phantom-zone/src/rgsw.rs
src/rgsw.rsRaw
1use std::{
2 clone,
3 fmt::Debug,
4 marker::PhantomData,
5 ops::{Div, Neg, Sub},
6};
7
8use itertools::{izip, Itertools};
9use num_traits::{PrimInt, Signed, ToPrimitive, Zero};
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, TryConvertFrom1, WithLocal},
20 Matrix, MatrixEntity, MatrixMut, Row, RowEntity, RowMut, Secret,
21};
22
23pub struct SeededAutoKey<M, S, Mod>
24where
25 M: Matrix,
26{
27 data: M,
28 seed: S,
29 modulus: Mod,
30}
31
32impl<M: Matrix + MatrixEntity, S, Mod: Modulus<Element = M::MatElement>> SeededAutoKey<M, S, Mod> {
33 fn empty<D: Decomposer>(ring_size: usize, auto_decomposer: &D, seed: S, modulus: Mod) -> Self {
34 SeededAutoKey {
35 data: M::zeros(auto_decomposer.decomposition_count(), ring_size),
36 seed,
37 modulus,
38 }
39 }
40}
41
42pub struct AutoKeyEvaluationDomain<M, R, N> {
43 data: M,
44 _phantom: PhantomData<(R, N)>,
45}
46
47impl<
48 M: MatrixMut + MatrixEntity,
49 Mod: Modulus<Element = M::MatElement> + Clone,
50 R: RandomFillUniformInModulus<[M::MatElement], Mod> + NewWithSeed,
51 N: NttInit<Mod> + Ntt<Element = M::MatElement>,
52 > From<&SeededAutoKey<M, R::Seed, Mod>> for AutoKeyEvaluationDomain<M, R, N>
53where
54 <M as Matrix>::R: RowMut,
55 M::MatElement: Copy,
56 R::Seed: Clone,
57{
58 fn from(value: &SeededAutoKey<M, R::Seed, Mod>) -> Self {
59 let (d, ring_size) = value.data.dimension();
60 let mut data = M::zeros(2 * d, ring_size);
61
62 // sample RLWE'_A(-s(X^k))
63 let mut p_rng = R::new_with_seed(value.seed.clone());
64 data.iter_rows_mut().take(d).for_each(|r| {
65 RandomFillUniformInModulus::random_fill(&mut p_rng, &value.modulus, r.as_mut());
66 });
67
68 // copy over RLWE'_B(-s(X^k))
69 izip!(data.iter_rows_mut().skip(d), value.data.iter_rows()).for_each(|(to_r, from_r)| {
70 to_r.as_mut().copy_from_slice(from_r.as_ref());
71 });
72
73 // send RLWE'(-s(X^k)) polynomials to evaluation domain
74 let ntt_op = N::new(&value.modulus, ring_size);
75 data.iter_rows_mut()
76 .for_each(|r| ntt_op.forward(r.as_mut()));
77
78 AutoKeyEvaluationDomain {
79 data,
80 _phantom: PhantomData,
81 }
82 }
83}
84
85pub struct RgswCiphertext<M: Matrix, Mod> {
86 /// Rgsw ciphertext polynomials
87 pub(crate) data: M,
88 modulus: Mod,
89 /// Decomposition for RLWE part A
90 d_a: usize,
91 /// Decomposition for RLWE part B
92 d_b: usize,
93}
94
95impl<M: MatrixEntity, Mod: Modulus<Element = M::MatElement>> RgswCiphertext<M, Mod> {
96 pub(crate) fn empty<D: RlweDecomposer>(
97 ring_size: usize,
98 decomposer: &D,
99 modulus: Mod,
100 ) -> RgswCiphertext<M, Mod> {
101 RgswCiphertext {
102 data: M::zeros(
103 decomposer.a().decomposition_count() * 2 + decomposer.b().decomposition_count() * 2,
104 ring_size,
105 ),
106 d_a: decomposer.a().decomposition_count(),
107 d_b: decomposer.b().decomposition_count(),
108 modulus,
109 }
110 }
111}
112
113pub struct SeededRgswCiphertext<M, S, Mod>
114where
115 M: Matrix,
116{
117 pub(crate) data: M,
118 seed: S,
119 modulus: Mod,
120 /// Decomposition for RLWE part A
121 d_a: usize,
122 /// Decomposition for RLWE part B
123 d_b: usize,
124}
125
126impl<M: Matrix + MatrixEntity, S, Mod> SeededRgswCiphertext<M, S, Mod> {
127 pub(crate) fn empty<D: RlweDecomposer>(
128 ring_size: usize,
129 decomposer: &D,
130 seed: S,
131 modulus: Mod,
132 ) -> SeededRgswCiphertext<M, S, Mod> {
133 SeededRgswCiphertext {
134 data: M::zeros(
135 decomposer.a().decomposition_count() * 2 + decomposer.b().decomposition_count(),
136 ring_size,
137 ),
138 seed,
139 modulus,
140 d_a: decomposer.a().decomposition_count(),
141 d_b: decomposer.b().decomposition_count(),
142 }
143 }
144}
145
146impl<M: Debug + Matrix, S: Debug, Mod: Debug> Debug for SeededRgswCiphertext<M, S, Mod>
147where
148 M::MatElement: Debug,
149{
150 fn fmt(&self, f: &mut std::fmt::Formatter<'_>) -> std::fmt::Result {
151 f.debug_struct("SeededRgswCiphertext")
152 .field("data", &self.data)
153 .field("seed", &self.seed)
154 .field("modulus", &self.modulus)
155 .finish()
156 }
157}
158
159pub struct RgswCiphertextEvaluationDomain<M, R, N> {
160 pub(crate) data: M,
161 _phantom: PhantomData<(R, N)>,
162}
163
164impl<
165 M: MatrixMut + MatrixEntity,
166 Mod: Modulus<Element = M::MatElement>,
167 R: NewWithSeed + RandomFillUniformInModulus<[M::MatElement], Mod>,
168 N: NttInit<Mod> + Ntt<Element = M::MatElement> + Debug,
169 > From<&SeededRgswCiphertext<M, R::Seed, Mod>> for RgswCiphertextEvaluationDomain<M, R, N>
170where
171 <M as Matrix>::R: RowMut,
172 M::MatElement: Copy,
173 R::Seed: Clone,
174 M: Debug,
175{
176 fn from(value: &SeededRgswCiphertext<M, R::Seed, Mod>) -> Self {
177 let mut data = M::zeros(value.d_a * 2 + value.d_b * 2, value.data.dimension().1);
178
179 // copy RLWE'(-sm)
180 izip!(
181 data.iter_rows_mut().take(value.d_a * 2),
182 value.data.iter_rows().take(value.d_a * 2)
183 )
184 .for_each(|(to_ri, from_ri)| {
185 to_ri.as_mut().copy_from_slice(from_ri.as_ref());
186 });
187
188 // sample A polynomials of RLWE'(m) - RLWE'A(m)
189 // TODO(Jay): Do we want to be generic over RandomGenerator used here? I think
190 // not.
191 let mut p_rng = R::new_with_seed(value.seed.clone());
192 izip!(data.iter_rows_mut().skip(value.d_a * 2).take(value.d_b * 1))
193 .for_each(|ri| p_rng.random_fill(&value.modulus, ri.as_mut()));
194
195 // RLWE'_B(m)
196 izip!(
197 data.iter_rows_mut().skip(value.d_a * 2 + value.d_b),
198 value.data.iter_rows().skip(value.d_a * 2)
199 )
200 .for_each(|(to_ri, from_ri)| {
201 to_ri.as_mut().copy_from_slice(from_ri.as_ref());
202 });
203
204 // Send polynomials to evaluation domain
205 let ring_size = data.dimension().1;
206 let nttop = N::new(&value.modulus, ring_size);
207 data.iter_rows_mut()
208 .for_each(|ri| nttop.forward(ri.as_mut()));
209
210 Self {
211 data: data,
212 _phantom: PhantomData,
213 }
214 }
215}
216
217impl<
218 M: MatrixMut + MatrixEntity,
219 Mod: Modulus<Element = M::MatElement>,
220 R,
221 N: NttInit<Mod> + Ntt<Element = M::MatElement>,
222 > From<&RgswCiphertext<M, Mod>> for RgswCiphertextEvaluationDomain<M, R, N>
223where
224 <M as Matrix>::R: RowMut,
225 M::MatElement: Copy,
226 M: Debug,
227{
228 fn from(value: &RgswCiphertext<M, Mod>) -> Self {
229 let mut data = M::zeros(value.d_a * 2 + value.d_b * 2, value.data.dimension().1);
230
231 // copy RLWE'(-sm)
232 izip!(
233 data.iter_rows_mut().take(value.d_a * 2),
234 value.data.iter_rows().take(value.d_a * 2)
235 )
236 .for_each(|(to_ri, from_ri)| {
237 to_ri.as_mut().copy_from_slice(from_ri.as_ref());
238 });
239
240 // copy RLWE'(m)
241 izip!(
242 data.iter_rows_mut().skip(value.d_a * 2),
243 value.data.iter_rows().skip(value.d_a * 2)
244 )
245 .for_each(|(to_ri, from_ri)| {
246 to_ri.as_mut().copy_from_slice(from_ri.as_ref());
247 });
248
249 // Send polynomials to evaluation domain
250 let ring_size = data.dimension().1;
251 let nttop = N::new(&value.modulus, ring_size);
252 data.iter_rows_mut()
253 .for_each(|ri| nttop.forward(ri.as_mut()));
254
255 Self {
256 data: data,
257 _phantom: PhantomData,
258 }
259 }
260}
261
262impl<M: Debug, R, N> Debug for RgswCiphertextEvaluationDomain<M, R, N> {
263 fn fmt(&self, f: &mut std::fmt::Formatter<'_>) -> std::fmt::Result {
264 f.debug_struct("RgswCiphertextEvaluationDomain")
265 .field("data", &self.data)
266 .field("_phantom", &self._phantom)
267 .finish()
268 }
269}
270
271impl<M: Matrix, R, N> Matrix for RgswCiphertextEvaluationDomain<M, R, N> {
272 type MatElement = M::MatElement;
273 type R = M::R;
274
275 fn dimension(&self) -> (usize, usize) {
276 self.data.dimension()
277 }
278
279 fn fits(&self, row: usize, col: usize) -> bool {
280 self.data.fits(row, col)
281 }
282}
283
284impl<M: Matrix, R, N> AsRef<[M::R]> for RgswCiphertextEvaluationDomain<M, R, N> {
285 fn as_ref(&self) -> &[M::R] {
286 self.data.as_ref()
287 }
288}
289
290pub struct SeededRlweCiphertext<R, S, Mod> {
291 pub(crate) data: R,
292 pub(crate) seed: S,
293 pub(crate) modulus: Mod,
294}
295
296impl<R: RowEntity, S, Mod> SeededRlweCiphertext<R, S, Mod> {
297 pub(crate) fn empty(ring_size: usize, seed: S, modulus: Mod) -> Self {
298 SeededRlweCiphertext {
299 data: R::zeros(ring_size),
300 seed,
301 modulus,
302 }
303 }
304}
305
306pub struct RlweCiphertext<M, Rng> {
307 pub(crate) data: M,
308 pub(crate) is_trivial: bool,
309 pub(crate) _phatom: PhantomData<Rng>,
310}
311
312impl<M, Rng> RlweCiphertext<M, Rng> {
313 pub(crate) fn new_trivial(data: M) -> Self {
