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_to_vec(&r[ri]);
522
523 for j in 0..d {
524 decomp_r[j].as_mut()[ri] = el_decomposed[j];
525 }
526 }
527}
528
529/// Sends RLWE_{s}(X) -> RLWE_{s}(X^k) where k is some galois element
530///
531/// - scratch_matrix: must have dimension at-least d+2 x ring_size. d rows to
532/// store decomposed polynomials and 2 for rlwe
533pub(crate) fn galois_auto<
534 MT: Matrix + IsTrivial + MatrixMut,
535 Mmut: MatrixMut<MatElement = MT::MatElement>,
536 ModOp: ArithmeticOps<Element = MT::MatElement> + VectorOps<Element = MT::MatElement>,
537 NttOp: Ntt<Element = MT::MatElement>,
538 D: Decomposer<Element = MT::MatElement>,
539>(
540 rlwe_in: &mut MT,
541 ksk: &Mmut,
542 scratch_matrix: &mut Mmut,
543 auto_map_index: &[usize],
544 auto_map_sign: &[bool],
545 mod_op: &ModOp,
546 ntt_op: &NttOp,
547 decomposer: &D,
548) where
549 <Mmut as Matrix>::R: RowMut,
550 <MT as Matrix>::R: RowMut,
551 MT::MatElement: Copy + Zero,
552{
553 let d = decomposer.decomposition_count();
554 let ring_size = rlwe_in.dimension().1;
555 assert!(rlwe_in.dimension().0 == 2);
556 assert!(scratch_matrix.fits(d + 2, ring_size));
557
558 let (scratch_matrix_d_ring, tmp_rlwe_out) = scratch_matrix.split_at_row_mut(d);
559
560 if !rlwe_in.is_trivial() {
561 tmp_rlwe_out.iter_mut().for_each(|r| {
562 r.as_mut().fill(Mmut::MatElement::zero());
563 });
564
565 // send a(X) -> a(X^k) and decompose a(X^k)
566 izip!(
567 rlwe_in.get_row(0),
568 auto_map_index.iter(),
569 auto_map_sign.iter()
570 )
571 .for_each(|(el_in, to_index, sign)| {
572 let el_out = if !*sign { mod_op.neg(el_in) } else { *el_in };
573
574 let el_out_decomposed = decomposer.decompose_to_vec(&el_out);
575 for j in 0..d {
576 scratch_matrix_d_ring[j].as_mut()[*to_index] = el_out_decomposed[j];
577 }
578 });
579
580 // transform decomposed a(X^k) to evaluation domain
581 scratch_matrix_d_ring.iter_mut().for_each(|r| {
582 ntt_op.forward(r.as_mut());
583 });
584
585 // RLWE(m^k) = a', b'; RLWE(m) = a, b
586 // key switch: (a * RLWE'(s(X^k)))
587 let (ksk_a, ksk_b) = ksk.split_at_row(d);
588 // a' = decomp<a> * RLWE'_A(s(X^k))
589 routine(
590 tmp_rlwe_out[0].as_mut(),
591 scratch_matrix_d_ring,
592 ksk_a,
593 mod_op,
594 );
595
596 // b' += decomp<a(X^k)> * RLWE'_B(s(X^k))
597 routine(
598 tmp_rlwe_out[1].as_mut(),
599 scratch_matrix_d_ring,
600 ksk_b,
601 mod_op,
602 );
603
604 // transform RLWE(m^k) to coefficient domain
605 tmp_rlwe_out
606 .iter_mut()
607 .for_each(|r| ntt_op.backward(r.as_mut()));
608
609 // send b(X) -> b(X^k) and then b'(X) += b(X^k)
610 izip!(
611 rlwe_in.get_row(1),
612 auto_map_index.iter(),
613 auto_map_sign.iter()
614 )
615 .for_each(|(el_in, to_index, sign)| {
616 let row = tmp_rlwe_out[1].as_mut();
617 if !*sign {
618 row[*to_index] = mod_op.sub(&row[*to_index], el_in);
619 } else {
620 row[*to_index] = mod_op.add(&row[*to_index], el_in);
621 }
622 });
623
624 // copy over A; Leave B for later
625 rlwe_in
626 .get_row_mut(0)
627 .copy_from_slice(tmp_rlwe_out[0].as_ref());
628 } else {
629 // RLWE is trivial, a(X) is 0.
630 // send b(X) -> b(X^k)
631 izip!(
632 rlwe_in.get_row(1),
633 auto_map_index.iter(),
634 auto_map_sign.iter()
635 )
636 .for_each(|(el_in, to_index, sign)| {
637 if !*sign {
638 tmp_rlwe_out[1].as_mut()[*to_index] = mod_op.neg(el_in);
639 } else {
640 tmp_rlwe_out[1].as_mut()[*to_index] = *el_in;
641 }
642 });
643 }
644
645 // Copy over B
646 rlwe_in
647 .get_row_mut(1)
648 .copy_from_slice(tmp_rlwe_out[1].as_ref());
649}
650
651/// Returns RLWE(m0m1) = RLWE(m0) x RGSW(m1). Mutates rlwe_in inplace to equal
652/// RLWE(m0m1)
653///
654/// - rlwe_in: is RLWE(m0) with polynomials in coefficient domain
655/// - rgsw_in: is RGSW(m1) with polynomials in evaluation domain
656/// - scratch_matrix_d_ring: is a matrix of dimension (d_rgsw, ring_size) used
657/// as scratch space to store decomposed Ring elements temporarily
658pub(crate) fn less1_rlwe_by_rgsw<
659 Mmut: MatrixMut,
660 MT: Matrix<MatElement = Mmut::MatElement> + MatrixMut<MatElement = Mmut::MatElement> + IsTrivial,
661 D: Decomposer<Element = Mmut::MatElement>,
662 ModOp: VectorOps<Element = Mmut::MatElement>,
663 NttOp: Ntt<Element = Mmut::MatElement>,
664>(
665 rlwe_in: &mut MT,
666 rgsw_in: &Mmut,
667 scratch_matrix_dplus2_ring: &mut Mmut,
668 decomposer: &D,
669 ntt_op: &NttOp,
670 mod_op: &ModOp,
671 skip0: usize,
672 skip1: usize,
673) where
674 Mmut::MatElement: Copy + Zero,
675 <Mmut as Matrix>::R: RowMut,
676 <MT as Matrix>::R: RowMut,
677{
678 let d_rgsw = decomposer.decomposition_count();
679 assert!(scratch_matrix_dplus2_ring.dimension() == (d_rgsw + 2, rlwe_in.dimension().1));
680 assert!(rgsw_in.dimension() == (d_rgsw * 4, rlwe_in.dimension().1));
681
682 // decomposed RLWE x RGSW
683 let (rlwe_dash_nsm, rlwe_dash_m) = rgsw_in.split_at_row(d_rgsw * 2);
684 let (scratch_matrix_d_ring, scratch_rlwe_out) =
685 scratch_matrix_dplus2_ring.split_at_row_mut(d_rgsw);
686 scratch_rlwe_out[0].as_mut().fill(Mmut::MatElement::zero());
687 scratch_rlwe_out[1].as_mut().fill(Mmut::MatElement::zero());
688 // RLWE_in = a_in, b_in; RLWE_out = a_out, b_out
689 if !rlwe_in.is_trivial() {
