_vector_b[j]);
709 beta_m0m1
710 };
711
712 let mut rlwe = vec![vec![0u64; ring_size as usize]; 2];
713 rlwe[0].copy_from_slice(rgsw_ct.get_row_slice(d_a * 2 + j));
714 rlwe[1].copy_from_slice(rgsw_ct.get_row_slice(d_a * 2 + d_b + j));
715 let noise = measure_noise(&rlwe, &ideal_m, &ntt_op, &mod_op, s);
716
717 println!(r"Noise RLWE(\beta^{j} m0m1): {noise}");
718 }
719 }
720
721 #[test]
722 fn rlwe_encrypt_decryption() {
723 let logq = 50;
724 let logp = 2;
725 let ring_size = 1 << 4;
726 let q = generate_prime(logq, ring_size, 1u64 << logq).unwrap();
727 let p = 1u64 << logp;
728
729 let mut rng = DefaultSecureRng::new();
730
731 let s = RlweSecret::random((ring_size >> 1) as usize, ring_size as usize);
732
733 // sample m0
734 let mut m0 = vec![0u64; ring_size as usize];
735 RandomFillUniformInModulus::<[u64], u64>::random_fill(
736 &mut rng,
737 &(1u64 << logp),
738 m0.as_mut_slice(),
739 );
740
741 let ntt_op = NttBackendU64::new(&q, ring_size as usize);
742 let mod_op = ModularOpsU64::new(q);
743
744 // encrypt m0
745 let encoded_m = m0
746 .iter()
747 .map(|v| (((*v as f64) * q as f64) / (p as f64)).round() as u64)
748 .collect_vec();
749 let rlwe_in_ct = _sk_encrypt_rlwe(&encoded_m, s.values(), &ntt_op, &mod_op);
750
751 let mut encoded_m_back = vec![0u64; ring_size as usize];
752 decrypt_rlwe(
753 &rlwe_in_ct,
754 s.values(),
755 &mut encoded_m_back,
756 &ntt_op,
757 &mod_op,
758 );
759 let m_back = encoded_m_back
760 .iter()
761 .map(|v| (((*v as f64 * p as f64) / q as f64).round() as u64) % p)
762 .collect_vec();
763 assert_eq!(m0, m_back);
764
765 // let noise = measure_noise(&rlwe_in_ct, &encoded_m, &ntt_op, &mod_op,
766 // s.values()); println!("Noise: {noise}");
767 }
768
769 #[test]
770 fn rlwe_by_rgsw_works() {
771 let logq = 50;
772 let logp = 2;
773 let ring_size = 1 << 9;
774 let q = generate_prime(logq, ring_size, 1u64 << logq).unwrap();
775 let p: u64 = 1u64 << logp;
776
777 let mut rng = DefaultSecureRng::new_seeded([0u8; 32]);
778
779 let s = RlweSecret::random((ring_size >> 1) as usize, ring_size as usize);
780
781 let mut m0 = vec![0u64; ring_size as usize];
782 RandomFillUniformInModulus::<[u64], _>::random_fill(
783 &mut rng,
784 &(1u64 << logp),
785 m0.as_mut_slice(),
786 );
787 let mut m1 = vec![0u64; ring_size as usize];
788 m1[thread_rng().gen_range(0..ring_size) as usize] = 1;
789
790 let ntt_op = NttBackendU64::new(&q, ring_size as usize);
791 let mod_op = ModularOpsU64::new(q);
792 let d_rgsw = 10;
793 let logb = 5;
794 let decomposer = (
795 DefaultDecomposer::new(q, logb, d_rgsw),
796 DefaultDecomposer::new(q, logb, d_rgsw),
797 );
798
799 // create public key
800 let mut pk_seed = [0u8; 32];
801 rng.fill_bytes(&mut pk_seed);
802 let mut pk_prng = DefaultSecureRng::new_seeded(pk_seed);
803 let mut seeded_pk =