314 RlweCiphertext {
315 data,
316 is_trivial: true,
317 _phatom: PhantomData,
318 }
319 }
320}
321
322impl<M: Matrix, Rng> Matrix for RlweCiphertext<M, Rng> {
323 type MatElement = M::MatElement;
324 type R = M::R;
325
326 fn dimension(&self) -> (usize, usize) {
327 self.data.dimension()
328 }
329
330 fn fits(&self, row: usize, col: usize) -> bool {
331 self.data.fits(row, col)
332 }
333}
334
335impl<M: MatrixMut, Rng> MatrixMut for RlweCiphertext<M, Rng> where <M as Matrix>::R: RowMut {}
336
337impl<M: Matrix, Rng> AsRef<[<M as Matrix>::R]> for RlweCiphertext<M, Rng> {
338 fn as_ref(&self) -> &[<M as Matrix>::R] {
339 self.data.as_ref()
340 }
341}
342
343impl<M: MatrixMut, Rng> AsMut<[<M as Matrix>::R]> for RlweCiphertext<M, Rng>
344where
345 <M as Matrix>::R: RowMut,
346{
347 fn as_mut(&mut self) -> &mut [<M as Matrix>::R] {
348 self.data.as_mut()
349 }
350}
351
352impl<M, Rng> IsTrivial for RlweCiphertext<M, Rng> {
353 fn is_trivial(&self) -> bool {
354 self.is_trivial
355 }
356 fn set_not_trivial(&mut self) {
357 self.is_trivial = false;
358 }
359}
360
361impl<
362 R: Row,
363 M: MatrixEntity<R = R, MatElement = R::Element> + MatrixMut,
364 Rng: NewWithSeed + RandomFillUniformInModulus<[M::MatElement], Mod>,
365 Mod: Modulus<Element = R::Element>,
366 > From<&SeededRlweCiphertext<R, Rng::Seed, Mod>> for RlweCiphertext<M, Rng>
367where
368 Rng::Seed: Clone,
369 <M as Matrix>::R: RowMut,
370 R::Element: Copy,
371{
372 fn from(value: &SeededRlweCiphertext<R, Rng::Seed, Mod>) -> Self {
373 let mut data = M::zeros(2, value.data.as_ref().len());
374
375 // sample a
376 let mut p_rng = Rng::new_with_seed(value.seed.clone());
377 RandomFillUniformInModulus::random_fill(&mut p_rng, &value.modulus, data.get_row_mut(0));
378
379 data.get_row_mut(1).copy_from_slice(value.data.as_ref());
380
381 RlweCiphertext {
382 data,
383 is_trivial: false,
384 _phatom: PhantomData,
385 }
386 }
387}
388
389pub trait IsTrivial {
390 fn is_trivial(&self) -> bool;
391 fn set_not_trivial(&mut self);
392}
393
394pub struct SeededRlwePublicKey<Ro: Row, S> {
395 data: Ro,
396 seed: S,
397 modulus: Ro::Element,
398}
399
400impl<Ro: RowEntity, S> SeededRlwePublicKey<Ro, S> {
401 pub(crate) fn empty(ring_size: usize, seed: S, modulus: Ro::Element) -> Self {
402 Self {
403 data: Ro::zeros(ring_size),
404 seed,
405 modulus,
406 }
407 }
408}
409
410pub struct RlwePublicKey<M, R> {
411 data: M,
412 _phantom: PhantomData<R>,
413}
414
415impl<
416 M: MatrixMut + MatrixEntity,
417 Rng: NewWithSeed + RandomFillUniformInModulus<[M::MatElement], M::MatElement>,
418 > From<&SeededRlwePublicKey<M::R, Rng::Seed>> for RlwePublicKey<M, Rng>
419where
420 <M as Matrix>::R: RowMut,
421 M::MatElement: Copy,
422 Rng::Seed: Copy,
423{
424 fn from(value: &SeededRlwePublicKey<M::R, Rng::Seed>) -> Self {
425 let mut data = M::zeros(2, value.data.as_ref().len());
426
427 // sample a
428 let mut p_rng = Rng::new_with_seed(value.seed);
429 RandomFillUniformInModulus::random_fill(&mut p_rng, &value.modulus, data.get_row_mut(0));
430
431 // copy over b
432 data.get_row_mut(1).copy_from_slice(value.data.as_ref());
433
434 Self {
435 data,
436 _phantom: PhantomData,
437 }
438 }
439}
440
441#[derive(Clone)]
442pub struct RlweSecret {
443 pub(crate) values: Vec<i32>,
444}
445
446impl Secret for RlweSecret {
447 type Element = i32;
448 fn values(&self) -> &[Self::Element] {
449 &self.values
450 }
451}
452
453impl RlweSecret {
454 pub fn random(hw: usize, n: usize) -> RlweSecret {
455 DefaultSecureRng::with_local_mut(|rng| {
456 let mut out = vec![0i32; n];
457 fill_random_ternary_secret_with_hamming_weight(&mut out, hw, rng);
458
459 RlweSecret { values: out }
460 })
461 }
462}
463
464pub(crate) fn generate_auto_map(ring_size: usize, k: isize) -> (Vec<usize>, Vec<bool>) {
465 assert!(k & 1 == 1, "Auto {k} must be odd");
466
467 let k = if k < 0 {
468 // k is -ve, return k%(2*N)
469 (2 * ring_size) - (k.abs() as usize % (2 * ring_size))
470 } else {
471 k as usize
472 };
473 let (auto_map_index, auto_sign_index): (Vec<usize>, Vec<bool>) = (0..ring_size)
474 .into_iter()
475 .map(|i| {
476 let mut to_index = (i * k) % (2 * ring_size);
477 let mut sign = true;
478
479 // wrap around. false implies negative
480 if to_index >= ring_size {
481 to_index = to_index - ring_size;
482 sign = false;
483 }
484
485 (to_index, sign)
486 })
487 .unzip();
488 (auto_map_index, auto_sign_index)
489}
490
491pub(crate) fn routine<R: RowMut, ModOp: VectorOps<Element = R::Element>>(
492 write_to_row: &mut [R::Element],
493 matrix_a: &[R],
494 matrix_b: &[R],
495 mod_op: &ModOp,
496) {
497 izip!(matrix_a.iter(), matrix_b.iter()).for_each(|(a, b)| {
498 mod_op.elwise_fma_mut(write_to_row, a.as_ref(), b.as_ref());
499 });
500}
501
502/// Decomposes ring polynomial r(X) into d polynomials using decomposer into
503/// output matrix decomp_r
504///
505/// Note that decomposition of r(X) requires decomposition of each of
506/// coefficients.
507///
508/// - decomp_r: must have dimensions d x ring_size. i^th decomposed polynomial
509/// will be stored at i^th row.
510pub(crate) fn decompose_r<R: RowMut, D: Decomposer<Element = R::Element>>(
511 r: &[R::Element],
512 decomp_r: &mut [R],
513 decomposer: &D,
514) where
515 R::Element: Copy,
516{
517 let ring_size = r.len();
518 let d = decomposer.decomposition_count();
519
520 for ri in 0..ring_size {
521 let el_decomposed = decomposer.decompose(&r[ri]);
522 for j in 0..d {
523 decomp_r[j].as_mut()[ri] = el_decomposed[j];
524 }
525 }
526}
527
528/// Sends RLWE_{s}(X) -> RLWE_{s}(X^k) where k is some galois element
529///
530/// - scratch_matrix: must have dimension at-least d+2 x ring_size. d rows to
531/// store decomposed polynomials and 2 for rlwe
532pub(crate) fn galois_auto<
533 MT: Matrix + IsTrivial + MatrixMut,
534 Mmut: MatrixMut<MatElement = MT::MatElement>,
535 ModOp: ArithmeticOps<Element = MT::MatElement> + VectorOps<Element = MT::MatElement>,
536 NttOp: Ntt<Element = MT::MatElement>,
537 D: Decomposer<Element = MT::MatElement>,
538>(
539 rlwe_in: &mut MT,
540 ksk: &Mmut,
541 scratch_matrix: &mut Mmut,
542 auto_map_index: &[usize],
543 auto_map_sign: &[bool],
544 mod_op: &ModOp,
545 ntt_op: &NttOp,
546 decomposer: &D,
547) where
548 <Mmut as Matrix>::R: RowMut,
549 <MT as Matrix>::R: RowMut,
550 MT::MatElement: Copy + Zero,
551{
552 let d = decomposer.decomposition_count();
553 let ring_size = rlwe_in.dimension().1;
554 assert!(rlwe_in.dimension().0 == 2);
555 assert!(scratch_matrix.fits(d + 2, ring_size));
556
557 let (scratch_matrix_d_ring, tmp_rlwe_out) = scratch_matrix.split_at_row_mut(d);
558
559 if !rlwe_in.is_trivial() {
560 tmp_rlwe_out.iter_mut().for_each(|r| {
561 r.as_mut().fill(Mmut::MatElement::zero());
562 });
563
564 // send a(X) -> a(X^k) and decompose a(X^k)
565 izip!(
566 rlwe_in.get_row(0),
567 auto_map_index.iter(),
568 auto_map_sign.iter()
569 )
570 .for_each(|(el_in, to_index, sign)| {
571 let el_out = if !*sign { mod_op.neg(el_in) } else { *el_in };
572
573 let el_out_decomposed = decomposer.decompose(&el_out);
574 for j in 0..d {
575 scratch_matrix_d_ring[j].as_mut()[*to_index] = el_out_decomposed[j];
576 }
577 });
578
579 // transform decomposed a(X^k) to evaluation domain
580 scratch_matrix_d_ring.iter_mut().for_each(|r| {
581 ntt_op.forward(r.as_mut());
582 });
583
584 // RLWE(m^k) = a', b'; RLWE(m) = a, b
585 // key switch: (a * RLWE'(s(X^k)))
586 let (ksk_a, ksk_b) = ksk.split_at_row(d);
587 // a' = decomp<a> * RLWE'_A(s(X^k))
588 routine(
589 tmp_rlwe_out[0].as_mut(),
590 scratch_matrix_d_ring,
591 ksk_a,
592 mod_op,
593 );
594
595 // b' += decomp<a(X^k)> * RLWE'_B(s(X^k))
596 routine(
597 tmp_rlwe_out[1].as_mut(),
598 scratch_matrix_d_ring,
599 ksk_b,
600 mod_op,
601 );
602
603 // transform RLWE(m^k) to coefficient domain
604 tmp_rlwe_out
605 .iter_mut()
606 .for_each(|r| ntt_op.backward(r.as_mut()));
607
608 // send b(X) -> b(X^k) and then b'(X) += b(X^k)
609 izip!(
610 rlwe_in.get_row(1),
611 auto_map_index.iter(),
612 auto_map_sign.iter()
613 )
614 .for_each(|(el_in, to_index, sign)| {
615 let row = tmp_rlwe_out[1].as_mut();
616 if !*sign {
617 row[*to_index] = mod_op.sub(&row[*to_index], el_in);
618 } else {
619 row[*to_index] = mod_op.add(&row[*to_index], el_in);
620 }
621 });
622
623 // copy over A; Leave B for later
624 rlwe_in
625 .get_row_mut(0)
626 .copy_from_slice(tmp_rlwe_out[0].as_ref());
627 } else {
628 // RLWE is trivial, a(X) is 0.