690 // a_in = 0 when RLWE_in is trivial RLWE ciphertext
691 // decomp<a_in>
692 decompose_r(rlwe_in.get_row_slice(0), scratch_matrix_d_ring, decomposer);
693 scratch_matrix_d_ring
694 .iter_mut()
695 .for_each(|r| ntt_op.forward(r.as_mut()));
696 // a_out += decomp<a_in> \cdot RLWE_A'(-sm)
697 routine(
698 scratch_rlwe_out[0].as_mut(),
699 scratch_matrix_d_ring[skip0..].as_ref(),
700 &rlwe_dash_nsm[skip0..d_rgsw],
701 mod_op,
702 );
703 // b_out += decomp<a_in> \cdot RLWE_B'(-sm)
704 routine(
705 scratch_rlwe_out[1].as_mut(),
706 scratch_matrix_d_ring[skip0..].as_ref(),
707 &rlwe_dash_nsm[d_rgsw + skip0..],
708 mod_op,
709 );
710 }
711 // decomp<b_in>
712 decompose_r(rlwe_in.get_row_slice(1), scratch_matrix_d_ring, decomposer);
713 scratch_matrix_d_ring
714 .iter_mut()
715 .for_each(|r| ntt_op.forward(r.as_mut()));
716 // a_out += decomp<b_in> \cdot RLWE_A'(m)
717 routine(
718 scratch_rlwe_out[0].as_mut(),
719 scratch_matrix_d_ring[skip1..].as_ref(),
720 &rlwe_dash_m[skip1..d_rgsw],
721 mod_op,
722 );
723 // b_out += decomp<b_in> \cdot RLWE_B'(m)
724 routine(
725 scratch_rlwe_out[1].as_mut(),
726 scratch_matrix_d_ring[skip1..].as_ref(),
727 &rlwe_dash_m[d_rgsw + skip1..],
728 mod_op,
729 );
730
731 // transform rlwe_out to coefficient domain
732 scratch_rlwe_out
733 .iter_mut()
734 .for_each(|r| ntt_op.backward(r.as_mut()));
735
736 rlwe_in
737 .get_row_mut(0)
738 .copy_from_slice(scratch_rlwe_out[0].as_mut());
739 rlwe_in
740 .get_row_mut(1)
741 .copy_from_slice(scratch_rlwe_out[1].as_mut());
742 rlwe_in.set_not_trivial();
743}
744
745/// Returns RLWE(m0m1) = RLWE(m0) x RGSW(m1). Mutates rlwe_in inplace to equal
746/// RLWE(m0m1)
747///
748/// - rlwe_in: is RLWE(m0) with polynomials in coefficient domain
749/// - rgsw_in: is RGSW(m1) with polynomials in evaluation domain
750/// - scratch_matrix_d_ring: is a matrix with atleast max(d_a, d_b) rows and
751/// ring_size columns. It's used to store decomposed polynomials and out RLWE
752/// temoporarily
753pub(crate) fn rlwe_by_rgsw<
754 Mmut: MatrixMut,
755 MT: Matrix<MatElement = Mmut::MatElement> + MatrixMut<MatElement = Mmut::MatElement> + IsTrivial,
756 D: RlweDecomposer<Element = Mmut::MatElement>,
757 ModOp: VectorOps<Element = Mmut::MatElement>,
758 NttOp: Ntt<Element = Mmut::MatElement>,
759>(
760 rlwe_in: &mut MT,
761 rgsw_in: &Mmut,
762 scratch_matrix: &mut Mmut,
763 decomposer: &D,
764 ntt_op: &NttOp,
765 mod_op: &ModOp,
766) where
767 Mmut::MatElement: Copy + Zero,
768 <Mmut as Matrix>::R: RowMut,
769 <MT as Matrix>::R: RowMut,
770{
771 let decomposer_a = decomposer.a();
772 let decomposer_b = decomposer.b();
773 let d_a = decomposer_a.decomposition_count();
774 let d_b = decomposer_b.decomposition_count();
775 let max_d = std::cmp::max(d_a, d_b);
776 assert!(scratch_matrix.fits(max_d + 2, rlwe_in.dimension().1));
777 assert!(rgsw_in.dimension() == (d_a * 2 + d_b * 2, rlwe_in.dimension().1));
778
779 // decomposed RLWE x RGSW
780 let (rlwe_dash_nsm, rlwe_dash_m) = rgsw_in.split_at_row(d_a * 2);
781 let (scratch_matrix_d_ring, scratch_rlwe_out) = scratch_matrix.split_at_row_mut(max_d);
782 scratch_rlwe_out[0].as_mut().fill(Mmut::MatElement::zero());
783 scratch_rlwe_out[1].as_mut().fill(Mmut::MatElement::zero());
784 // RLWE_in = a_in, b_in; RLWE_out = a_out, b_out
785 if !rlwe_in.is_trivial() {
786 // a_in = 0 when RLWE_in is trivial RLWE ciphertext
787 // decomp<a_in>
788 decompose_r(
789 rlwe_in.get_row_slice(0),
790 scratch_matrix_d_ring,
791 decomposer_a,
792 );
793 scratch_matrix_d_ring
794 .iter_mut()
795 .take(d_a)
796 .for_each(|r| ntt_op.forward(r.as_mut()));
797 // a_out += decomp<a_in> \cdot RLWE_A'(-sm)
798 routine(
799 scratch_rlwe_out[0].as_mut(),
800 scratch_matrix_d_ring.as_ref(),
801 &rlwe_dash_nsm[..d_a],
802 mod_op,
803 );
804 // b_out += decomp<a_in> \cdot RLWE_B'(-sm)
805 routine(
806 scratch_rlwe_out[1].as_mut(),
807 scratch_matrix_d_ring.as_ref(),
808 &rlwe_dash_nsm[d_a..],
809 mod_op,
810 );
811 }
812 // decomp<b_in>
813 decompose_r(
814 rlwe_in.get_row_slice(1),
815 scratch_matrix_d_ring,
816 decomposer_b,
817 );
818 scratch_matrix_d_ring
819 .iter_mut()
820 .take(d_b)
821 .for_each(|r| ntt_op.forward(r.as_mut()));
822 // a_out += decomp<b_in> \cdot RLWE_A'(m)
823 routine(
824 scratch_rlwe_out[0].as_mut(),
825 scratch_matrix_d_ring.as_ref(),
826 &rlwe_dash_m[..d_b],
827 mod_op,
828 );
829 // b_out += decomp<b_in> \cdot RLWE_B'(m)
830 routine(
831 scratch_rlwe_out[1].as_mut(),
832 scratch_matrix_d_ring.as_ref(),
833 &rlwe_dash_m[d_b..],
834 mod_op,
835 );
836
837 // transform rlwe_out to coefficient domain
838 scratch_rlwe_out
839 .iter_mut()
840 .for_each(|r| ntt_op.backward(r.as_mut()));
841
842 rlwe_in
843 .get_row_mut(0)
844 .copy_from_slice(scratch_rlwe_out[0].as_mut());
845 rlwe_in
846 .get_row_mut(1)
847 .copy_from_slice(scratch_rlwe_out[1].as_mut());
848 rlwe_in.set_not_trivial();
849}
850
851/// Inplace mutates rlwe_0 to equal RGSW(m0m1) = RGSW(m0)xRGSW(m1)
852/// in evaluation domain
853///
854/// Warning -
855/// Pass a fresh RGSW ciphertext as the second operand, i.e. as `rgsw_1`.
856/// This is to assure minimal error growth in the resulting RGSW ciphertext.