804 SeededRlwePublicKey::<Vec<u64>, _>::empty(ring_size as usize, pk_seed, q);
805 gen_rlwe_public_key(
806 &mut seeded_pk.data,
807 s.values(),
808 &ntt_op,
809 &mod_op,
810 &mut pk_prng,
811 &mut rng,
812 );
813 let pk = RlwePublicKey::<Vec<Vec<u64>>, DefaultSecureRng>::from(&seeded_pk);
814
815 // Encrypt m1 as RGSW(m1)
816 let rgsw_ct = {
817 //TODO(Jay): Figure out better way to test secret key and public key variant of
818 // RGSW ciphertext encryption within the same test
819
820 if true {
821 // Encryption m1 as RGSW(m1) using secret key
822 let seeded_rgsw_ct =
823 _sk_encrypt_rgsw(&m1, s.values(), &decomposer, &mod_op, &ntt_op);
824 RgswCiphertextEvaluationDomain::<Vec<Vec<u64>>, _,DefaultSecureRng, NttBackendU64>::from(&seeded_rgsw_ct)
825 } else {
826 // Encrypt m1 as RGSW(m1) using public key
827 let rgsw_ct = _pk_encrypt_rgsw(&m1, &pk, &decomposer, &mod_op, &ntt_op);
828 RgswCiphertextEvaluationDomain::<_, _, DefaultSecureRng, NttBackendU64>::from(
829 &rgsw_ct,
830 )
831 }
832 };
833
834 // Encrypt m0 as RLWE(m0)
835 let mut rlwe_in_ct = {
836 let encoded_m = m0
837 .iter()
838 .map(|v| (((*v as f64) * q as f64) / (p as f64)).round() as u64)
839 .collect_vec();
840
841 _sk_encrypt_rlwe(&encoded_m, s.values(), &ntt_op, &mod_op)
842 };
843
844 // RLWE(m0m1) = RLWE(m0) x RGSW(m1)
845 let mut scratch_space = vec![
846 vec![0u64; ring_size as usize];
847 std::cmp::max(
848 decomposer.a().decomposition_count(),
849 decomposer.b().decomposition_count()
850 ) + 2
851 ];
852
853 // rlwe x rgsw with additional RGSW ciphertexts in shoup repr
854 let rlwe_in_ct_shoup = {
855 let mut rlwe_in_ct_shoup = RlweCiphertext::<_, DefaultSecureRng> {
856 data: rlwe_in_ct.data.clone(),
857 is_trivial: rlwe_in_ct.is_trivial,
858 _phatom: PhantomData::default(),
859 };
860
861 let rgsw_ct_shoup = ShoupRgswCiphertextEvaluationDomain::from(&rgsw_ct);
862
863 rlwe_by_rgsw_shoup(
864 &mut rlwe_in_ct_shoup,
865 &rgsw_ct.data,
866 &rgsw_ct_shoup.data,
867 &mut scratch_space,
868 &decomposer,
869 &ntt_op,
870 &mod_op,
871 );
872
873 rlwe_in_ct_shoup
874 };
875
876 // rlwe x rgsw normal
877 {
878 rlwe_by_rgsw(
879 &mut rlwe_in_ct,
880 &rgsw_ct.data,
881 &mut scratch_space,
882 &decomposer,
883 &ntt_op,
884 &mod_op,
885 );
886 }
887
888 // output from both functions must be equal
889 {
890 assert_eq!(rlwe_in_ct.data, rlwe_in_ct_shoup.data);
891 }
892
893 // Decrypt RLWE(m0m1)
894 let mut encoded_m0m1_back = vec![0u64; ring_size as usize];
895 decrypt_rlwe(
896 &rlwe_in_ct,
897 s.values(),
898 &mut encoded_m0m1_back,
899 &ntt_op,
900 &mod_op,
901 );
902 let m0m1_back = encoded_m0m1_back
903 .iter()
904 .map(|v| (((*v as f64 * p as f64) / (q as f64)).round() as u64) % p)
905 .collect_vec();
906
907 let mul_mod = |v0: &u64, v1: &u64| (v0 * v1) % p;