629 // send b(X) -> b(X^k)
630 izip!(
631 rlwe_in.get_row(1),
632 auto_map_index.iter(),
633 auto_map_sign.iter()
634 )
635 .for_each(|(el_in, to_index, sign)| {
636 if !*sign {
637 tmp_rlwe_out[1].as_mut()[*to_index] = mod_op.neg(el_in);
638 } else {
639 tmp_rlwe_out[1].as_mut()[*to_index] = *el_in;
640 }
641 });
642 }
643
644 // Copy over B
645 rlwe_in
646 .get_row_mut(1)
647 .copy_from_slice(tmp_rlwe_out[1].as_ref());
648}
649
650/// Returns RLWE(m0m1) = RLWE(m0) x RGSW(m1). Mutates rlwe_in inplace to equal
651/// RLWE(m0m1)
652///
653/// - rlwe_in: is RLWE(m0) with polynomials in coefficient domain
654/// - rgsw_in: is RGSW(m1) with polynomials in evaluation domain
655/// - scratch_matrix_d_ring: is a matrix of dimension (d_rgsw, ring_size) used
656/// as scratch space to store decomposed Ring elements temporarily
657pub(crate) fn less1_rlwe_by_rgsw<
658 Mmut: MatrixMut,
659 MT: Matrix<MatElement = Mmut::MatElement> + MatrixMut<MatElement = Mmut::MatElement> + IsTrivial,
660 D: Decomposer<Element = Mmut::MatElement>,
661 ModOp: VectorOps<Element = Mmut::MatElement>,
662 NttOp: Ntt<Element = Mmut::MatElement>,
663>(
664 rlwe_in: &mut MT,
665 rgsw_in: &Mmut,
666 scratch_matrix_dplus2_ring: &mut Mmut,
667 decomposer: &D,
668 ntt_op: &NttOp,
669 mod_op: &ModOp,
670 skip0: usize,
671 skip1: usize,
672) where
673 Mmut::MatElement: Copy + Zero,
674 <Mmut as Matrix>::R: RowMut,
675 <MT as Matrix>::R: RowMut,
676{
677 let d_rgsw = decomposer.decomposition_count();
678 assert!(scratch_matrix_dplus2_ring.dimension() == (d_rgsw + 2, rlwe_in.dimension().1));
679 assert!(rgsw_in.dimension() == (d_rgsw * 4, rlwe_in.dimension().1));
680
681 // decomposed RLWE x RGSW
682 let (rlwe_dash_nsm, rlwe_dash_m) = rgsw_in.split_at_row(d_rgsw * 2);
683 let (scratch_matrix_d_ring, scratch_rlwe_out) =
684 scratch_matrix_dplus2_ring.split_at_row_mut(d_rgsw);
685 scratch_rlwe_out[0].as_mut().fill(Mmut::MatElement::zero());
686 scratch_rlwe_out[1].as_mut().fill(Mmut::MatElement::zero());
687 // RLWE_in = a_in, b_in; RLWE_out = a_out, b_out
688 if !rlwe_in.is_trivial() {
689 // a_in = 0 when RLWE_in is trivial RLWE ciphertext
690 // decomp<a_in>
691 decompose_r(rlwe_in.get_row_slice(0), scratch_matrix_d_ring, decomposer);
692 scratch_matrix_d_ring
693 .iter_mut()
694 .for_each(|r| ntt_op.forward(r.as_mut()));
695 // a_out += decomp<a_in> \cdot RLWE_A'(-sm)
696 routine(
697 scratch_rlwe_out[0].as_mut(),
698 scratch_matrix_d_ring[skip0..].as_ref(),
699 &rlwe_dash_nsm[skip0..d_rgsw],
700 mod_op,
701 );
702 // b_out += decomp<a_in> \cdot RLWE_B'(-sm)
703 routine(
704 scratch_rlwe_out[1].as_mut(),
705 scratch_matrix_d_ring[skip0..].as_ref(),
706 &rlwe_dash_nsm[d_rgsw + skip0..],
707 mod_op,
708 );
709 }
710 // decomp<b_in>
711 decompose_r(rlwe_in.get_row_slice(1), scratch_matrix_d_ring, decomposer);
712 scratch_matrix_d_ring
713 .iter_mut()
714 .for_each(|r| ntt_op.forward(r.as_mut()));
715 // a_out += decomp<b_in> \cdot RLWE_A'(m)
716 routine(
717 scratch_rlwe_out[0].as_mut(),
718 scratch_matrix_d_ring[skip1..].as_ref(),
719 &rlwe_dash_m[skip1..d_rgsw],
720 mod_op,
721 );
722 // b_out += decomp<b_in> \cdot RLWE_B'(m)
723 routine(
724 scratch_rlwe_out[1].as_mut(),
725 scratch_matrix_d_ring[skip1..].as_ref(),
726 &rlwe_dash_m[d_rgsw + skip1..],
727 mod_op,
728 );
729
730 // transform rlwe_out to coefficient domain
731 scratch_rlwe_out
732 .iter_mut()
733 .for_each(|r| ntt_op.backward(r.as_mut()));
734
735 rlwe_in
736 .get_row_mut(0)
737 .copy_from_slice(scratch_rlwe_out[0].as_mut());
738 rlwe_in
739 .get_row_mut(1)
740 .copy_from_slice(scratch_rlwe_out[1].as_mut());
741 rlwe_in.set_not_trivial();
742}
743
744/// Returns RLWE(m0m1) = RLWE(m0) x RGSW(m1). Mutates rlwe_in inplace to equal
745/// RLWE(m0m1)
746///
747/// - rlwe_in: is RLWE(m0) with polynomials in coefficient domain
748/// - rgsw_in: is RGSW(m1) with polynomials in evaluation domain
749/// - scratch_matrix_d_ring: is a matrix with atleast max(d_a, d_b) rows and
750/// ring_size columns. It's used to store decomposed polynomials and out RLWE
751/// temoporarily
752pub(crate) fn rlwe_by_rgsw<
753 Mmut: MatrixMut,
754 MT: Matrix<MatElement = Mmut::MatElement> + MatrixMut<MatElement = Mmut::MatElement> + IsTrivial,
755 D: RlweDecomposer<Element = Mmut::MatElement>,
756 ModOp: VectorOps<Element = Mmut::MatElement>,
757 NttOp: Ntt<Element = Mmut::MatElement>,
758>(
759 rlwe_in: &mut MT,
760 rgsw_in: &Mmut,
761 scratch_matrix: &mut Mmut,
762 decomposer: &D,
763 ntt_op: &NttOp,
764 mod_op: &ModOp,
765) where
766 Mmut::MatElement: Copy + Zero,
767 <Mmut as Matrix>::R: RowMut,
768 <MT as Matrix>::R: RowMut,
769{
770 let decomposer_a = decomposer.a();
771 let decomposer_b = decomposer.b();
772 let d_a = decomposer_a.decomposition_count();
773 let d_b = decomposer_b.decomposition_count();
774 let max_d = std::cmp::max(d_a, d_b);
775 assert!(scratch_matrix.fits(max_d + 2, rlwe_in.dimension().1));
776 assert!(rgsw_in.dimension() == (d_a * 2 + d_b * 2, rlwe_in.dimension().1));
777
778 // decomposed RLWE x RGSW
779 let (rlwe_dash_nsm, rlwe_dash_m) = rgsw_in.split_at_row(d_a * 2);
780 let (scratch_matrix_d_ring, scratch_rlwe_out) = scratch_matrix.split_at_row_mut(max_d);
781 scratch_rlwe_out[0].as_mut().fill(Mmut::MatElement::zero());
782 scratch_rlwe_out[1].as_mut().fill(Mmut::MatElement::zero());
783 // RLWE_in = a_in, b_in; RLWE_out = a_out, b_out
784 if !rlwe_in.is_trivial() {
785 // a_in = 0 when RLWE_in is trivial RLWE ciphertext
786 // decomp<a_in>
787 decompose_r(
788 rlwe_in.get_row_slice(0),
789 scratch_matrix_d_ring,
790 decomposer_a,
791 );
792 scratch_matrix_d_ring
793 .iter_mut()
794 .for_each(|r| ntt_op.forward(r.as_mut()));
795 // a_out += decomp<a_in> \cdot RLWE_A'(-sm)
796 routine(
797 scratch_rlwe_out[0].as_mut(),
798 scratch_matrix_d_ring.as_ref(),
799 &rlwe_dash_nsm[..d_a],
800 mod_op,
801 );
802 // b_out += decomp<a_in> \cdot RLWE_B'(-sm)
803 routine(
804 scratch_rlwe_out[1].as_mut(),
805 scratch_matrix_d_ring.as_ref(),
806 &rlwe_dash_nsm[d_a..],
807 mod_op,
808 );
809 }
810 // decomp<b_in>
811 decompose_r(
812 rlwe_in.get_row_slice(1),
813 scratch_matrix_d_ring,
814 decomposer_b,
815 );
816 scratch_matrix_d_ring
817 .iter_mut()
818 .for_each(|r| ntt_op.forward(r.as_mut()));
819 // a_out += decomp<b_in> \cdot RLWE_A'(m)
820 routine(
821 scratch_rlwe_out[0].as_mut(),
822 scratch_matrix_d_ring.as_ref(),
823 &rlwe_dash_m[..d_b],
824 mod_op,
825 );
826 // b_out += decomp<b_in> \cdot RLWE_B'(m)
827 routine(
828 scratch_rlwe_out[1].as_mut(),
829 scratch_matrix_d_ring.as_ref(),
830 &rlwe_dash_m[d_b..],
831 mod_op,
832 );
833
834 // transform rlwe_out to coefficient domain
835 scratch_rlwe_out
836 .iter_mut()
837 .for_each(|r| ntt_op.backward(r.as_mut()));
838
839 rlwe_in
840 .get_row_mut(0)
841 .copy_from_slice(scratch_rlwe_out[0].as_mut());
842 rlwe_in
843 .get_row_mut(1)
844 .copy_from_slice(scratch_rlwe_out[1].as_mut());
845 rlwe_in.set_not_trivial();
846}
847
848/// Inplace mutates rlwe_0 to equal RGSW(m0m1) = RGSW(m0)xRGSW(m1)
849/// in evaluation domain
850///
851/// Warning -
852/// Pass a fresh RGSW ciphertext as the second operand, i.e. as `rgsw_1`.
853/// This is to assure minimal error growth in the resulting RGSW ciphertext.
854/// RGSWxRGSW boils down to d_rgsw*2 RLWExRGSW multiplications. Hence, the noise
855/// growth in resulting ciphertext depends on the norm of second RGSW
856/// ciphertext, not the first. This is useful in cases where one is accumulating
857/// multiple RGSW ciphertexts into 1. In which case, pass the accumulating RGSW
858/// ciphertext as rlwe_0 (the one with higher noise) and subsequent RGSW
859/// ciphertexts, with lower noise, to be accumulated as second
860/// operand.
861///
862/// - rgsw_0: RGSW(m0)
863/// - rgsw_1_eval: RGSW(m1) in Evaluation domain
864/// - scratch_matrix_d_plus_rgsw_by_ring: scratch space matrix with rows
865/// (max(d_a, d_b) + d_a*2+d_b*2) and columns ring_size
866pub(crate) fn rgsw_by_rgsw_inplace<
867 Mmut: MatrixMut,
868 D: RlweDecomposer<Element = Mmut::MatElement>,
869 ModOp: VectorOps<Element = Mmut::MatElement>,
870 NttOp: Ntt<Element = Mmut::MatElement>,
871>(
872 rgsw_0: &mut Mmut,
873 rgsw_1_eval: &Mmut,
874 decomposer: &D,
875 scratch_matrix: &mut Mmut,
876 ntt_op: &NttOp,
877 mod_op: &ModOp,
878) where
879 <Mmut as Matrix>::R: RowMut,
880 Mmut::MatElement: Copy + Zero,
881{
882 let decomposer_a = decomposer.a();
883 let decomposer_b = decomposer.b();
884 let d_a = decomposer_a.decomposition_count();
885 let d_b = decomposer_b.decomposition_count();
886 let max_d = std::cmp::max(d_a, d_b);
887 let rgsw_rows = d_a * 2 + d_b * 2;
888 assert!(rgsw_0.dimension().0 == rgsw_rows);
889 let ring_size = rgsw_0.dimension().1;
890 assert!(rgsw_1_eval.dimension() == (rgsw_rows, ring_size));
891 assert!(scratch_matrix.fits(max_d + rgsw_rows, ring_size));
892
893 let (decomp_r_space, rgsw_space) = scratch_matrix.split_at_row_mut(max_d);
894
895 // zero rgsw_space
896 rgsw_space
897 .iter_mut()
898 .for_each(|ri| ri.as_mut().fill(Mmut::MatElement::zero()));
899 let (rlwe_dash_space_nsm, rlwe_dash_space_m) = rgsw_space.split_at_mut(d_a * 2);
900 let (rlwe_dash_space_nsm_parta, rlwe_dash_space_nsm_partb) =
901 rlwe_dash_space_nsm.split_at_mut(d_a);
902 let (rlwe_dash_space_m_parta, rlwe_dash_space_m_partb) = rlwe_dash_space_m.split_at_mut(d_b);
903
904 let (rgsw0_nsm, rgsw0_m) = rgsw_0.split_at_row(d_a * 2);
905 let (rgsw1_nsm, rgsw1_m) = rgsw_1_eval.split_at_row(d_a * 2);
906
907 // RGSW x RGSW
908 izip!(
909 rgsw0_nsm.iter().take(d_a).chain(rgsw0_m.iter().take(d_b)),
910 rgsw0_nsm.iter().skip(d_a).chain(rgsw0_m.iter().skip(d_b)),
911 rlwe_dash_space_nsm_parta
912 .iter_mut()
913 .chain(rlwe_dash_space_m_parta.iter_mut()),
914 rlwe_dash_space_nsm_partb
915 .iter_mut()
916 .chain(rlwe_dash_space_m_partb.iter_mut()),
917 )
918 .for_each(|(rlwe_a, rlwe_b, rlwe_out_a, rlwe_out_b)| {
919 // Part A
920 decompose_r(rlwe_a.as_ref(), decomp_r_space.as_mut(), decomposer_a);
921 decomp_r_space
922 .iter_mut()
923 .take(d_a)
924 .for_each(|ri| ntt_op.forward(ri.as_mut()));
925 routine(
926 rlwe_out_a.as_mut(),
927 &decomp_r_space[..d_a],
928 &rgsw1_nsm[..d_a],
929 mod_op,
930 );
931 routine(
932 rlwe_out_b.as_mut(),
933 &decomp_r_space[..d_a],
934 &rgsw1_nsm[d_a..],
935 mod_op,
936 );
937
938 // Part B
939 decompose_r(rlwe_b.as_ref(), decomp_r_space.as_mut(), decomposer_b);
940 decomp_r_space
941 .iter_mut()
942 .take(d_b)
943 .for_each(|ri| ntt_op.forward(ri.as_mut()));
944 routine(
945 rlwe_out_a.as_mut(),
946 &decomp_r_space[..d_b],
947 &rgsw1_m[..d_b],
948 mod_op,
949 );
950 routine(
951 rlwe_out_b.as_mut(),
952 &decomp_r_space[..d_b],
953 &rgsw1_m[d_b..],
954 mod_op,
955 );
956 });
957
958 // copy over RGSW(m0m1) into RGSW(m0)
959 izip!(rgsw_0.iter_rows_mut(), rgsw_space.iter())
960 .for_each(|(to_ri, from_ri)| to_ri.as_mut().copy_from_slice(from_ri.as_ref()));
961
962 // send back to coefficient domain
963 rgsw_0
964 .iter_rows_mut()
965 .for_each(|ri| ntt_op.backward(ri.as_mut()));
966}
967
968/// Encrypts message m as a RGSW ciphertext.