857/// RGSWxRGSW boils down to d_rgsw*2 RLWExRGSW multiplications. Hence, the noise
858/// growth in resulting ciphertext depends on the norm of second RGSW
859/// ciphertext, not the first. This is useful in cases where one is accumulating
860/// multiple RGSW ciphertexts into 1. In which case, pass the accumulating RGSW
861/// ciphertext as rlwe_0 (the one with higher noise) and subsequent RGSW
862/// ciphertexts, with lower noise, to be accumulated as second
863/// operand.
864///
865/// - rgsw_0: RGSW(m0)
866/// - rgsw_1_eval: RGSW(m1) in Evaluation domain
867/// - scratch_matrix_d_plus_rgsw_by_ring: scratch space matrix with rows
868/// (max(d_a, d_b) + d_a*2+d_b*2) and columns ring_size
869pub(crate) fn rgsw_by_rgsw_inplace<
870 Mmut: MatrixMut,
871 D: RlweDecomposer<Element = Mmut::MatElement>,
872 ModOp: VectorOps<Element = Mmut::MatElement>,
873 NttOp: Ntt<Element = Mmut::MatElement>,
874>(
875 rgsw_0: &mut Mmut,
876 rgsw_1_eval: &Mmut,
877 decomposer: &D,
878 scratch_matrix: &mut Mmut,
879 ntt_op: &NttOp,
880 mod_op: &ModOp,
881) where
882 <Mmut as Matrix>::R: RowMut,
883 Mmut::MatElement: Copy + Zero,
884{
885 let decomposer_a = decomposer.a();
886 let decomposer_b = decomposer.b();
887 let d_a = decomposer_a.decomposition_count();
888 let d_b = decomposer_b.decomposition_count();
889 let max_d = std::cmp::max(d_a, d_b);
890 let rgsw_rows = d_a * 2 + d_b * 2;
891 assert!(rgsw_0.dimension().0 == rgsw_rows);
892 let ring_size = rgsw_0.dimension().1;
893 assert!(rgsw_1_eval.dimension() == (rgsw_rows, ring_size));
894 assert!(scratch_matrix.fits(max_d + rgsw_rows, ring_size));
895
896 let (decomp_r_space, rgsw_space) = scratch_matrix.split_at_row_mut(max_d);
897
898 // zero rgsw_space
899 rgsw_space
900 .iter_mut()
901 .for_each(|ri| ri.as_mut().fill(Mmut::MatElement::zero()));
902 let (rlwe_dash_space_nsm, rlwe_dash_space_m) = rgsw_space.split_at_mut(d_a * 2);
903 let (rlwe_dash_space_nsm_parta, rlwe_dash_space_nsm_partb) =
904 rlwe_dash_space_nsm.split_at_mut(d_a);
905 let (rlwe_dash_space_m_parta, rlwe_dash_space_m_partb) = rlwe_dash_space_m.split_at_mut(d_b);
906
907 let (rgsw0_nsm, rgsw0_m) = rgsw_0.split_at_row(d_a * 2);
908 let (rgsw1_nsm, rgsw1_m) = rgsw_1_eval.split_at_row(d_a * 2);
909
910 // RGSW x RGSW
911 izip!(
912 rgsw0_nsm.iter().take(d_a).chain(rgsw0_m.iter().take(d_b)),
913 rgsw0_nsm.iter().skip(d_a).chain(rgsw0_m.iter().skip(d_b)),
914 rlwe_dash_space_nsm_parta
915 .iter_mut()
916 .chain(rlwe_dash_space_m_parta.iter_mut()),
917 rlwe_dash_space_nsm_partb
918 .iter_mut()
919 .chain(rlwe_dash_space_m_partb.iter_mut()),
920 )
921 .for_each(|(rlwe_a, rlwe_b, rlwe_out_a, rlwe_out_b)| {
922 // Part A
923 decompose_r(rlwe_a.as_ref(), decomp_r_space.as_mut(), decomposer_a);
924 decomp_r_space
925 .iter_mut()
926 .take(d_a)
927 .for_each(|ri| ntt_op.forward(ri.as_mut()));
928 routine(
929 rlwe_out_a.as_mut(),
930 &decomp_r_space[..d_a],
931 &rgsw1_nsm[..d_a],
932 mod_op,
933 );
934 routine(
935 rlwe_out_b.as_mut(),
936 &decomp_r_space[..d_a],
937 &rgsw1_nsm[d_a..],
938 mod_op,
939 );
940
941 // Part B
942 decompose_r(rlwe_b.as_ref(), decomp_r_space.as_mut(), decomposer_b);
943 decomp_r_space
944 .iter_mut()
945 .take(d_b)
946 .for_each(|ri| ntt_op.forward(ri.as_mut()));
947 routine(
948 rlwe_out_a.as_mut(),
949 &decomp_r_space[..d_b],
950 &rgsw1_m[..d_b],
951 mod_op,
952 );
953 routine(
954 rlwe_out_b.as_mut(),
955 &decomp_r_space[..d_b],
956 &rgsw1_m[d_b..],
957 mod_op,
958 );
959 });
960
961 // copy over RGSW(m0m1) into RGSW(m0)
962 izip!(rgsw_0.iter_rows_mut(), rgsw_space.iter())
963 .for_each(|(to_ri, from_ri)| to_ri.as_mut().copy_from_slice(from_ri.as_ref()));
964
965 // send back to coefficient domain
966 rgsw_0
967 .iter_rows_mut()
968 .for_each(|ri| ntt_op.backward(ri.as_mut()));
969}
970
971/// Encrypts message m as a RGSW ciphertext.