908 let m0m1 = negacyclic_mul(&m0, &m1, mul_mod, p);
909
910 // {
911 // // measure noise
912 // let encoded_m_ideal = m0m1
913 // .iter()
914 // .map(|v| (((*v as f64) * q as f64) / (p as f64)).round() as u64)
915 // .collect_vec();
916
917 // let noise = measure_noise(&rlwe_in_ct, &encoded_m_ideal, &ntt_op,
918 // &mod_op, s.values()); println!("Noise RLWE(m0m1)(=
919 // RLWE(m0)xRGSW(m1)) : {noise}"); }
920
921 assert!(
922 m0m1 == m0m1_back,
923 "Expected {:?} \n Got {:?}",
924 m0m1,
925 m0m1_back
926 );
927 }
928
929 #[test]
930 fn galois_auto_works() {
931 let logq = 55;
932 let ring_size = 1 << 11;
933 let q = generate_prime(logq, 2 * ring_size, 1u64 << logq).unwrap();
934 let logp = 3;
935 let p = 1u64 << logp;
936 let d_rgsw = 5;
937 let logb = 11;
938
939 let mut rng = DefaultSecureRng::new();
940 let s = RlweSecret::random((ring_size >> 1) as usize, ring_size as usize);
941
942 let mut m = vec![0u64; ring_size as usize];
943 RandomFillUniformInModulus::random_fill(&mut rng, &p, m.as_mut_slice());
944 let encoded_m = m
945 .iter()
946 .map(|v| (((*v as f64 * q as f64) / (p as f64)).round() as u64))
947 .collect_vec();
948
949 let ntt_op = NttBackendU64::new(&q, ring_size as usize);
950 let mod_op = ModularOpsU64::new(q);
951
952 // RLWE_{s}(m)
953 let mut seed_rlwe = [0u8; 32];
954 rng.fill_bytes(&mut seed_rlwe);
955 let mut seeded_rlwe_m = SeededRlweCiphertext::empty(ring_size as usize, seed_rlwe, q);
956 let mut p_rng = DefaultSecureRng::new_seeded(seed_rlwe);
957 secret_key_encrypt_rlwe(
958 &encoded_m,
959 &mut seeded_rlwe_m.data,
960 s.values(),
961 &mod_op,
962 &ntt_op,
963 &mut p_rng,
964 &mut rng,
965 );
966 let mut rlwe_m = RlweCiphertext::<Vec<Vec<u64>>, DefaultSecureRng>::from(&seeded_rlwe_m);
967
968 let auto_k = -125;
969
970 // Generate galois key to key switch from s^k to s
971 let decomposer = DefaultDecomposer::new(q, logb, d_rgsw);
972 let mut seed_auto = [0u8; 32];
973 rng.fill_bytes(&mut seed_auto);
974 let mut seeded_auto_key =
975 SeededAutoKey::empty(ring_size as usize, &decomposer, seed_auto, q);
976 let mut p_rng = DefaultSecureRng::new_seeded(seed_auto);
977 let gadget_vector = decomposer.gadget_vector();
978 galois_key_gen(
979 &mut seeded_auto_key.data,
980 s.values(),
981 auto_k,
982 &gadget_vector,
983 &mod_op,
984 &ntt_op,
985 &mut p_rng,
986 &mut rng,
987 );
988 let auto_key =
989 AutoKeyEvaluationDomain::<Vec<Vec<u64>>, _, DefaultSecureRng, NttBackendU64>::from(
990 &seeded_auto_key,
991 );
992
993 // Send RLWE_{s}(m) -> RLWE_{s}(m^k)
994 let mut scratch_space = vec![vec![0u64; ring_size as usize]; d_rgsw + 2];
995 let (auto_map_index, auto_map_sign) = generate_auto_map(ring_size as usize, auto_k);
996
997 // galois auto with additional auto key in shoup repr
998 let rlwe_m_shoup = {