969///
970/// - m_eval: is `m` is evaluation domain
971/// - out_rgsw: RGSW(m) is stored as single matrix of dimension (d_rgsw * 3,
972/// ring_size). The matrix has the following structure [RLWE'_A(-sm) ||
973/// RLWE'_B(-sm) || RLWE'_B(m)]^T and RLWE'_A(m) is generated via seed (where
974/// p_rng is assumed to be seeded with seed)
975pub(crate) fn secret_key_encrypt_rgsw<
976 Mmut: MatrixMut + MatrixEntity,
977 S,
978 R: RandomFillGaussianInModulus<[Mmut::MatElement], ModOp::M>
979 + RandomFillUniformInModulus<[Mmut::MatElement], ModOp::M>,
980 PR: RandomFillUniformInModulus<[Mmut::MatElement], ModOp::M>,
981 ModOp: VectorOps<Element = Mmut::MatElement> + GetModulus<Element = Mmut::MatElement>,
982 NttOp: Ntt<Element = Mmut::MatElement>,
983>(
984 out_rgsw: &mut Mmut,
985 m: &[Mmut::MatElement],
986 gadget_a: &[Mmut::MatElement],
987 gadget_b: &[Mmut::MatElement],
988 s: &[S],
989 mod_op: &ModOp,
990 ntt_op: &NttOp,
991 p_rng: &mut PR,
992 rng: &mut R,
993) where
994 <Mmut as Matrix>::R: RowMut + RowEntity + TryConvertFrom1<[S], ModOp::M> + Debug,
995 Mmut::MatElement: Copy + Debug,
996{
997 let d_a = gadget_a.len();
998 let d_b = gadget_b.len();
999 let q = mod_op.modulus();
1000 let ring_size = s.len();
1001 assert!(out_rgsw.dimension() == (d_a * 2 + d_b, ring_size));
1002 assert!(m.as_ref().len() == ring_size);
1003
1004 // RLWE(-sm), RLWE(m)
1005 let (rlwe_dash_nsm, b_rlwe_dash_m) = out_rgsw.split_at_row_mut(d_a * 2);
1006
1007 let mut s_eval = Mmut::R::try_convert_from(s, &q);
1008 ntt_op.forward(s_eval.as_mut());
1009
1010 let mut scratch_space = Mmut::R::zeros(ring_size);
1011
1012 // RLWE'(-sm)
1013 let (a_rlwe_dash_nsm, b_rlwe_dash_nsm) = rlwe_dash_nsm.split_at_mut(d_a);
1014 izip!(
1015 a_rlwe_dash_nsm.iter_mut(),
1016 b_rlwe_dash_nsm.iter_mut(),
1017 gadget_a.iter()
1018 )
1019 .for_each(|(ai, bi, beta_i)| {
1020 // Sample a_i
1021 RandomFillUniformInModulus::random_fill(rng, &q, ai.as_mut());
1022
1023 // a_i * s
1024 scratch_space.as_mut().copy_from_slice(ai.as_ref());
1025 ntt_op.forward(scratch_space.as_mut());
1026 mod_op.elwise_mul_mut(scratch_space.as_mut(), s_eval.as_ref());
1027 ntt_op.backward(scratch_space.as_mut());
1028
1029 // b_i = e_i + a_i * s
1030 RandomFillGaussianInModulus::random_fill(rng, &q, bi.as_mut());
1031 mod_op.elwise_add_mut(bi.as_mut(), scratch_space.as_ref());
1032
1033 // a_i + \beta_i * m
1034 mod_op.elwise_scalar_mul(scratch_space.as_mut(), m.as_ref(), beta_i);
1035 mod_op.elwise_add_mut(ai.as_mut(), scratch_space.as_ref());
1036 });
1037
1038 // RLWE(m)
1039 let mut a_rlwe_dash_m = {
1040 // polynomials of part A of RLWE'(m) are sampled from seed
1041 let mut a = Mmut::zeros(d_b, ring_size);
1042 a.iter_rows_mut()
1043 .for_each(|ai| RandomFillUniformInModulus::random_fill(p_rng, &q, ai.as_mut()));
1044 a
1045 };
1046
1047 izip!(
1048 a_rlwe_dash_m.iter_rows_mut(),
1049 b_rlwe_dash_m.iter_mut(),
1050 gadget_b.iter()
1051 )
1052 .for_each(|(ai, bi, beta_i)| {
1053 // ai * s
1054 ntt_op.forward(ai.as_mut());
1055 mod_op.elwise_mul_mut(ai.as_mut(), s_eval.as_ref());
1056 ntt_op.backward(ai.as_mut());
1057
1058 // beta_i * m
1059 mod_op.elwise_scalar_mul(scratch_space.as_mut(), m.as_ref(), beta_i);
1060
1061 // Sample e_i
1062 RandomFillGaussianInModulus::random_fill(rng, &q, bi.as_mut());
1063 // e_i + beta_i * m + ai*s
1064 mod_op.elwise_add_mut(bi.as_mut(), scratch_space.as_ref());
1065 mod_op.elwise_add_mut(bi.as_mut(), ai.as_ref());
1066 });
1067}
1068
1069pub(crate) fn public_key_encrypt_rgsw<
1070 Mmut: MatrixMut + MatrixEntity,
1071 M: Matrix<MatElement = Mmut::MatElement>,
1072 R: RandomFillGaussianInModulus<[Mmut::MatElement], ModOp::M>
1073 + RandomFill<[u8]>
1074 + RandomElementInModulus<usize, usize>,
1075 ModOp: VectorOps<Element = Mmut::MatElement> + GetModulus<Element = Mmut::MatElement>,
1076 NttOp: Ntt<Element = Mmut::MatElement>,
1077>(
1078 out_rgsw: &mut Mmut,
1079 m: &[M::MatElement],
1080 public_key: &M,
1081 gadget_a: &[Mmut::MatElement],
1082 gadget_b: &[Mmut::MatElement],
1083 mod_op: &ModOp,
1084 ntt_op: &NttOp,
1085 rng: &mut R,
1086) where
1087 <Mmut as Matrix>::R: RowMut + RowEntity + TryConvertFrom1<[i32], ModOp::M>,
1088 Mmut::MatElement: Copy,
1089{
1090 let ring_size = public_key.dimension().1;
1091 let d_a = gadget_a.len();
1092 let d_b = gadget_b.len();
1093 assert!(public_key.dimension().0 == 2);
1094 assert!(out_rgsw.dimension() == (d_a * 2 + d_b * 2, ring_size));
1095
1096 let mut pk_eval = Mmut::zeros(2, ring_size);
1097 izip!(pk_eval.iter_rows_mut(), public_key.iter_rows()).for_each(|(to_i, from_i)| {
1098 to_i.as_mut().copy_from_slice(from_i.as_ref());
1099 ntt_op.forward(to_i.as_mut());
1100 });
1101 let p0 = pk_eval.get_row_slice(0);
1102 let p1 = pk_eval.get_row_slice(1);
1103
1104 let q = mod_op.modulus();
1105
1106 // RGSW(m) = RLWE'(-sm), RLWE(m)
1107 let (rlwe_dash_nsm, rlwe_dash_m) = out_rgsw.split_at_row_mut(d_a * 2);
1108
1109 // RLWE(-sm)
1110 let (rlwe_dash_nsm_parta, rlwe_dash_nsm_partb) = rlwe_dash_nsm.split_at_mut(d_a);
1111 izip!(
1112 rlwe_dash_nsm_parta.iter_mut(),
1113 rlwe_dash_nsm_partb.iter_mut(),
1114 gadget_a.iter()
1115 )
1116 .for_each(|(ai, bi, beta_i)| {
1117 // sample ephemeral secret u_i
1118 let mut u = vec![0i32; ring_size];
1119 fill_random_ternary_secret_with_hamming_weight(u.as_mut(), ring_size >> 1, rng);
1120 let mut u_eval = Mmut::R::try_convert_from(u.as_ref(), &q);
1121 ntt_op.forward(u_eval.as_mut());
1122
1123 let mut u_eval_copy = Mmut::R::zeros(ring_size);
1124 u_eval_copy.as_mut().copy_from_slice(u_eval.as_ref());
1125
1126 // p0 * u
1127 mod_op.elwise_mul_mut(u_eval.as_mut(), p0.as_ref());
1128 // p1 * u
1129 mod_op.elwise_mul_mut(u_eval_copy.as_mut(), p1.as_ref());
1130 ntt_op.backward(u_eval.as_mut());
1131 ntt_op.backward(u_eval_copy.as_mut());
1132
1133 // sample error
1134 RandomFillGaussianInModulus::random_fill(rng, &q, ai.as_mut());
1135 RandomFillGaussianInModulus::random_fill(rng, &q, bi.as_mut());
1136
1137 // a = p0*u+e0
1138 mod_op.elwise_add_mut(ai.as_mut(), u_eval.as_ref());
1139 // b = p1*u+e1
1140 mod_op.elwise_add_mut(bi.as_mut(), u_eval_copy.as_ref());
1141
1142 // a = p0*u + e0 + \beta*m
1143 // use u_eval as scratch
1144 mod_op.elwise_scalar_mul(u_eval.as_mut(), m.as_ref(), beta_i);
1145 mod_op.elwise_add_mut(ai.as_mut(), u_eval.as_ref());
1146 });
1147
1148 // RLWE(m)
1149 let (rlwe_dash_m_parta, rlwe_dash_m_partb) = rlwe_dash_m.split_at_mut(d_b);
1150 izip!(
1151 rlwe_dash_m_parta.iter_mut(),
1152 rlwe_dash_m_partb.iter_mut(),
1153 gadget_b.iter()
1154 )
1155 .for_each(|(ai, bi, beta_i)| {
1156 // sample ephemeral secret u_i
1157 let mut u = vec![0i32; ring_size];
1158 fill_random_ternary_secret_with_hamming_weight(u.as_mut(), ring_size >> 1, rng);
1159 let mut u_eval = Mmut::R::try_convert_from(u.as_ref(), &q);
1160 ntt_op.forward(u_eval.as_mut());
1161
1162 let mut u_eval_copy = Mmut::R::zeros(ring_size);
1163 u_eval_copy.as_mut().copy_from_slice(u_eval.as_ref());
1164
1165 // p0 * u
1166 mod_op.elwise_mul_mut(u_eval.as_mut(), p0.as_ref());
1167 // p1 * u
1168 mod_op.elwise_mul_mut(u_eval_copy.as_mut(), p1.as_ref());
1169 ntt_op.backward(u_eval.as_mut());
1170 ntt_op.backward(u_eval_copy.as_mut());
1171
1172 // sample error
1173 RandomFillGaussianInModulus::random_fill(rng, &q, ai.as_mut());
1174 RandomFillGaussianInModulus::random_fill(rng, &q, bi.as_mut());
1175
1176 // a = p0*u+e0
1177 mod_op.elwise_add_mut(ai.as_mut(), u_eval.as_ref());
1178 // b = p1*u+e1
1179 mod_op.elwise_add_mut(bi.as_mut(), u_eval_copy.as_ref());
1180
1181 // b = p1*u + e0 + \beta*m
1182 // use u_eval as scratch
1183 mod_op.elwise_scalar_mul(u_eval.as_mut(), m.as_ref(), beta_i);
1184 mod_op.elwise_add_mut(bi.as_mut(), u_eval.as_ref());
1185 });
1186}
1187
1188/// Generates RLWE Key switching key to key switch ciphertext RLWE_{from_s}(m)
1189/// to RLWE_{to_s}(m).