972///
973/// - m_eval: is `m` is evaluation domain
974/// - out_rgsw: RGSW(m) is stored as single matrix of dimension (d_rgsw * 3,
975/// ring_size). The matrix has the following structure [RLWE'_A(-sm) ||
976/// RLWE'_B(-sm) || RLWE'_B(m)]^T and RLWE'_A(m) is generated via seed (where
977/// p_rng is assumed to be seeded with seed)
978pub(crate) fn secret_key_encrypt_rgsw<
979 Mmut: MatrixMut + MatrixEntity,
980 S,
981 R: RandomFillGaussianInModulus<[Mmut::MatElement], ModOp::M>
982 + RandomFillUniformInModulus<[Mmut::MatElement], ModOp::M>,
983 PR: RandomFillUniformInModulus<[Mmut::MatElement], ModOp::M>,
984 ModOp: VectorOps<Element = Mmut::MatElement> + GetModulus<Element = Mmut::MatElement>,
985 NttOp: Ntt<Element = Mmut::MatElement>,
986>(
987 out_rgsw: &mut Mmut,
988 m: &[Mmut::MatElement],
989 gadget_a: &[Mmut::MatElement],
990 gadget_b: &[Mmut::MatElement],
991 s: &[S],
992 mod_op: &ModOp,
993 ntt_op: &NttOp,
994 p_rng: &mut PR,
995 rng: &mut R,
996) where
997 <Mmut as Matrix>::R: RowMut + RowEntity + TryConvertFrom1<[S], ModOp::M> + Debug,
998 Mmut::MatElement: Copy + Debug,
999{
1000 let d_a = gadget_a.len();
1001 let d_b = gadget_b.len();
1002 let q = mod_op.modulus();
1003 let ring_size = s.len();
1004 assert!(out_rgsw.dimension() == (d_a * 2 + d_b, ring_size));
1005 assert!(m.as_ref().len() == ring_size);
1006
1007 // RLWE(-sm), RLWE(m)
1008 let (rlwe_dash_nsm, b_rlwe_dash_m) = out_rgsw.split_at_row_mut(d_a * 2);
1009
1010 let mut s_eval = Mmut::R::try_convert_from(s, &q);
1011 ntt_op.forward(s_eval.as_mut());
1012
1013 let mut scratch_space = Mmut::R::zeros(ring_size);
1014
1015 // RLWE'(-sm)
1016 let (a_rlwe_dash_nsm, b_rlwe_dash_nsm) = rlwe_dash_nsm.split_at_mut(d_a);
1017 izip!(
1018 a_rlwe_dash_nsm.iter_mut(),
1019 b_rlwe_dash_nsm.iter_mut(),
1020 gadget_a.iter()
1021 )
1022 .for_each(|(ai, bi, beta_i)| {
1023 // Sample a_i
1024 RandomFillUniformInModulus::random_fill(rng, &q, ai.as_mut());
1025
1026 // a_i * s
1027 scratch_space.as_mut().copy_from_slice(ai.as_ref());
1028 ntt_op.forward(scratch_space.as_mut());
1029 mod_op.elwise_mul_mut(scratch_space.as_mut(), s_eval.as_ref());
1030 ntt_op.backward(scratch_space.as_mut());
1031
1032 // b_i = e_i + a_i * s
1033 RandomFillGaussianInModulus::random_fill(rng, &q, bi.as_mut());
1034 mod_op.elwise_add_mut(bi.as_mut(), scratch_space.as_ref());
1035
1036 // a_i + \beta_i * m
1037 mod_op.elwise_scalar_mul(scratch_space.as_mut(), m.as_ref(), beta_i);
1038 mod_op.elwise_add_mut(ai.as_mut(), scratch_space.as_ref());
1039 });
1040
1041 // RLWE(m)
1042 let mut a_rlwe_dash_m = {
1043 // polynomials of part A of RLWE'(m) are sampled from seed
1044 let mut a = Mmut::zeros(d_b, ring_size);
1045 a.iter_rows_mut()
1046 .for_each(|ai| RandomFillUniformInModulus::random_fill(p_rng, &q, ai.as_mut()));
1047 a
1048 };
1049
1050 izip!(
1051 a_rlwe_dash_m.iter_rows_mut(),
1052 b_rlwe_dash_m.iter_mut(),
1053 gadget_b.iter()
1054 )
1055 .for_each(|(ai, bi, beta_i)| {
1056 // ai * s
1057 ntt_op.forward(ai.as_mut());
1058 mod_op.elwise_mul_mut(ai.as_mut(), s_eval.as_ref());
1059 ntt_op.backward(ai.as_mut());
1060
1061 // beta_i * m
1062 mod_op.elwise_scalar_mul(scratch_space.as_mut(), m.as_ref(), beta_i);
1063
1064 // Sample e_i
1065 RandomFillGaussianInModulus::random_fill(rng, &q, bi.as_mut());
1066 // e_i + beta_i * m + ai*s
1067 mod_op.elwise_add_mut(bi.as_mut(), scratch_space.as_ref());
1068 mod_op.elwise_add_mut(bi.as_mut(), ai.as_ref());
1069 });
1070}
1071
1072pub(crate) fn public_key_encrypt_rgsw<
1073 Mmut: MatrixMut + MatrixEntity,
1074 M: Matrix<MatElement = Mmut::MatElement>,
1075 R: RandomFillGaussianInModulus<[Mmut::MatElement], ModOp::M>
1076 + RandomFill<[u8]>
1077 + RandomElementInModulus<usize, usize>,
1078 ModOp: VectorOps<Element = Mmut::MatElement> + GetModulus<Element = Mmut::MatElement>,
1079 NttOp: Ntt<Element = Mmut::MatElement>,
1080>(
1081 out_rgsw: &mut Mmut,
1082 m: &[M::MatElement],
1083 public_key: &M,
1084 gadget_a: &[Mmut::MatElement],
1085 gadget_b: &[Mmut::MatElement],
1086 mod_op: &ModOp,
1087 ntt_op: &NttOp,
1088 rng: &mut R,
1089) where
1090 <Mmut as Matrix>::R: RowMut + RowEntity + TryConvertFrom1<[i32], ModOp::M>,
1091 Mmut::MatElement: Copy,
1092{
1093 let ring_size = public_key.dimension().1;
1094 let d_a = gadget_a.len();
1095 let d_b = gadget_b.len();
1096 assert!(public_key.dimension().0 == 2);
1097 assert!(out_rgsw.dimension() == (d_a * 2 + d_b * 2, ring_size));
1098
1099 let mut pk_eval = Mmut::zeros(2, ring_size);
1100 izip!(pk_eval.iter_rows_mut(), public_key.iter_rows()).for_each(|(to_i, from_i)| {
1101 to_i.as_mut().copy_from_slice(from_i.as_ref());
1102 ntt_op.forward(to_i.as_mut());
1103 });
1104 let p0 = pk_eval.get_row_slice(0);
1105 let p1 = pk_eval.get_row_slice(1);
1106
1107 let q = mod_op.modulus();
1108
1109 // RGSW(m) = RLWE'(-sm), RLWE(m)
1110 let (rlwe_dash_nsm, rlwe_dash_m) = out_rgsw.split_at_row_mut(d_a * 2);
1111
1112 // RLWE(-sm)
1113 let (rlwe_dash_nsm_parta, rlwe_dash_nsm_partb) = rlwe_dash_nsm.split_at_mut(d_a);
1114 izip!(
1115 rlwe_dash_nsm_parta.iter_mut(),
1116 rlwe_dash_nsm_partb.iter_mut(),
1117 gadget_a.iter()
1118 )
1119 .for_each(|(ai, bi, beta_i)| {
1120 // sample ephemeral secret u_i
1121 let mut u = vec![0i32; ring_size];
1122 fill_random_ternary_secret_with_hamming_weight(u.as_mut(), ring_size >> 1, rng);
1123 let mut u_eval = Mmut::R::try_convert_from(u.as_ref(), &q);
1124 ntt_op.forward(u_eval.as_mut());
1125
1126 let mut u_eval_copy = Mmut::R::zeros(ring_size);
1127 u_eval_copy.as_mut().copy_from_slice(u_eval.as_ref());
1128
1129 // p0 * u
1130 mod_op.elwise_mul_mut(u_eval.as_mut(), p0.as_ref());
1131 // p1 * u
1132 mod_op.elwise_mul_mut(u_eval_copy.as_mut(), p1.as_ref());
1133 ntt_op.backward(u_eval.as_mut());
1134 ntt_op.backward(u_eval_copy.as_mut());
1135
1136 // sample error
1137 RandomFillGaussianInModulus::random_fill(rng, &q, ai.as_mut());
1138 RandomFillGaussianInModulus::random_fill(rng, &q, bi.as_mut());
1139
1140 // a = p0*u+e0
1141 mod_op.elwise_add_mut(ai.as_mut(), u_eval.as_ref());
1142 // b = p1*u+e1
1143 mod_op.elwise_add_mut(bi.as_mut(), u_eval_copy.as_ref());
1144
1145 // a = p0*u + e0 + \beta*m
1146 // use u_eval as scratch
1147 mod_op.elwise_scalar_mul(u_eval.as_mut(), m.as_ref(), beta_i);
1148 mod_op.elwise_add_mut(ai.as_mut(), u_eval.as_ref());
1149 });
1150
1151 // RLWE(m)
1152 let (rlwe_dash_m_parta, rlwe_dash_m_partb) = rlwe_dash_m.split_at_mut(d_b);
1153 izip!(
1154 rlwe_dash_m_parta.iter_mut(),
1155 rlwe_dash_m_partb.iter_mut(),
1156 gadget_b.iter()
1157 )
1158 .for_each(|(ai, bi, beta_i)| {
1159 // sample ephemeral secret u_i
1160 let mut u = vec![0i32; ring_size];
1161 fill_random_ternary_secret_with_hamming_weight(u.as_mut(), ring_size >> 1, rng);
1162 let mut u_eval = Mmut::R::try_convert_from(u.as_ref(), &q);
1163 ntt_op.forward(u_eval.as_mut());
1164
1165 let mut u_eval_copy = Mmut::R::zeros(ring_size);
1166 u_eval_copy.as_mut().copy_from_slice(u_eval.as_ref());
1167
1168 // p0 * u
1169 mod_op.elwise_mul_mut(u_eval.as_mut(), p0.as_ref());
1170 // p1 * u
1171 mod_op.elwise_mul_mut(u_eval_copy.as_mut(), p1.as_ref());
1172 ntt_op.backward(u_eval.as_mut());
1173 ntt_op.backward(u_eval_copy.as_mut());
1174
1175 // sample error
1176 RandomFillGaussianInModulus::random_fill(rng, &q, ai.as_mut());
1177 RandomFillGaussianInModulus::random_fill(rng, &q, bi.as_mut());
1178
1179 // a = p0*u+e0
1180 mod_op.elwise_add_mut(ai.as_mut(), u_eval.as_ref());
1181 // b = p1*u+e1
1182 mod_op.elwise_add_mut(bi.as_mut(), u_eval_copy.as_ref());
1183
1184 // b = p1*u + e0 + \beta*m
1185 // use u_eval as scratch
1186 mod_op.elwise_scalar_mul(u_eval.as_mut(), m.as_ref(), beta_i);
1187 mod_op.elwise_add_mut(bi.as_mut(), u_eval.as_ref());
1188 });
1189}
1190
1191/// Generates RLWE Key switching key to key switch ciphertext RLWE_{from_s}(m)
1192/// to RLWE_{to_s}(m).