999 let auto_key_shoup = ShoupAutoKeyEvaluationDomain::from(&auto_key);
1000 let mut rlwe_m_shoup = RlweCiphertext::<_, DefaultSecureRng> {
1001 data: rlwe_m.data.clone(),
1002 is_trivial: rlwe_m.is_trivial,
1003 _phatom: PhantomData::default(),
1004 };
1005 galois_auto_shoup(
1006 &mut rlwe_m_shoup,
1007 &auto_key.data,
1008 &auto_key_shoup.data,
1009 &mut scratch_space,
1010 &auto_map_index,
1011 &auto_map_sign,
1012 &mod_op,
1013 &ntt_op,
1014 &decomposer,
1015 );
1016 rlwe_m_shoup
1017 };
1018
1019 // normal galois auto
1020 {
1021 galois_auto(
1022 &mut rlwe_m,
1023 &auto_key.data,
1024 &mut scratch_space,
1025 &auto_map_index,
1026 &auto_map_sign,
1027 &mod_op,
1028 &ntt_op,
1029 &decomposer,
1030 );
1031 }
1032
1033 // rlwe out from both functions must be same
1034 assert_eq!(rlwe_m.data, rlwe_m_shoup.data);
1035
1036 let rlwe_m_k = rlwe_m;
1037
1038 // Decrypt RLWE_{s}(m^k) and check
1039 let mut encoded_m_k_back = vec![0u64; ring_size as usize];
1040 decrypt_rlwe(
1041 &rlwe_m_k,
1042 s.values(),
1043 &mut encoded_m_k_back,
1044 &ntt_op,
1045 &mod_op,
1046 );
1047 let m_k_back = encoded_m_k_back
1048 .iter()
1049 .map(|v| (((*v as f64 * p as f64) / q as f64).round() as u64) % p)
1050 .collect_vec();
1051
1052 let mut m_k = vec![0u64; ring_size as usize];
1053 // Send \delta m -> \delta m^k
1054 izip!(m.iter(), auto_map_index.iter(), auto_map_sign.iter()).for_each(
1055 |(v, to_index, sign)| {
1056 if !*sign {
1057 m_k[*to_index] = (p - *v) % p;
1058 } else {
1059 m_k[*to_index] = *v;
1060 }
1061 },
1062 );
1063
1064 {
1065 let encoded_m_k = m_k
1066 .iter()
1067 .map(|v| ((*v as f64 * q as f64) / p as f64).round() as u64)
1068 .collect_vec();
1069
1070 let noise = measure_noise(&rlwe_m_k, &encoded_m_k, &ntt_op, &mod_op, s.values());
1071 println!("Ksk noise: {noise}");
1072 }
1073
1074 assert_eq!(m_k_back, m_k);
1075 }
1076
1077 #[test]
1078 fn sk_rgsw_by_rgsw() {
1079 let logq = 60;
1080 let logp = 2;
1081 let ring_size = 1 << 11;
1082 let q = generate_prime(logq, ring_size, 1u64 << logq).unwrap();
1083 let p = 1u64 << logp;
1084 let d_rgsw = 5;
1085 let logb = 12;
1086
1087 let s = RlweSecret::random((ring_size >> 1) as usize, ring_size as usize);
1088
1089 let mut rng = DefaultSecureRng::new();
1090 let ntt_op = NttBackendU64::new(&q, ring_size as usize);
1091 let mod_op = ModularOpsU64::new(q);
1092 let decomposer = (
1093 DefaultDecomposer::new(q, logb, d_rgsw),
1094 DefaultDecomposer::new(q, logb, d_rgsw),
1095 );
1096
1097 let mul_mod = |a: &u64, b: &u64| ((*a as u128 * *b as u128) % q as u128) as u64;
1098
1099 let mut carry_m = vec![0u64; ring_size as usize];
1100 carry_m[thread_rng().gen_range(0..ring_size) as usize] = 1;
1101
1102 // RGSW(carry_m)
1103 let mut rgsw_carrym = {
1104 let seeded_rgsw = _sk_encrypt_rgsw(&carry_m, s.values(), &decomposer, &mod_op, &ntt_op);