1190///
1191/// Key switching equals
1192/// \sum decompose(c_1)_i * RLWE_{to_s}(\beta^i -from_s)
1193/// Hence, key switchin key equals RLWE'(-from_s) = RLWE(-from_s), RLWE(beta^1
1194/// -from_s), ..., RLWE(beta^{d-1} -from_s).
1195///
1196/// - ksk_out: Output Key switching key. Key switching key stores only part B
1197/// polynomials of ksk RLWE ciphertexts (i.e. RLWE'_B(-from_s)) in coefficient
1198/// domain
1199/// - neg_from_s: Negative of secret polynomial to key switch from
1200/// - to_s: secret polynomial to key switch to.
1201pub(crate) fn rlwe_ksk_gen<
1202 Mmut: MatrixMut + MatrixEntity,
1203 ModOp: ArithmeticOps<Element = Mmut::MatElement>
1204 + VectorOps<Element = Mmut::MatElement>
1205 + GetModulus<Element = Mmut::MatElement>,
1206 NttOp: Ntt<Element = Mmut::MatElement>,
1207 R: RandomFillGaussianInModulus<[Mmut::MatElement], ModOp::M>,
1208 PR: RandomFillUniformInModulus<[Mmut::MatElement], ModOp::M>,
1209>(
1210 ksk_out: &mut Mmut,
1211 neg_from_s: Mmut::R,
1212 mut to_s: Mmut::R,
1213 gadget_vector: &[Mmut::MatElement],
1214 mod_op: &ModOp,
1215 ntt_op: &NttOp,
1216 p_rng: &mut PR,
1217 rng: &mut R,
1218) where
1219 <Mmut as Matrix>::R: RowMut,
1220{
1221 let ring_size = neg_from_s.as_ref().len();
1222 let d = gadget_vector.len();
1223 assert!(ksk_out.dimension() == (d, ring_size));
1224
1225 let q = mod_op.modulus();
1226
1227 ntt_op.forward(to_s.as_mut());
1228
1229 // RLWE'_{to_s}(-from_s)
1230 let mut part_a = {
1231 let mut a = Mmut::zeros(d, ring_size);
1232 a.iter_rows_mut()
1233 .for_each(|ai| RandomFillUniformInModulus::random_fill(p_rng, q, ai.as_mut()));
1234 a
1235 };
1236 izip!(
1237 part_a.iter_rows_mut(),
1238 ksk_out.iter_rows_mut(),
1239 gadget_vector.iter(),
1240 )
1241 .for_each(|(ai, bi, beta_i)| {
1242 // si * ai
1243 ntt_op.forward(ai.as_mut());
1244 mod_op.elwise_mul_mut(ai.as_mut(), to_s.as_ref());
1245 ntt_op.backward(ai.as_mut());
1246
1247 // ei + to_s*ai
1248 RandomFillGaussianInModulus::random_fill(rng, &q, bi.as_mut());
1249 mod_op.elwise_add_mut(bi.as_mut(), ai.as_ref());
1250
1251 // beta_i * -from_s
1252 // use ai as scratch space
1253 mod_op.elwise_scalar_mul(ai.as_mut(), neg_from_s.as_ref(), beta_i);
1254
1255 // bi = ei + to_s*ai + beta_i*-from_s
1256 mod_op.elwise_add_mut(bi.as_mut(), ai.as_ref());
1257 });
1258}
1259
1260pub(crate) fn galois_key_gen<
1261 Mmut: MatrixMut + MatrixEntity,
1262 ModOp: ArithmeticOps<Element = Mmut::MatElement>
1263 + VectorOps<Element = Mmut::MatElement>
1264 + GetModulus<Element = Mmut::MatElement>,
1265 NttOp: Ntt<Element = Mmut::MatElement>,
1266 S,
1267 R: RandomFillGaussianInModulus<[Mmut::MatElement], ModOp::M>,
1268 PR: RandomFillUniformInModulus<[Mmut::MatElement], ModOp::M>,
1269>(
1270 ksk_out: &mut Mmut,
1271 s: &[S],
1272 auto_k: isize,
1273 gadget_vector: &[Mmut::MatElement],
1274 mod_op: &ModOp,
1275 ntt_op: &NttOp,
1276 p_rng: &mut PR,
1277 rng: &mut R,
1278) where
1279 <Mmut as Matrix>::R: RowMut,
1280 Mmut::R: TryConvertFrom1<[S], ModOp::M> + RowEntity,
1281 Mmut::MatElement: Copy + Sub<Output = Mmut::MatElement>,
1282{
1283 let ring_size = s.len();
1284 let (auto_map_index, auto_map_sign) = generate_auto_map(ring_size, auto_k);
1285
1286 let q = mod_op.modulus();
1287
1288 // s(X) -> -s(X^k)
1289 let s = Mmut::R::try_convert_from(s, q);
1290 let mut neg_s_auto = Mmut::R::zeros(s.as_ref().len());
1291 izip!(s.as_ref(), auto_map_index.iter(), auto_map_sign.iter()).for_each(
1292 |(el, to_index, sign)| {
1293 // if sign is +ve (true), then negate because we need -s(X) (i.e. do the
1294 // opposite than the usual case)
1295 if *sign {
1296 neg_s_auto.as_mut()[*to_index] = mod_op.neg(el);
1297 } else {
1298 neg_s_auto.as_mut()[*to_index] = *el;
1299 }
1300 },
1301 );
1302
1303 // Ksk from -s(X^k) to s(X)
1304 rlwe_ksk_gen(
1305 ksk_out,
1306 neg_s_auto,
1307 s,
1308 gadget_vector,
1309 mod_op,
1310 ntt_op,
1311 p_rng,
1312 rng,
1313 );
1314}
1315
1316/// Encrypt polynomial m(X) as RLWE ciphertext.
1317///
1318/// - rlwe_out: returned RLWE ciphertext RLWE(m) in coefficient domain. RLWE
1319/// ciphertext is a matirx with first row consiting polynomial `a` and the
1320/// second rows consting polynomial `b`
1321pub(crate) fn secret_key_encrypt_rlwe<
1322 Ro: Row + RowMut + RowEntity,
1323 ModOp: VectorOps<Element = Ro::Element> + GetModulus<Element = Ro::Element>,
1324 NttOp: Ntt<Element = Ro::Element>,
1325 S,
1326 R: RandomFillGaussianInModulus<[Ro::Element], ModOp::M>,
1327 PR: RandomFillUniformInModulus<[Ro::Element], ModOp::M>,
1328>(
1329 m: &[Ro::Element],
1330 b_rlwe_out: &mut Ro,
1331 s: &[S],
1332 mod_op: &ModOp,
1333 ntt_op: &NttOp,
1334 p_rng: &mut PR,
1335 rng: &mut R,
1336) where
1337 Ro: TryConvertFrom1<[S], ModOp::M> + Debug,
1338{
1339 let ring_size = s.len();
1340 assert!(m.as_ref().len() == ring_size);
1341 assert!(b_rlwe_out.as_ref().len() == ring_size);
1342
1343 let q = mod_op.modulus();
1344
1345 // sample a
1346 let mut a = {
1347 let mut a = Ro::zeros(ring_size);
1348 RandomFillUniformInModulus::random_fill(p_rng, q, a.as_mut());
1349 a
1350 };
1351
1352 // s * a
1353 let mut sa = Ro::try_convert_from(s, q);
1354 ntt_op.forward(sa.as_mut());
1355 ntt_op.forward(a.as_mut());
1356 mod_op.elwise_mul_mut(sa.as_mut(), a.as_ref());
1357 ntt_op.backward(sa.as_mut());
1358
1359 // sample e
1360 RandomFillGaussianInModulus::random_fill(rng, q, b_rlwe_out.as_mut());
1361 mod_op.elwise_add_mut(b_rlwe_out.as_mut(), m.as_ref());
1362 mod_op.elwise_add_mut(b_rlwe_out.as_mut(), sa.as_ref());
1363}
1364
1365pub(crate) fn public_key_encrypt_rlwe<
1366 M: Matrix,
1367 Mmut: MatrixMut<MatElement = M::MatElement>,
1368 ModOp: VectorOps<Element = M::MatElement> + GetModulus<Element = M::MatElement>,
1369 NttOp: Ntt<Element = M::MatElement>,
1370 S,
1371 R: RandomFillGaussianInModulus<[M::MatElement], ModOp::M>
1372 + RandomFillUniformInModulus<[M::MatElement], ModOp::M>
1373 + RandomFill<[u8]>
1374 + RandomElementInModulus<usize, usize>,
1375>(
1376 rlwe_out: &mut Mmut,
1377 pk: &M,
1378 m: &[M::MatElement],
1379 mod_op: &ModOp,
1380 ntt_op: &NttOp,
1381 rng: &mut R,
1382) where
1383 <Mmut as Matrix>::R: RowMut + TryConvertFrom1<[S], ModOp::M> + RowEntity,
1384 M::MatElement: Copy,
1385 S: Zero + Signed + Copy,
1386{
1387 let ring_size = m.len();
1388 assert!(rlwe_out.dimension() == (2, ring_size));
1389
1390 let q = mod_op.modulus();
1391
1392 let mut u = vec![S::zero(); ring_size];
1393 fill_random_ternary_secret_with_hamming_weight(u.as_mut(), ring_size >> 1, rng);
1394 let mut u = Mmut::R::try_convert_from(&u, q);
1395 ntt_op.forward(u.as_mut());
1396
1397 let mut ua = Mmut::R::zeros(ring_size);
1398 ua.as_mut().copy_from_slice(pk.get_row_slice(0));
1399 let mut ub = Mmut::R::zeros(ring_size);
1400 ub.as_mut().copy_from_slice(pk.get_row_slice(1));
1401
1402 // a*u
1403 ntt_op.forward(ua.as_mut());
1404 mod_op.elwise_mul_mut(ua.as_mut(), u.as_ref());
1405 ntt_op.backward(ua.as_mut());
1406
1407 // b*u
1408 ntt_op.forward(ub.as_mut());
1409 mod_op.elwise_mul_mut(ub.as_mut(), u.as_ref());
1410 ntt_op.backward(ub.as_mut());
1411
1412 // sample error
1413 rlwe_out.iter_rows_mut().for_each(|ri| {
1414 RandomFillGaussianInModulus::random_fill(rng, &q, ri.as_mut());
1415 });
1416
1417 // a*u + e0
1418 mod_op.elwise_add_mut(rlwe_out.get_row_mut(0), ua.as_ref());
1419 // b*u + e1
1420 mod_op.elwise_add_mut(rlwe_out.get_row_mut(1), ub.as_ref());
1421
1422 // b*u + e1 + m
1423 mod_op.elwise_add_mut(rlwe_out.get_row_mut(1), m);
1424}
1425
1426/// Generates RLWE public key
1427pub(crate) fn gen_rlwe_public_key<
1428 Ro: RowMut + RowEntity,
1429 S,
1430 ModOp: VectorOps<Element = Ro::Element> + GetModulus<Element = Ro::Element>,
1431 NttOp: Ntt<Element = Ro::Element>,
1432 PRng: RandomFillUniformInModulus<[Ro::Element], ModOp::M>,
1433 Rng: RandomFillGaussianInModulus<[Ro::Element], ModOp::M>,
1434>(
1435 part_b_out: &mut Ro,
1436 s: &[S],
1437 ntt_op: &NttOp,
1438 mod_op: &ModOp,
1439 p_rng: &mut PRng,
1440 rng: &mut Rng,
1441) where
1442 Ro: TryConvertFrom1<[S], ModOp::M>,
1443{
1444 let ring_size = s.len();
1445 assert!(part_b_out.as_ref().len() == ring_size);
1446
1447 let q = mod_op.modulus();
1448
1449 // sample a
1450 let mut a = {
1451 let mut tmp = Ro::zeros(ring_size);
1452 RandomFillUniformInModulus::random_fill(p_rng, &q, tmp.as_mut());
1453 tmp
1454 };
1455 ntt_op.forward(a.as_mut());
1456
1457 // s*a
1458 let mut sa = Ro::try_convert_from(s, &q);
1459 ntt_op.forward(sa.as_mut());
1460 mod_op.elwise_mul_mut(sa.as_mut(), a.as_ref());
1461 ntt_op.backward(sa.as_mut());
1462
1463 // s*a + e
1464 RandomFillGaussianInModulus::random_fill(rng, &q, part_b_out.as_mut());
1465 mod_op.elwise_add_mut(part_b_out.as_mut(), sa.as_ref());
1466}
1467
1468/// Decrypts degree 1 RLWE ciphertext RLWE(m) and returns m
1469///
1470/// - rlwe_ct: input degree 1 ciphertext RLWE(m).