1193///
1194/// Key switching equals
1195/// \sum decompose(c_1)_i * RLWE_{to_s}(\beta^i -from_s)
1196/// Hence, key switchin key equals RLWE'(-from_s) = RLWE(-from_s), RLWE(beta^1
1197/// -from_s), ..., RLWE(beta^{d-1} -from_s).
1198///
1199/// - ksk_out: Output Key switching key. Key switching key stores only part B
1200/// polynomials of ksk RLWE ciphertexts (i.e. RLWE'_B(-from_s)) in coefficient
1201/// domain
1202/// - neg_from_s: Negative of secret polynomial to key switch from
1203/// - to_s: secret polynomial to key switch to.
1204pub(crate) fn rlwe_ksk_gen<
1205 Mmut: MatrixMut + MatrixEntity,
1206 ModOp: ArithmeticOps<Element = Mmut::MatElement>
1207 + VectorOps<Element = Mmut::MatElement>
1208 + GetModulus<Element = Mmut::MatElement>,
1209 NttOp: Ntt<Element = Mmut::MatElement>,
1210 R: RandomFillGaussianInModulus<[Mmut::MatElement], ModOp::M>,
1211 PR: RandomFillUniformInModulus<[Mmut::MatElement], ModOp::M>,
1212>(
1213 ksk_out: &mut Mmut,
1214 neg_from_s: Mmut::R,
1215 mut to_s: Mmut::R,
1216 gadget_vector: &[Mmut::MatElement],
1217 mod_op: &ModOp,
1218 ntt_op: &NttOp,
1219 p_rng: &mut PR,
1220 rng: &mut R,
1221) where
1222 <Mmut as Matrix>::R: RowMut,
1223{
1224 let ring_size = neg_from_s.as_ref().len();
1225 let d = gadget_vector.len();
1226 assert!(ksk_out.dimension() == (d, ring_size));
1227
1228 let q = mod_op.modulus();
1229
1230 ntt_op.forward(to_s.as_mut());
1231
1232 // RLWE'_{to_s}(-from_s)
1233 let mut part_a = {
1234 let mut a = Mmut::zeros(d, ring_size);
1235 a.iter_rows_mut()
1236 .for_each(|ai| RandomFillUniformInModulus::random_fill(p_rng, q, ai.as_mut()));
1237 a
1238 };
1239 izip!(
1240 part_a.iter_rows_mut(),
1241 ksk_out.iter_rows_mut(),
1242 gadget_vector.iter(),
1243 )
1244 .for_each(|(ai, bi, beta_i)| {
1245 // si * ai
1246 ntt_op.forward(ai.as_mut());
1247 mod_op.elwise_mul_mut(ai.as_mut(), to_s.as_ref());
1248 ntt_op.backward(ai.as_mut());
1249
1250 // ei + to_s*ai
1251 RandomFillGaussianInModulus::random_fill(rng, &q, bi.as_mut());
1252 mod_op.elwise_add_mut(bi.as_mut(), ai.as_ref());
1253
1254 // beta_i * -from_s
1255 // use ai as scratch space
1256 mod_op.elwise_scalar_mul(ai.as_mut(), neg_from_s.as_ref(), beta_i);
1257
1258 // bi = ei + to_s*ai + beta_i*-from_s
1259 mod_op.elwise_add_mut(bi.as_mut(), ai.as_ref());
1260 });
1261}
1262
1263pub(crate) fn galois_key_gen<
1264 Mmut: MatrixMut + MatrixEntity,
1265 ModOp: ArithmeticOps<Element = Mmut::MatElement>
1266 + VectorOps<Element = Mmut::MatElement>
1267 + GetModulus<Element = Mmut::MatElement>,
1268 NttOp: Ntt<Element = Mmut::MatElement>,
1269 S,
1270 R: RandomFillGaussianInModulus<[Mmut::MatElement], ModOp::M>,
1271 PR: RandomFillUniformInModulus<[Mmut::MatElement], ModOp::M>,
1272>(
1273 ksk_out: &mut Mmut,
1274 s: &[S],
1275 auto_k: isize,
1276 gadget_vector: &[Mmut::MatElement],
1277 mod_op: &ModOp,
1278 ntt_op: &NttOp,
1279 p_rng: &mut PR,
1280 rng: &mut R,
1281) where
1282 <Mmut as Matrix>::R: RowMut,
1283 Mmut::R: TryConvertFrom1<[S], ModOp::M> + RowEntity,
1284 Mmut::MatElement: Copy + Sub<Output = Mmut::MatElement>,
1285{
1286 let ring_size = s.len();
1287 let (auto_map_index, auto_map_sign) = generate_auto_map(ring_size, auto_k);
1288
1289 let q = mod_op.modulus();
1290
1291 // s(X) -> -s(X^k)
1292 let s = Mmut::R::try_convert_from(s, q);
1293 let mut neg_s_auto = Mmut::R::zeros(s.as_ref().len());
1294 izip!(s.as_ref(), auto_map_index.iter(), auto_map_sign.iter()).for_each(
1295 |(el, to_index, sign)| {
1296 // if sign is +ve (true), then negate because we need -s(X) (i.e. do the
1297 // opposite than the usual case)
1298 if *sign {
1299 neg_s_auto.as_mut()[*to_index] = mod_op.neg(el);
1300 } else {
1301 neg_s_auto.as_mut()[*to_index] = *el;
1302 }
1303 },
1304 );
1305
1306 // Ksk from -s(X^k) to s(X)
1307 rlwe_ksk_gen(
1308 ksk_out,
1309 neg_s_auto,
1310 s,
1311 gadget_vector,
1312 mod_op,
1313 ntt_op,
1314 p_rng,
1315 rng,
1316 );
1317}
1318
1319/// Encrypt polynomial m(X) as RLWE ciphertext.