1105 let mut rgsw_eval =
1106 RgswCiphertextEvaluationDomain::<_, _, DefaultSecureRng, NttBackendU64>::from(
1107 &seeded_rgsw,
1108 );
1109 rgsw_eval
1110 .data
1111 .iter_mut()
1112 .for_each(|ri| ntt_op.backward(ri.as_mut()));
1113 rgsw_eval.data
1114 };
1115
1116 let mut scratch_matrix = vec![
1117 vec![0u64; ring_size as usize];
1118 decomposer.a().decomposition_count() * 2
1119 + decomposer.b().decomposition_count() * 2
1120 + std::cmp::max(
1121 decomposer.a().decomposition_count(),
1122 decomposer.b().decomposition_count()
1123 )
1124 ];
1125
1126 _measure_noise_rgsw(&rgsw_carrym, &carry_m, s.values(), &decomposer, &q);
1127
1128 for i in 0..2 {
1129 let mut m = vec![0u64; ring_size as usize];
1130 m[thread_rng().gen_range(0..ring_size) as usize] = if (i & 1) == 1 { q - 1 } else { 1 };
1131 let rgsw_m =
1132 RgswCiphertextEvaluationDomain::<_, _, DefaultSecureRng, NttBackendU64>::from(
1133 &_sk_encrypt_rgsw(&m, s.values(), &decomposer, &mod_op, &ntt_op),
1134 );
1135 rgsw_by_rgsw_inplace(
1136 &mut rgsw_carrym,
1137 &rgsw_m.data,
1138 &decomposer,
1139 &mut scratch_matrix,
1140 &ntt_op,
1141 &mod_op,
1142 );
1143
1144 // measure noise
1145 carry_m = negacyclic_mul(&carry_m, &m, mul_mod, q);
1146 println!("########### Noise RGSW(carrym) in {i}^th loop ###########");
1147 _measure_noise_rgsw(&rgsw_carrym, &carry_m, s.values(), &decomposer, &q);
1148 }
1149 {
1150 // RLWE(m) x RGSW(carry_m)
1151 let mut m = vec![0u64; ring_size as usize];
1152 RandomFillUniformInModulus::random_fill(&mut rng, &q, m.as_mut_slice());
1153 let mut rlwe_ct = _sk_encrypt_rlwe(&m, s.values(), &ntt_op, &mod_op);
1154
1155 // send rgsw to evaluation domain
1156 rgsw_carrym
1157 .iter_mut()
1158 .for_each(|ri| ntt_op.forward(ri.as_mut_slice()));
1159
1160 rlwe_by_rgsw(
1161 &mut rlwe_ct,
1162 &rgsw_carrym,
1163 &mut scratch_matrix,
1164 &decomposer,
1165 &ntt_op,
1166 &mod_op,
1167 );
1168 let m_expected = negacyclic_mul(&carry_m, &m, mul_mod, q);
1169 let noise = measure_noise(&rlwe_ct, &m_expected, &ntt_op, &mod_op, s.values());
1170 println!("RLWE(m) x RGSW(carry_m): {noise}");
1171 }
1172 }
1173
1174 #[test]
1175 fn some_work() {
1176 let logq = 50;
1177 let ring_size = 1 << 11;
1178 let q = generate_prime(logq, ring_size, 1u64 << logq).unwrap();
1179 let d_rgsw = 10;
1180 let logb = 5;
1181 let decomposer = (
1182 DefaultDecomposer::new(q, logb, d_rgsw),
1183 DefaultDecomposer::new(q, logb, d_rgsw),
1184 );
1185
1186 let ntt_op = NttBackendU64::new(&q, ring_size as usize);
1187 let mod_op = ModularOpsU64::new(q);
1188 let mut rng = DefaultSecureRng::new_seeded([0u8; 32]);
1189
1190 let s = RlweSecret::random((ring_size >> 1) as usize, ring_size as usize);
1191
1192 let mut check = Stats { samples: vec![] };
1193