1471pub(crate) fn decrypt_rlwe<
1472 R: RowMut,
1473 M: Matrix<MatElement = R::Element>,
1474 ModOp: VectorOps<Element = R::Element> + GetModulus<Element = R::Element>,
1475 NttOp: Ntt<Element = R::Element>,
1476 S,
1477>(
1478 rlwe_ct: &M,
1479 s: &[S],
1480 m_out: &mut R,
1481 ntt_op: &NttOp,
1482 mod_op: &ModOp,
1483) where
1484 R: TryConvertFrom1<[S], ModOp::M>,
1485 R::Element: Copy,
1486{
1487 let ring_size = s.len();
1488 assert!(rlwe_ct.dimension() == (2, ring_size));
1489 assert!(m_out.as_ref().len() == ring_size);
1490
1491 // transform a to evluation form
1492 m_out.as_mut().copy_from_slice(rlwe_ct.get_row_slice(0));
1493 ntt_op.forward(m_out.as_mut());
1494
1495 // -s*a
1496 let mut s = R::try_convert_from(&s, mod_op.modulus());
1497 ntt_op.forward(s.as_mut());
1498 mod_op.elwise_mul_mut(m_out.as_mut(), s.as_ref());
1499 mod_op.elwise_neg_mut(m_out.as_mut());
1500 ntt_op.backward(m_out.as_mut());
1501
1502 // m+e = b - s*a
1503 mod_op.elwise_add_mut(m_out.as_mut(), rlwe_ct.get_row_slice(1));
1504}
1505
1506// Measures noise in degree 1 RLWE ciphertext against encoded ideal message
1507// encoded_m
1508pub(crate) fn measure_noise<
1509 Mmut: MatrixMut + Matrix,
1510 ModOp: VectorOps<Element = Mmut::MatElement> + GetModulus<Element = Mmut::MatElement>,
1511 NttOp: Ntt<Element = Mmut::MatElement>,
1512 S,
1513>(
1514 rlwe_ct: &Mmut,
1515 encoded_m_ideal: &Mmut::R,
1516 ntt_op: &NttOp,
1517 mod_op: &ModOp,
1518 s: &[S],
1519) -> f64
1520where
1521 <Mmut as Matrix>::R: RowMut,
1522 Mmut::R: RowEntity + TryConvertFrom1<[S], ModOp::M>,
1523 Mmut::MatElement: PrimInt + ToPrimitive + Debug,
1524{
1525 let ring_size = s.len();
1526 assert!(rlwe_ct.dimension() == (2, ring_size));
1527 assert!(encoded_m_ideal.as_ref().len() == ring_size);
1528
1529 // -(s * a)
1530 let q = mod_op.modulus();
1531 let mut s = Mmut::R::try_convert_from(s, &q);
1532 ntt_op.forward(s.as_mut());
1533 let mut a = Mmut::R::zeros(ring_size);
1534 a.as_mut().copy_from_slice(rlwe_ct.get_row_slice(0));
1535 ntt_op.forward(a.as_mut());
1536 mod_op.elwise_mul_mut(s.as_mut(), a.as_ref());
1537 mod_op.elwise_neg_mut(s.as_mut());
1538 ntt_op.backward(s.as_mut());
1539
1540 // m+e = b - s*a
1541 let mut m_plus_e = s;
1542 mod_op.elwise_add_mut(m_plus_e.as_mut(), rlwe_ct.get_row_slice(1));
1543
1544 // difference
1545 mod_op.elwise_sub_mut(m_plus_e.as_mut(), encoded_m_ideal.as_ref());
1546
1547 let mut max_diff_bits = f64::MIN;
1548 m_plus_e.as_ref().iter().for_each(|v| {
1549 let bits = (q.map_element_to_i64(v).to_f64().unwrap()).log2();
1550
1551 if max_diff_bits < bits {
1552 max_diff_bits = bits;
1553 }
1554 });
1555
1556 return max_diff_bits;
1557}
1558
1559#[cfg(test)]
1560pub(crate) mod tests {
1561 use std::{marker::PhantomData, ops::Mul, vec};
1562
1563 use itertools::{izip, Itertools};
1564 use rand::{thread_rng, Rng};
1565
1566 use crate::{
1567 backend::{GetModulus, ModInit, ModularOpsU64, Modulus, VectorOps},
1568 decomposer::{Decomposer, DefaultDecomposer, RlweDecomposer},
1569 ntt::{self, Ntt, NttBackendU64, NttInit},
1570 random::{DefaultSecureRng, NewWithSeed, RandomFillUniformInModulus},
1571 rgsw::{
1572 gen_rlwe_public_key, measure_noise, public_key_encrypt_rgsw, AutoKeyEvaluationDomain,
1573 RgswCiphertext, RgswCiphertextEvaluationDomain, RlweCiphertext, RlwePublicKey,
1574 SeededAutoKey, SeededRgswCiphertext, SeededRlweCiphertext, SeededRlwePublicKey,
1575 },
1576 utils::{generate_prime, negacyclic_mul, Stats, TryConvertFrom1},
1577 Matrix, Secret,
1578 };
1579
1580 use super::{
1581 decrypt_rlwe, galois_auto, galois_key_gen, generate_auto_map, public_key_encrypt_rlwe,
1582 rgsw_by_rgsw_inplace, rlwe_by_rgsw, secret_key_encrypt_rgsw, secret_key_encrypt_rlwe,
1583 RlweSecret,
1584 };
1585
1586 pub(crate) fn _sk_encrypt_rlwe<T: Modulus<Element = u64> + Clone>(
1587 m: &[u64],
1588 s: &[i32],
1589 ntt_op: &NttBackendU64,
1590 mod_op: &ModularOpsU64<T>,
1591 ) -> RlweCiphertext<Vec<Vec<u64>>, DefaultSecureRng> {
1592 let ring_size = m.len();
1593 let q = mod_op.modulus();
1594 assert!(s.len() == ring_size);
1595
1596 let mut rng = DefaultSecureRng::new();
1597 let mut rlwe_seed = [0u8; 32];
1598 rng.fill_bytes(&mut rlwe_seed);
1599 let mut seeded_rlwe_ct =
1600 SeededRlweCiphertext::<_, [u8; 32], _>::empty(ring_size as usize, rlwe_seed, q.clone());
1601 let mut p_rng = DefaultSecureRng::new_seeded(rlwe_seed);
1602 secret_key_encrypt_rlwe(
1603 &m,
1604 &mut seeded_rlwe_ct.data,
1605 s,
1606 mod_op,
1607 ntt_op,
1608 &mut p_rng,
1609 &mut rng,
1610 );
1611
1612 RlweCiphertext::<Vec<Vec<u64>>, DefaultSecureRng>::from(&seeded_rlwe_ct)
1613 }
1614
1615 // Encrypt m as RGSW ciphertext RGSW(m) using supplied public key
1616 pub(crate) fn _pk_encrypt_rgsw<T: Modulus<Element = u64> + Clone>(
1617 m: &[u64],
1618 public_key: &RlwePublicKey<Vec<Vec<u64>>, DefaultSecureRng>,
1619 decomposer: &(DefaultDecomposer<u64>, DefaultDecomposer<u64>),
1620 mod_op: &ModularOpsU64<T>,
1621 ntt_op: &NttBackendU64,
1622 ) -> RgswCiphertext<Vec<Vec<u64>>, T> {
1623 let (_, ring_size) = Matrix::dimension(&public_key.data);
1624 let gadget_vector_a = decomposer.a().gadget_vector();
1625 let gadget_vector_b = decomposer.b().gadget_vector();
1626
1627 let mut rng = DefaultSecureRng::new();
1628
1629 assert!(m.len() == ring_size);
1630
1631 // public key encrypt RGSW(m1)
1632 let mut rgsw_ct = RgswCiphertext::empty(ring_size, decomposer, mod_op.modulus().clone());
1633 public_key_encrypt_rgsw(
1634 &mut rgsw_ct.data,
1635 m,
1636 &public_key.data,
1637 &gadget_vector_a,
1638 &gadget_vector_b,
1639 mod_op,
1640 ntt_op,
1641 &mut rng,
1642 );
1643
1644 rgsw_ct
1645 }
1646
1647 /// Encrypts m as RGSW ciphertext RGSW(m) using supplied secret key. Returns
1648 /// unseeded RGSW ciphertext in coefficient domain
1649 pub(crate) fn _sk_encrypt_rgsw<T: Modulus<Element = u64> + Clone>(
1650 m: &[u64],
1651 s: &[i32],
1652 decomposer: &(DefaultDecomposer<u64>, DefaultDecomposer<u64>),
1653 mod_op: &ModularOpsU64<T>,
1654 ntt_op: &NttBackendU64,
1655 ) -> SeededRgswCiphertext<Vec<Vec<u64>>, [u8; 32], T> {
1656 let ring_size = s.len();
1657 assert!(m.len() == s.len());
1658
1659 let q = mod_op.modulus();
1660
1661 let gadget_vector_a = decomposer.a().gadget_vector();
1662 let gadget_vector_b = decomposer.b().gadget_vector();
1663
1664 let mut rng = DefaultSecureRng::new();
1665 let mut rgsw_seed = [0u8; 32];
1666 rng.fill_bytes(&mut rgsw_seed);
1667 let mut seeded_rgsw_ct = SeededRgswCiphertext::<Vec<Vec<u64>>, [u8; 32], T>::empty(
1668 ring_size as usize,
1669 decomposer,
1670 rgsw_seed,
1671 q.clone(),
1672 );
1673 let mut p_rng = DefaultSecureRng::new_seeded(rgsw_seed);
1674 secret_key_encrypt_rgsw(
1675 &mut seeded_rgsw_ct.data,
1676 m,
1677 &gadget_vector_a,
1678 &gadget_vector_b,
1679 s,
1680 mod_op,
1681 ntt_op,
1682 &mut p_rng,
1683 &mut rng,
1684 );
1685 seeded_rgsw_ct
1686 }
1687
1688 /// Prints noise in RGSW ciphertext RGSW(m).