1320///
1321/// - rlwe_out: returned RLWE ciphertext RLWE(m) in coefficient domain. RLWE
1322/// ciphertext is a matirx with first row consiting polynomial `a` and the
1323/// second rows consting polynomial `b`
1324pub(crate) fn secret_key_encrypt_rlwe<
1325 Ro: Row + RowMut + RowEntity,
1326 ModOp: VectorOps<Element = Ro::Element> + GetModulus<Element = Ro::Element>,
1327 NttOp: Ntt<Element = Ro::Element>,
1328 S,
1329 R: RandomFillGaussianInModulus<[Ro::Element], ModOp::M>,
1330 PR: RandomFillUniformInModulus<[Ro::Element], ModOp::M>,
1331>(
1332 m: &[Ro::Element],
1333 b_rlwe_out: &mut Ro,
1334 s: &[S],
1335 mod_op: &ModOp,
1336 ntt_op: &NttOp,
1337 p_rng: &mut PR,
1338 rng: &mut R,
1339) where
1340 Ro: TryConvertFrom1<[S], ModOp::M> + Debug,
1341{
1342 let ring_size = s.len();
1343 assert!(m.as_ref().len() == ring_size);
1344 assert!(b_rlwe_out.as_ref().len() == ring_size);
1345
1346 let q = mod_op.modulus();
1347
1348 // sample a
1349 let mut a = {
1350 let mut a = Ro::zeros(ring_size);
1351 RandomFillUniformInModulus::random_fill(p_rng, q, a.as_mut());
1352 a
1353 };
1354
1355 // s * a
1356 let mut sa = Ro::try_convert_from(s, q);
1357 ntt_op.forward(sa.as_mut());
1358 ntt_op.forward(a.as_mut());
1359 mod_op.elwise_mul_mut(sa.as_mut(), a.as_ref());
1360 ntt_op.backward(sa.as_mut());
1361
1362 // sample e
1363 RandomFillGaussianInModulus::random_fill(rng, q, b_rlwe_out.as_mut());
1364 mod_op.elwise_add_mut(b_rlwe_out.as_mut(), m.as_ref());
1365 mod_op.elwise_add_mut(b_rlwe_out.as_mut(), sa.as_ref());
1366}
1367
1368pub(crate) fn public_key_encrypt_rlwe<
1369 M: Matrix,
1370 Mmut: MatrixMut<MatElement = M::MatElement>,
1371 ModOp: VectorOps<Element = M::MatElement> + GetModulus<Element = M::MatElement>,
1372 NttOp: Ntt<Element = M::MatElement>,
1373 S,
1374 R: RandomFillGaussianInModulus<[M::MatElement], ModOp::M>
1375 + RandomFillUniformInModulus<[M::MatElement], ModOp::M>
1376 + RandomFill<[u8]>
1377 + RandomElementInModulus<usize, usize>,
1378>(
1379 rlwe_out: &mut Mmut,
1380 pk: &M,
1381 m: &[M::MatElement],
1382 mod_op: &ModOp,
1383 ntt_op: &NttOp,
1384 rng: &mut R,
1385) where
1386 <Mmut as Matrix>::R: RowMut + TryConvertFrom1<[S], ModOp::M> + RowEntity,
1387 M::MatElement: Copy,
1388 S: Zero + Signed + Copy,
1389{
1390 let ring_size = m.len();
1391 assert!(rlwe_out.dimension() == (2, ring_size));
1392
1393 let q = mod_op.modulus();
1394
1395 let mut u = vec![S::zero(); ring_size];
1396 fill_random_ternary_secret_with_hamming_weight(u.as_mut(), ring_size >> 1, rng);
1397 let mut u = Mmut::R::try_convert_from(&u, q);
1398 ntt_op.forward(u.as_mut());
1399
1400 let mut ua = Mmut::R::zeros(ring_size);
1401 ua.as_mut().copy_from_slice(pk.get_row_slice(0));
1402 let mut ub = Mmut::R::zeros(ring_size);
1403 ub.as_mut().copy_from_slice(pk.get_row_slice(1));
1404
1405 // a*u
1406 ntt_op.forward(ua.as_mut());
1407 mod_op.elwise_mul_mut(ua.as_mut(), u.as_ref());
1408 ntt_op.backward(ua.as_mut());
1409
1410 // b*u
1411 ntt_op.forward(ub.as_mut());
1412 mod_op.elwise_mul_mut(ub.as_mut(), u.as_ref());
1413 ntt_op.backward(ub.as_mut());
1414
1415 // sample error
1416 rlwe_out.iter_rows_mut().for_each(|ri| {
1417 RandomFillGaussianInModulus::random_fill(rng, &q, ri.as_mut());
1418 });
1419
1420 // a*u + e0
1421 mod_op.elwise_add_mut(rlwe_out.get_row_mut(0), ua.as_ref());
1422 // b*u + e1
1423 mod_op.elwise_add_mut(rlwe_out.get_row_mut(1), ub.as_ref());
1424
1425 // b*u + e1 + m
1426 mod_op.elwise_add_mut(rlwe_out.get_row_mut(1), m);
1427}
1428
1429/// Generates RLWE public key
1430pub(crate) fn gen_rlwe_public_key<
1431 Ro: RowMut + RowEntity,
1432 S,
1433 ModOp: VectorOps<Element = Ro::Element> + GetModulus<Element = Ro::Element>,
1434 NttOp: Ntt<Element = Ro::Element>,
1435 PRng: RandomFillUniformInModulus<[Ro::Element], ModOp::M>,
1436 Rng: RandomFillGaussianInModulus<[Ro::Element], ModOp::M>,
1437>(
1438 part_b_out: &mut Ro,
1439 s: &[S],
1440 ntt_op: &NttOp,
1441 mod_op: &ModOp,
1442 p_rng: &mut PRng,
1443 rng: &mut Rng,
1444) where
1445 Ro: TryConvertFrom1<[S], ModOp::M>,
1446{
1447 let ring_size = s.len();
1448 assert!(part_b_out.as_ref().len() == ring_size);
1449
1450 let q = mod_op.modulus();
1451
1452 // sample a
1453 let mut a = {
1454 let mut tmp = Ro::zeros(ring_size);
1455 RandomFillUniformInModulus::random_fill(p_rng, &q, tmp.as_mut());
1456 tmp
1457 };
1458 ntt_op.forward(a.as_mut());
1459
1460 // s*a
1461 let mut sa = Ro::try_convert_from(s, &q);
1462 ntt_op.forward(sa.as_mut());
1463 mod_op.elwise_mul_mut(sa.as_mut(), a.as_ref());
1464 ntt_op.backward(sa.as_mut());
1465
1466 // s*a + e
1467 RandomFillGaussianInModulus::random_fill(rng, &q, part_b_out.as_mut());
1468 mod_op.elwise_add_mut(part_b_out.as_mut(), sa.as_ref());
1469}
1470
1471/// Decrypts degree 1 RLWE ciphertext RLWE(m) and returns m
1472///
1473/// - rlwe_ct: input degree 1 ciphertext RLWE(m).