1194 for _ in 0..100 {
1195 let mut m0 = vec![0u64; ring_size as usize];
1196 m0[thread_rng().gen_range(0..ring_size) as usize] = 1;
1197 let mut m1 = vec![0u64; ring_size as usize];
1198 m1[thread_rng().gen_range(0..ring_size) as usize] = 1;
1199
1200 let mut rgsw_ct0 = {
1201 let seeded_rgsw_ct =
1202 _sk_encrypt_rgsw(&m0, s.values(), &decomposer, &mod_op, &ntt_op);
1203 RgswCiphertextEvaluationDomain::<Vec<Vec<u64>>, _,DefaultSecureRng, NttBackendU64>::from(&seeded_rgsw_ct)
1204 };
1205 let rgsw_ct1 = {
1206 let seeded_rgsw_ct =
1207 _sk_encrypt_rgsw(&m1, s.values(), &decomposer, &mod_op, &ntt_op);
1208 RgswCiphertextEvaluationDomain::<Vec<Vec<u64>>,_, DefaultSecureRng, NttBackendU64>::from(&seeded_rgsw_ct)
1209 };
1210
1211 // RGSW x RGSW
1212 // send RGSW(m0) to coefficient domain
1213 rgsw_ct0
1214 .data
1215 .iter_mut()
1216 .for_each(|r| ntt_op.backward(r.as_mut_slice()));
1217 let mut scratch_matrix = vec![
1218 vec![0u64; ring_size as usize];
1219 std::cmp::max(
1220 decomposer.a().decomposition_count(),
1221 decomposer.b().decomposition_count()
1222 ) + decomposer.a().decomposition_count() * 2
1223 + decomposer.b().decomposition_count() * 2
1224 ];
1225 rgsw_by_rgsw_inplace(
1226 &mut rgsw_ct0.data,
1227 &rgsw_ct1.data,
1228 &decomposer,
1229 &mut scratch_matrix,
1230 &ntt_op,
1231 &mod_op,
1232 );
1233 let mut rgsw_m0m1 = rgsw_ct0;
1234 // Back to Evaluation for RLWExRGSW
1235 rgsw_m0m1
1236 .data
1237 .iter_mut()
1238 .for_each(|r| ntt_op.forward(r.as_mut_slice()));
1239
1240 // Sample m2, encrypt it as RLWE(m2) and multiply RLWE(m2)xRGSW(m0m1)
1241 let mut m2 = vec![0u64; ring_size as usize];
1242 RandomFillUniformInModulus::random_fill(&mut rng, &q, m2.as_mut_slice());
1243 let mut rlwe_in_ct = { _sk_encrypt_rlwe(&m2, s.values(), &ntt_op, &mod_op) };
1244 let mut scratch_space = vec![
1245 vec![0u64; ring_size as usize];
1246 std::cmp::max(
1247 decomposer.a().decomposition_count(),
1248 decomposer.b().decomposition_count()
1249 ) + 2
1250 ];
1251 rlwe_by_rgsw(
1252 &mut rlwe_in_ct,
1253 &rgsw_m0m1.data,
1254 &mut scratch_space,
1255 &decomposer,
1256 &ntt_op,
1257 &mod_op,
1258 );
1259
1260 // Decrypt RLWE(m0m1m2)
1261 let mut m0m1m2_back = vec![0u64; ring_size as usize];
1262 decrypt_rlwe(&rlwe_in_ct, s.values(), &mut m0m1m2_back, &ntt_op, &mod_op);
1263
1264 // Calculate m0m1m2
1265 let mul_mod = |v0: &u64, v1: &u64| ((*v0 as u128 * *v1 as u128) % q as u128) as u64;
1266 let m0m1 = negacyclic_mul(&m0, &m1, mul_mod, q);
1267 let m0m1m2 = negacyclic_mul(&m2, &m0m1, mul_mod, q);
1268
1269 // diff
1270 mod_op.elwise_sub_mut(m0m1m2_back.as_mut_slice(), m0m1m2.as_ref());
1271
1272 check.add_more(&Vec::<i64>::try_convert_from(&m0m1m2_back, &q));
1273 }
1274
1275 println!("Std: {}", check.std_dev().abs().log2());
1276 }
1277}