1689 ///
1690 /// - rgsw_ct: RGSW ciphertext in coefficient domain
1691 pub(crate) fn _measure_noise_rgsw<T: Modulus<Element = u64> + Clone>(
1692 rgsw_ct: &[Vec<u64>],
1693 m: &[u64],
1694 s: &[i32],
1695 decomposer: &(DefaultDecomposer<u64>, DefaultDecomposer<u64>),
1696 q: &T,
1697 ) {
1698 let gadget_vector_a = decomposer.a().gadget_vector();
1699 let gadget_vector_b = decomposer.b().gadget_vector();
1700 let d_a = gadget_vector_a.len();
1701 let d_b = gadget_vector_b.len();
1702 let ring_size = s.len();
1703 assert!(Matrix::dimension(&rgsw_ct) == (d_a * 2 + d_b * 2, ring_size));
1704 assert!(m.len() == ring_size);
1705
1706 let mod_op = ModularOpsU64::new(q.clone());
1707 let ntt_op = NttBackendU64::new(q, ring_size);
1708
1709 let mul_mod =
1710 |a: &u64, b: &u64| ((*a as u128 * *b as u128) % q.q().unwrap() as u128) as u64;
1711 let s_poly = Vec::<u64>::try_convert_from(s, q);
1712 let mut neg_s = s_poly.clone();
1713 mod_op.elwise_neg_mut(neg_s.as_mut());
1714 let neg_sm0m1 = negacyclic_mul(&neg_s, &m, mul_mod, q.q().unwrap());
1715
1716 // RLWE(\beta^j -s * m)
1717 for j in 0..d_a {
1718 let ideal_m = {
1719 // RLWE(\beta^j -s * m)
1720 let mut beta_neg_sm0m1 = vec![0u64; ring_size as usize];
1721 mod_op.elwise_scalar_mul(beta_neg_sm0m1.as_mut(), &neg_sm0m1, &gadget_vector_a[j]);
1722 beta_neg_sm0m1
1723 };
1724
1725 let mut rlwe = vec![vec![0u64; ring_size as usize]; 2];
1726 rlwe[0].copy_from_slice(rgsw_ct.get_row_slice(j));
1727 rlwe[1].copy_from_slice(rgsw_ct.get_row_slice(d_a + j));
1728 let noise = measure_noise(&rlwe, &ideal_m, &ntt_op, &mod_op, s);
1729
1730 println!(r"Noise RLWE(\beta^{j} -sm0m1): {noise}");
1731 }
1732
1733 // RLWE(\beta^j m)
1734 for j in 0..d_b {
1735 let ideal_m = {
1736 // RLWE(\beta^j m)
1737 let mut beta_m0m1 = vec![0u64; ring_size as usize];
1738 mod_op.elwise_scalar_mul(beta_m0m1.as_mut(), &m, &gadget_vector_b[j]);
1739 beta_m0m1
1740 };
1741
1742 let mut rlwe = vec![vec![0u64; ring_size as usize]; 2];
1743 rlwe[0].copy_from_slice(rgsw_ct.get_row_slice(d_a * 2 + j));
1744 rlwe[1].copy_from_slice(rgsw_ct.get_row_slice(d_a * 2 + d_b + j));
1745 let noise = measure_noise(&rlwe, &ideal_m, &ntt_op, &mod_op, s);
1746
1747 println!(r"Noise RLWE(\beta^{j} m0m1): {noise}");
1748 }
1749 }
1750
1751 #[test]
1752 fn rlwe_encrypt_decryption() {
1753 let logq = 50;
1754 let logp = 2;
1755 let ring_size = 1 << 4;
1756 let q = generate_prime(logq, ring_size, 1u64 << logq).unwrap();
1757 let p = 1u64 << logp;
1758
1759 let mut rng = DefaultSecureRng::new();
1760
1761 let s = RlweSecret::random((ring_size >> 1) as usize, ring_size as usize);
1762
1763 // sample m0
1764 let mut m0 = vec![0u64; ring_size as usize];
1765 RandomFillUniformInModulus::<[u64], u64>::random_fill(
1766 &mut rng,
1767 &(1u64 << logp),
1768 m0.as_mut_slice(),
1769 );
1770
1771 let ntt_op = NttBackendU64::new(&q, ring_size as usize);
1772 let mod_op = ModularOpsU64::new(q);
1773
1774 // encrypt m0
1775 let encoded_m = m0
1776 .iter()
1777 .map(|v| (((*v as f64) * q as f64) / (p as f64)).round() as u64)
1778 .collect_vec();
1779 let rlwe_in_ct = _sk_encrypt_rlwe(&encoded_m, s.values(), &ntt_op, &mod_op);
1780
1781 let mut encoded_m_back = vec![0u64; ring_size as usize];
1782 decrypt_rlwe(
1783 &rlwe_in_ct,
1784 s.values(),
1785 &mut encoded_m_back,
1786 &ntt_op,
1787 &mod_op,
1788 );
1789 let m_back = encoded_m_back
1790 .iter()
1791 .map(|v| (((*v as f64 * p as f64) / q as f64).round() as u64) % p)
1792 .collect_vec();
1793 assert_eq!(m0, m_back);
1794
1795 // let noise = measure_noise(&rlwe_in_ct, &encoded_m, &ntt_op, &mod_op,
1796 // s.values()); println!("Noise: {noise}");
1797 }
1798
1799 #[test]
1800 fn rlwe_by_rgsw_works() {
1801 let logq = 50;
1802 let logp = 2;
1803 let ring_size = 1 << 9;
1804 let q = generate_prime(logq, ring_size, 1u64 << logq).unwrap();
1805 let p: u64 = 1u64 << logp;
1806
1807 let mut rng = DefaultSecureRng::new_seeded([0u8; 32]);
1808
1809 let s = RlweSecret::random((ring_size >> 1) as usize, ring_size as usize);
1810
1811 let mut m0 = vec![0u64; ring_size as usize];
1812 RandomFillUniformInModulus::<[u64], _>::random_fill(
1813 &mut rng,
1814 &(1u64 << logp),
1815 m0.as_mut_slice(),
1816 );
1817 let mut m1 = vec![0u64; ring_size as usize];
1818 m1[thread_rng().gen_range(0..ring_size) as usize] = 1;
1819
1820 let ntt_op = NttBackendU64::new(&q, ring_size as usize);
1821 let mod_op = ModularOpsU64::new(q);
1822 let d_rgsw = 10;
1823 let logb = 5;
1824 let decomposer = (
1825 DefaultDecomposer::new(q, logb, d_rgsw),
1826 DefaultDecomposer::new(q, logb, d_rgsw),
1827 );
1828
1829 // create public key
1830 let mut pk_seed = [0u8; 32];
1831 rng.fill_bytes(&mut pk_seed);
1832 let mut pk_prng = DefaultSecureRng::new_seeded(pk_seed);
1833 let mut seeded_pk =
1834 SeededRlwePublicKey::<Vec<u64>, _>::empty(ring_size as usize, pk_seed, q);
1835 gen_rlwe_public_key(
1836 &mut seeded_pk.data,
1837 s.values(),
1838 &ntt_op,
1839 &mod_op,
1840 &mut pk_prng,
1841 &mut rng,
1842 );
1843 let pk = RlwePublicKey::<Vec<Vec<u64>>, DefaultSecureRng>::from(&seeded_pk);
1844
1845 // Encrypt m1 as RGSW(m1)
1846 let rgsw_ct = {
1847 //TODO(Jay): Figure out better way to test secret key and public key variant of
1848 // RGSW ciphertext encryption within the same test
1849
1850 if true {
1851 // Encryption m1 as RGSW(m1) using secret key
1852 let seeded_rgsw_ct =
1853 _sk_encrypt_rgsw(&m1, s.values(), &decomposer, &mod_op, &ntt_op);
1854 RgswCiphertextEvaluationDomain::<Vec<Vec<u64>>, DefaultSecureRng, NttBackendU64>::from(&seeded_rgsw_ct)
1855 } else {
1856 // Encrypt m1 as RGSW(m1) using public key
1857 let rgsw_ct = _pk_encrypt_rgsw(&m1, &pk, &decomposer, &mod_op, &ntt_op);
1858 RgswCiphertextEvaluationDomain::<_, DefaultSecureRng, NttBackendU64>::from(&rgsw_ct)
1859 }
1860 };
1861
1862 // Encrypt m0 as RLWE(m0)
1863 let mut rlwe_in_ct = {
1864 let encoded_m = m0
1865 .iter()
1866 .map(|v| (((*v as f64) * q as f64) / (p as f64)).round() as u64)
1867 .collect_vec();
1868
1869 _sk_encrypt_rlwe(&encoded_m, s.values(), &ntt_op, &mod_op)
1870 };
1871
1872 // RLWE(m0m1) = RLWE(m0) x RGSW(m1)
1873 let mut scratch_space = vec![
1874 vec![0u64; ring_size as usize];
1875 std::cmp::max(
1876 decomposer.a().decomposition_count(),
1877 decomposer.b().decomposition_count()
1878 ) + 2
1879 ];
1880 rlwe_by_rgsw(
1881 &mut rlwe_in_ct,
1882 &rgsw_ct.data,
1883 &mut scratch_space,
1884 &decomposer,
1885 &ntt_op,
1886 &mod_op,
1887 );
1888
1889 // Decrypt RLWE(m0m1)
1890 let mut encoded_m0m1_back = vec![0u64; ring_size as usize];
1891 decrypt_rlwe(
1892 &rlwe_in_ct,
1893 s.values(),
1894 &mut encoded_m0m1_back,
1895 &ntt_op,
1896 &mod_op,
1897 );
1898 let m0m1_back = encoded_m0m1_back
1899 .iter()
1900 .map(|v| (((*v as f64 * p as f64) / (q as f64)).round() as u64) % p)
1901 .collect_vec();
1902
1903 let mul_mod = |v0: &u64, v1: &u64| (v0 * v1) % p;
1904 let m0m1 = negacyclic_mul(&m0, &m1, mul_mod, p);
1905
1906 // {
1907 // // measure noise
1908 // let encoded_m_ideal = m0m1
1909 // .iter()
1910 // .map(|v| (((*v as f64) * q as f64) / (p as f64)).round() as u64)
1911 // .collect_vec();
1912
1913 // let noise = measure_noise(&rlwe_in_ct, &encoded_m_ideal, &ntt_op,
1914 // &mod_op, s.values()); println!("Noise RLWE(m0m1)(=
1915 // RLWE(m0)xRGSW(m1)) : {noise}"); }
1916
1917 assert!(
1918 m0m1 == m0m1_back,
1919 "Expected {:?} \n Got {:?}",
1920 m0m1,
1921 m0m1_back
1922 );
1923 }
1924
1925 #[test]
1926 fn galois_auto_works() {
1927 let logq = 55;
1928 let ring_size = 1 << 11;
1929 let q = generate_prime(logq, 2 * ring_size, 1u64 << logq).unwrap();
1930 let logp = 3;
1931 let p = 1u64 << logp;
1932 let d_rgsw = 5;
1933 let logb = 11;
1934
1935 let mut rng = DefaultSecureRng::new();
1936 let s = RlweSecret::random((ring_size >> 1) as usize, ring_size as usize);
1937
1938 let mut m = vec![0u64; ring_size as usize];
1939 RandomFillUniformInModulus::random_fill(&mut rng, &p, m.as_mut_slice());
1940 let encoded_m = m
1941 .iter()
1942 .map(|v| (((*v as f64 * q as f64) / (p as f64)).round() as u64))
1943 .collect_vec();
1944
1945 let ntt_op = NttBackendU64::new(&q, ring_size as usize);
1946 let mod_op = ModularOpsU64::new(q);
1947
1948 // RLWE_{s}(m)
1949 let mut seed_rlwe = [0u8; 32];
1950 rng.fill_bytes(&mut seed_rlwe);
1951 let mut seeded_rlwe_m = SeededRlweCiphertext::empty(ring_size as usize, seed_rlwe, q);
1952 let mut p_rng = DefaultSecureRng::new_seeded(seed_rlwe);
1953 secret_key_encrypt_rlwe(
1954 &encoded_m,
1955 &mut seeded_rlwe_m.data,
1956 s.values(),
1957 &mod_op,
1958 &ntt_op,
1959 &mut p_rng,
1960 &mut rng,
1961 );
1962 let mut rlwe_m = RlweCiphertext::<Vec<Vec<u64>>, DefaultSecureRng>::from(&seeded_rlwe_m);
1963