1474pub(crate) fn decrypt_rlwe<
1475 R: RowMut,
1476 M: Matrix<MatElement = R::Element>,
1477 ModOp: VectorOps<Element = R::Element> + GetModulus<Element = R::Element>,
1478 NttOp: Ntt<Element = R::Element>,
1479 S,
1480>(
1481 rlwe_ct: &M,
1482 s: &[S],
1483 m_out: &mut R,
1484 ntt_op: &NttOp,
1485 mod_op: &ModOp,
1486) where
1487 R: TryConvertFrom1<[S], ModOp::M>,
1488 R::Element: Copy,
1489{
1490 let ring_size = s.len();
1491 assert!(rlwe_ct.dimension() == (2, ring_size));
1492 assert!(m_out.as_ref().len() == ring_size);
1493
1494 // transform a to evluation form
1495 m_out.as_mut().copy_from_slice(rlwe_ct.get_row_slice(0));
1496 ntt_op.forward(m_out.as_mut());
1497
1498 // -s*a
1499 let mut s = R::try_convert_from(&s, mod_op.modulus());
1500 ntt_op.forward(s.as_mut());
1501 mod_op.elwise_mul_mut(m_out.as_mut(), s.as_ref());
1502 mod_op.elwise_neg_mut(m_out.as_mut());
1503 ntt_op.backward(m_out.as_mut());
1504
1505 // m+e = b - s*a
1506 mod_op.elwise_add_mut(m_out.as_mut(), rlwe_ct.get_row_slice(1));
1507}
1508
1509// Measures noise in degree 1 RLWE ciphertext against encoded ideal message
1510// encoded_m
1511pub(crate) fn measure_noise<
1512 Mmut: MatrixMut + Matrix,
1513 ModOp: VectorOps<Element = Mmut::MatElement> + GetModulus<Element = Mmut::MatElement>,
1514 NttOp: Ntt<Element = Mmut::MatElement>,
1515 S,
1516>(
1517 rlwe_ct: &Mmut,
1518 encoded_m_ideal: &Mmut::R,
1519 ntt_op: &NttOp,
1520 mod_op: &ModOp,
1521 s: &[S],
1522) -> f64
1523where
1524 <Mmut as Matrix>::R: RowMut,
1525 Mmut::R: RowEntity + TryConvertFrom1<[S], ModOp::M>,
1526 Mmut::MatElement: PrimInt + ToPrimitive + Debug,
1527{
1528 let ring_size = s.len();
1529 assert!(rlwe_ct.dimension() == (2, ring_size));
1530 assert!(encoded_m_ideal.as_ref().len() == ring_size);
1531
1532 // -(s * a)
1533 let q = mod_op.modulus();
1534 let mut s = Mmut::R::try_convert_from(s, &q);
1535 ntt_op.forward(s.as_mut());
1536 let mut a = Mmut::R::zeros(ring_size);
1537 a.as_mut().copy_from_slice(rlwe_ct.get_row_slice(0));
1538 ntt_op.forward(a.as_mut());
1539 mod_op.elwise_mul_mut(s.as_mut(), a.as_ref());
1540 mod_op.elwise_neg_mut(s.as_mut());
1541 ntt_op.backward(s.as_mut());
1542
1543 // m+e = b - s*a
1544 let mut m_plus_e = s;
1545 mod_op.elwise_add_mut(m_plus_e.as_mut(), rlwe_ct.get_row_slice(1));
1546
1547 // difference
1548 mod_op.elwise_sub_mut(m_plus_e.as_mut(), encoded_m_ideal.as_ref());
1549
1550 let mut max_diff_bits = f64::MIN;
1551 m_plus_e.as_ref().iter().for_each(|v| {
1552 let bits = (q.map_element_to_i64(v).to_f64().unwrap()).log2();
1553
1554 if max_diff_bits < bits {
1555 max_diff_bits = bits;
1556 }
1557 });
1558
1559 return max_diff_bits;
1560}
1561
1562#[cfg(test)]
1563pub(crate) mod tests {
1564 use std::{marker::PhantomData, ops::Mul, vec};
1565
1566 use itertools::{izip, Itertools};
1567 use rand::{thread_rng, Rng};
1568
1569 use crate::{
1570 backend::{GetModulus, ModInit, ModularOpsU64, Modulus, VectorOps},
1571 decomposer::{Decomposer, DefaultDecomposer, RlweDecomposer},
1572 ntt::{self, Ntt, NttBackendU64, NttInit},
1573 random::{DefaultSecureRng, NewWithSeed, RandomFillUniformInModulus},
1574 rgsw::{
1575 gen_rlwe_public_key, measure_noise, public_key_encrypt_rgsw, AutoKeyEvaluationDomain,
1576 RgswCiphertext, RgswCiphertextEvaluationDomain, RlweCiphertext, RlwePublicKey,
1577 SeededAutoKey, SeededRgswCiphertext, SeededRlweCiphertext, SeededRlwePublicKey,
1578 },
1579 utils::{generate_prime, negacyclic_mul, Stats, TryConvertFrom1},
1580 Matrix, Secret,
1581 };
1582
1583 use super::{
1584 decrypt_rlwe, galois_auto, galois_key_gen, generate_auto_map, public_key_encrypt_rlwe,
1585 rgsw_by_rgsw_inplace, rlwe_by_rgsw, secret_key_encrypt_rgsw, secret_key_encrypt_rlwe,
1586 RlweSecret,
1587 };
1588
1589 pub(crate) fn _sk_encrypt_rlwe<T: Modulus<Element = u64> + Clone>(
1590 m: &[u64],
1591 s: &[i32],
1592 ntt_op: &NttBackendU64,
1593 mod_op: &ModularOpsU64<T>,
1594 ) -> RlweCiphertext<Vec<Vec<u64>>, DefaultSecureRng> {
1595 let ring_size = m.len();
1596 let q = mod_op.modulus();
1597 assert!(s.len() == ring_size);
1598
1599 let mut rng = DefaultSecureRng::new();
1600 let mut rlwe_seed = [0u8; 32];
1601 rng.fill_bytes(&mut rlwe_seed);
1602 let mut seeded_rlwe_ct =
1603 SeededRlweCiphertext::<_, [u8; 32], _>::empty(ring_size as usize, rlwe_seed, q.clone());
1604 let mut p_rng = DefaultSecureRng::new_seeded(rlwe_seed);
1605 secret_key_encrypt_rlwe(
1606 &m,
1607 &mut seeded_rlwe_ct.data,
1608 s,
1609 mod_op,
1610 ntt_op,
1611 &mut p_rng,
1612 &mut rng,
1613 );
1614
1615 RlweCiphertext::<Vec<Vec<u64>>, DefaultSecureRng>::from(&seeded_rlwe_ct)
1616 }
1617
1618 // Encrypt m as RGSW ciphertext RGSW(m) using supplied public key
1619 pub(crate) fn _pk_encrypt_rgsw<T: Modulus<Element = u64> + Clone>(
1620 m: &[u64],
1621 public_key: &RlwePublicKey<Vec<Vec<u64>>, DefaultSecureRng>,
1622 decomposer: &(DefaultDecomposer<u64>, DefaultDecomposer<u64>),
1623 mod_op: &ModularOpsU64<T>,
1624 ntt_op: &NttBackendU64,
1625 ) -> RgswCiphertext<Vec<Vec<u64>>, T> {
1626 let (_, ring_size) = Matrix::dimension(&public_key.data);