1964 let auto_k = -125;
1965
1966 // Generate galois key to key switch from s^k to s
1967 let decomposer = DefaultDecomposer::new(q, logb, d_rgsw);
1968 let mut seed_auto = [0u8; 32];
1969 rng.fill_bytes(&mut seed_auto);
1970 let mut seeded_auto_key =
1971 SeededAutoKey::empty(ring_size as usize, &decomposer, seed_auto, q);
1972 let mut p_rng = DefaultSecureRng::new_seeded(seed_auto);
1973 let gadget_vector = decomposer.gadget_vector();
1974 galois_key_gen(
1975 &mut seeded_auto_key.data,
1976 s.values(),
1977 auto_k,
1978 &gadget_vector,
1979 &mod_op,
1980 &ntt_op,
1981 &mut p_rng,
1982 &mut rng,
1983 );
1984 let auto_key =
1985 AutoKeyEvaluationDomain::<Vec<Vec<u64>>, DefaultSecureRng, NttBackendU64>::from(
1986 &seeded_auto_key,
1987 );
1988
1989 // Send RLWE_{s}(m) -> RLWE_{s}(m^k)
1990 let mut scratch_space = vec![vec![0u64; ring_size as usize]; d_rgsw + 2];
1991 let (auto_map_index, auto_map_sign) = generate_auto_map(ring_size as usize, auto_k);
1992 galois_auto(
1993 &mut rlwe_m,
1994 &auto_key.data,
1995 &mut scratch_space,
1996 &auto_map_index,
1997 &auto_map_sign,
1998 &mod_op,
1999 &ntt_op,
2000 &decomposer,
2001 );
2002
2003 let rlwe_m_k = rlwe_m;
2004
2005 // Decrypt RLWE_{s}(m^k) and check
2006 let mut encoded_m_k_back = vec![0u64; ring_size as usize];
2007 decrypt_rlwe(
2008 &rlwe_m_k,
2009 s.values(),
2010 &mut encoded_m_k_back,
2011 &ntt_op,
2012 &mod_op,
2013 );
2014 let m_k_back = encoded_m_k_back
2015 .iter()
2016 .map(|v| (((*v as f64 * p as f64) / q as f64).round() as u64) % p)
2017 .collect_vec();
2018
2019 let mut m_k = vec![0u64; ring_size as usize];
2020 // Send \delta m -> \delta m^k
2021 izip!(m.iter(), auto_map_index.iter(), auto_map_sign.iter()).for_each(
2022 |(v, to_index, sign)| {
2023 if !*sign {
2024 m_k[*to_index] = (p - *v) % p;
2025 } else {
2026 m_k[*to_index] = *v;
2027 }
2028 },
2029 );
2030
2031 {
2032 let encoded_m_k = m_k
2033 .iter()
2034 .map(|v| ((*v as f64 * q as f64) / p as f64).round() as u64)
2035 .collect_vec();
2036
2037 let noise = measure_noise(&rlwe_m_k, &encoded_m_k, &ntt_op, &mod_op, s.values());
2038 println!("Ksk noise: {noise}");
2039 }
2040
2041 assert_eq!(m_k_back, m_k);
2042 }
2043
2044 #[test]
2045 fn sk_rgsw_by_rgsw() {
2046 let logq = 60;
2047 let logp = 2;
2048 let ring_size = 1 << 11;
2049 let q = generate_prime(logq, ring_size, 1u64 << logq).unwrap();
2050 let p = 1u64 << logp;
2051 let d_rgsw = 5;
2052 let logb = 12;
2053
2054 let s = RlweSecret::random((ring_size >> 1) as usize, ring_size as usize);
2055
2056 let mut rng = DefaultSecureRng::new();
2057 let ntt_op = NttBackendU64::new(&q, ring_size as usize);
2058 let mod_op = ModularOpsU64::new(q);
2059 let decomposer = (
2060 DefaultDecomposer::new(q, logb, d_rgsw),
2061 DefaultDecomposer::new(q, logb, d_rgsw),
2062 );
2063
2064 let mul_mod = |a: &u64, b: &u64| ((*a as u128 * *b as u128) % q as u128) as u64;
2065
2066 let mut carry_m = vec![0u64; ring_size as usize];
2067 carry_m[thread_rng().gen_range(0..ring_size) as usize] = 1;
2068
2069 // RGSW(carry_m)
2070 let mut rgsw_carrym = {
2071 let seeded_rgsw = _sk_encrypt_rgsw(&carry_m, s.values(), &decomposer, &mod_op, &ntt_op);
2072 let mut rgsw_eval =
2073 RgswCiphertextEvaluationDomain::<_, DefaultSecureRng, NttBackendU64>::from(
2074 &seeded_rgsw,
2075 );
2076 rgsw_eval
2077 .data
2078 .iter_mut()
2079 .for_each(|ri| ntt_op.backward(ri.as_mut()));
2080 rgsw_eval.data
2081 };
2082
2083 let mut scratch_matrix = vec![
2084 vec![0u64; ring_size as usize];
2085 decomposer.a().decomposition_count() * 2
2086 + decomposer.b().decomposition_count() * 2
2087 + std::cmp::max(
2088 decomposer.a().decomposition_count(),
2089 decomposer.b().decomposition_count()
2090 )
2091 ];
2092
2093 _measure_noise_rgsw(&rgsw_carrym, &carry_m, s.values(), &decomposer, &q);
2094
2095 for i in 0..2 {
2096 let mut m = vec![0u64; ring_size as usize];
2097 m[thread_rng().gen_range(0..ring_size) as usize] = if (i & 1) == 1 { q - 1 } else { 1 };
2098 let rgsw_m = RgswCiphertextEvaluationDomain::<_, DefaultSecureRng, NttBackendU64>::from(
2099 &_sk_encrypt_rgsw(&m, s.values(), &decomposer, &mod_op, &ntt_op),
2100 );
2101 rgsw_by_rgsw_inplace(
2102 &mut rgsw_carrym,
2103 &rgsw_m.data,
2104 &decomposer,
2105 &mut scratch_matrix,
2106 &ntt_op,
2107 &mod_op,
2108 );
2109
2110 // measure noise
2111 carry_m = negacyclic_mul(&carry_m, &m, mul_mod, q);
2112 println!("########### Noise RGSW(carrym) in {i}^th loop ###########");
2113 _measure_noise_rgsw(&rgsw_carrym, &carry_m, s.values(), &decomposer, &q);
2114 }
2115 {
2116 // RLWE(m) x RGSW(carry_m)
2117 let mut m = vec![0u64; ring_size as usize];
2118 RandomFillUniformInModulus::random_fill(&mut rng, &q, m.as_mut_slice());
2119 let mut rlwe_ct = _sk_encrypt_rlwe(&m, s.values(), &ntt_op, &mod_op);
2120
2121 // send rgsw to evaluation domain
2122 rgsw_carrym
2123 .iter_mut()
2124 .for_each(|ri| ntt_op.forward(ri.as_mut_slice()));
2125
2126 rlwe_by_rgsw(
2127 &mut rlwe_ct,
2128 &rgsw_carrym,
2129 &mut scratch_matrix,
2130 &decomposer,
2131 &ntt_op,
2132 &mod_op,
2133 );
2134 let m_expected = negacyclic_mul(&carry_m, &m, mul_mod, q);
2135 let noise = measure_noise(&rlwe_ct, &m_expected, &ntt_op, &mod_op, s.values());
2136 println!("RLWE(m) x RGSW(carry_m): {noise}");
2137 }
2138 }
2139
2140 #[test]
2141 fn some_work() {
2142 let logq = 50;
2143 let ring_size = 1 << 11;
2144 let q = generate_prime(logq, ring_size, 1u64 << logq).unwrap();
2145 let d_rgsw = 10;
2146 let logb = 5;
2147 let decomposer = (
2148 DefaultDecomposer::new(q, logb, d_rgsw),
2149 DefaultDecomposer::new(q, logb, d_rgsw),
2150 );
2151
2152 let ntt_op = NttBackendU64::new(&q, ring_size as usize);
2153 let mod_op = ModularOpsU64::new(q);
2154 let mut rng = DefaultSecureRng::new_seeded([0u8; 32]);
2155
2156 let s = RlweSecret::random((ring_size >> 1) as usize, ring_size as usize);
2157
2158 let mut check = Stats { samples: vec![] };
2159
2160 for _ in 0..100 {
2161 let mut m0 = vec![0u64; ring_size as usize];
2162 m0[thread_rng().gen_range(0..ring_size) as usize] = 1;
2163 let mut m1 = vec![0u64; ring_size as usize];
2164 m1[thread_rng().gen_range(0..ring_size) as usize] = 1;
2165
2166 let mut rgsw_ct0 = {
2167 let seeded_rgsw_ct =
2168 _sk_encrypt_rgsw(&m0, s.values(), &decomposer, &mod_op, &ntt_op);
2169 RgswCiphertextEvaluationDomain::<Vec<Vec<u64>>, DefaultSecureRng, NttBackendU64>::from(&seeded_rgsw_ct)
2170 };
2171 let rgsw_ct1 = {
2172 let seeded_rgsw_ct =
2173 _sk_encrypt_rgsw(&m1, s.values(), &decomposer, &mod_op, &ntt_op);
2174 RgswCiphertextEvaluationDomain::<Vec<Vec<u64>>, DefaultSecureRng, NttBackendU64>::from(&seeded_rgsw_ct)
2175 };
2176
2177 // RGSW x RGSW
2178 // send RGSW(m0) to coefficient domain
2179 rgsw_ct0
2180 .data
2181 .iter_mut()
2182 .for_each(|r| ntt_op.backward(r.as_mut_slice()));
2183 let mut scratch_matrix = vec![
2184 vec![0u64; ring_size as usize];
2185 std::cmp::max(
2186 decomposer.a().decomposition_count(),
2187 decomposer.b().decomposition_count()
2188 ) + decomposer.a().decomposition_count() * 2
2189 + decomposer.b().decomposition_count() * 2
2190 ];
2191 rgsw_by_rgsw_inplace(
2192 &mut rgsw_ct0.data,
2193 &rgsw_ct1.data,
2194 &decomposer,
2195 &mut scratch_matrix,
2196 &ntt_op,
2197 &mod_op,
2198 );
2199 let mut rgsw_m0m1 = rgsw_ct0;
2200 // Back to Evaluation for RLWExRGSW
2201 rgsw_m0m1
2202 .data
2203 .iter_mut()
2204 .for_each(|r| ntt_op.forward(r.as_mut_slice()));
2205
2206 // Sample m2, encrypt it as RLWE(m2) and multiply RLWE(m2)xRGSW(m0m1)
2207 let mut m2 = vec![0u64; ring_size as usize];
2208 RandomFillUniformInModulus::random_fill(&mut rng, &q, m2.as_mut_slice());
2209 let mut rlwe_in_ct = { _sk_encrypt_rlwe(&m2, s.values(), &ntt_op, &mod_op) };
2210 let mut scratch_space = vec![
2211 vec![0u64; ring_size as usize];
2212 std::cmp::max(
2213 decomposer.a().decomposition_count(),
2214 decomposer.b().decomposition_count()
2215 ) + 2
2216 ];
2217 rlwe_by_rgsw(
2218 &mut rlwe_in_ct,
2219 &rgsw_m0m1.data,
2220 &mut scratch_space,
2221 &decomposer,
2222 &ntt_op,
2223 &mod_op,
2224 );
2225
2226 // Decrypt RLWE(m0m1m2)
2227 let mut m0m1m2_back = vec![0u64; ring_size as usize];
2228 decrypt_rlwe(&rlwe_in_ct, s.values(), &mut m0m1m2_back, &ntt_op, &mod_op);
2229
2230 // Calculate m0m1m2
2231 let mul_mod = |v0: &u64, v1: &u64| ((*v0 as u128 * *v1 as u128) % q as u128) as u64;
2232 let m0m1 = negacyclic_mul(&m0, &m1, mul_mod, q);
2233 let m0m1m2 = negacyclic_mul(&m2, &m0m1, mul_mod, q);
2234
2235 // diff
2236 mod_op.elwise_sub_mut(m0m1m2_back.as_mut_slice(), m0m1m2.as_ref());
2237
2238 check.add_more(&Vec::<i64>::try_convert_from(&m0m1m2_back, &q));
2239 }
2240
2241 println!("Std: {}", check.std_dev().abs().log2());
2242 }
2243}