1627 let gadget_vector_a = decomposer.a().gadget_vector();
1628 let gadget_vector_b = decomposer.b().gadget_vector();
1629
1630 let mut rng = DefaultSecureRng::new();
1631
1632 assert!(m.len() == ring_size);
1633
1634 // public key encrypt RGSW(m1)
1635 let mut rgsw_ct = RgswCiphertext::empty(ring_size, decomposer, mod_op.modulus().clone());
1636 public_key_encrypt_rgsw(
1637 &mut rgsw_ct.data,
1638 m,
1639 &public_key.data,
1640 &gadget_vector_a,
1641 &gadget_vector_b,
1642 mod_op,
1643 ntt_op,
1644 &mut rng,
1645 );
1646
1647 rgsw_ct
1648 }
1649
1650 /// Encrypts m as RGSW ciphertext RGSW(m) using supplied secret key. Returns
1651 /// unseeded RGSW ciphertext in coefficient domain
1652 pub(crate) fn _sk_encrypt_rgsw<T: Modulus<Element = u64> + Clone>(
1653 m: &[u64],
1654 s: &[i32],
1655 decomposer: &(DefaultDecomposer<u64>, DefaultDecomposer<u64>),
1656 mod_op: &ModularOpsU64<T>,
1657 ntt_op: &NttBackendU64,
1658 ) -> SeededRgswCiphertext<Vec<Vec<u64>>, [u8; 32], T> {
1659 let ring_size = s.len();
1660 assert!(m.len() == s.len());
1661
1662 let q = mod_op.modulus();
1663
1664 let gadget_vector_a = decomposer.a().gadget_vector();
1665 let gadget_vector_b = decomposer.b().gadget_vector();
1666
1667 let mut rng = DefaultSecureRng::new();
1668 let mut rgsw_seed = [0u8; 32];
1669 rng.fill_bytes(&mut rgsw_seed);
1670 let mut seeded_rgsw_ct = SeededRgswCiphertext::<Vec<Vec<u64>>, [u8; 32], T>::empty(
1671 ring_size as usize,
1672 decomposer,
1673 rgsw_seed,
1674 q.clone(),
1675 );
1676 let mut p_rng = DefaultSecureRng::new_seeded(rgsw_seed);
1677 secret_key_encrypt_rgsw(
1678 &mut seeded_rgsw_ct.data,
1679 m,
1680 &gadget_vector_a,
1681 &gadget_vector_b,
1682 s,
1683 mod_op,
1684 ntt_op,
1685 &mut p_rng,
1686 &mut rng,
1687 );
1688 seeded_rgsw_ct
1689 }
1690
1691 /// Prints noise in RGSW ciphertext RGSW(m).
1692 ///
1693 /// - rgsw_ct: RGSW ciphertext in coefficient domain
1694 pub(crate) fn _measure_noise_rgsw<T: Modulus<Element = u64> + Clone>(
1695 rgsw_ct: &[Vec<u64>],
1696 m: &[u64],
1697 s: &[i32],
1698 decomposer: &(DefaultDecomposer<u64>, DefaultDecomposer<u64>),
1699 q: &T,
1700 ) {
1701 let gadget_vector_a = decomposer.a().gadget_vector();
1702 let gadget_vector_b = decomposer.b().gadget_vector();
1703 let d_a = gadget_vector_a.len();
1704 let d_b = gadget_vector_b.len();
1705 let ring_size = s.len();
1706 assert!(Matrix::dimension(&rgsw_ct) == (d_a * 2 + d_b * 2, ring_size));
1707 assert!(m.len() == ring_size);
1708
1709 let mod_op = ModularOpsU64::new(q.clone());
1710 let ntt_op = NttBackendU64::new(q, ring_size);
1711
1712 let mul_mod =
1713 |a: &u64, b: &u64| ((*a as u128 * *b as u128) % q.q().unwrap() as u128) as u64;
1714 let s_poly = Vec::<u64>::try_convert_from(s, q);
1715 let mut neg_s = s_poly.clone();
1716 mod_op.elwise_neg_mut(neg_s.as_mut());
1717 let neg_sm0m1 = negacyclic_mul(&neg_s, &m, mul_mod, q.q().unwrap());
1718
1719 // RLWE(\beta^j -s * m)
1720 for j in 0..d_a {
1721 let ideal_m = {
1722 // RLWE(\beta^j -s * m)
1723 let mut beta_neg_sm0m1 = vec![0u64; ring_size as usize];
1724 mod_op.elwise_scalar_mul(beta_neg_sm0m1.as_mut(), &neg_sm0m1, &gadget_vector_a[j]);
1725 beta_neg_sm0m1
1726 };
1727
1728 let mut rlwe = vec![vec![0u64; ring_size as usize]; 2];
1729 rlwe[0].copy_from_slice(rgsw_ct.get_row_slice(j));
1730 rlwe[1].copy_from_slice(rgsw_ct.get_row_slice(d_a + j));
1731 let noise = measure_noise(&rlwe, &ideal_m, &ntt_op, &mod_op, s);
1732
1733 println!(r"Noise RLWE(\beta^{j} -sm0m1): {noise}");
1734 }
1735
1736 // RLWE(\beta^j m)
1737 for j in 0..d_b {
1738 let ideal_m = {
1739 // RLWE(\beta^j m)
1740 let mut beta_m0m1 = vec![0u64; ring_size as usize];
1741 mod_op.elwise_scalar_mul(beta_m0m1.as_mut(), &m, &gadget_vector_b[j]);
1742 beta_m0m1
1743 };
1744
1745 let mut rlwe = vec![vec![0u64; ring_size as usize]; 2];
1746 rlwe[0].copy_from_slice(rgsw_ct.get_row_slice(d_a * 2 + j));
1747 rlwe[1].copy_from_slice(rgsw_ct.get_row_slice(d_a * 2 + d_b + j));
1748 let noise = measure_noise(&rlwe, &ideal_m, &ntt_op, &mod_op, s);
1749
1750 println!(r"Noise RLWE(\beta^{j} m0m1): {noise}");
1751 }
1752 }
1753
1754 #[test]
1755 fn rlwe_encrypt_decryption() {
1756 let logq = 50;
1757 let logp = 2;
1758 let ring_size = 1 << 4;
1759 let q = generate_prime(logq, ring_size, 1u64 << logq).unwrap();
1760 let p = 1u64 << logp;
1761
1762 let mut rng = DefaultSecureRng::new();
1763
1764 let s = RlweSecret::random((ring_size >> 1) as usize, ring_size as usize);
1765
1766 // sample m0
1767 let mut m0 = vec![0u64; ring_size as usize];
1768 RandomFillUniformInModulus::<[u64], u64>::random_fill(
1769 &mut rng,
1770 &(1u64 << logp),
1771 m0.as_mut_slice(),
1772 );
1773
1774 let ntt_op = NttBackendU64::new(&q, ring_size as usize);
1775 let mod_op = ModularOpsU64::new(q);
1776
1777 // encrypt m0
1778 let encoded_m = m0
1779 .iter()
1780 .map(|v| (((*v as f64) * q as f64) / (p as f64)).round() as u64)
1781 .collect_vec();
1782 let rlwe_in_ct = _sk_encrypt_rlwe(&encoded_m, s.values(), &ntt_op, &mod_op);
1783
1784 let mut encoded_m_back = vec![0u64; ring_size as usize];
1785 decrypt_rlwe(
1786 &rlwe_in_ct,
1787 s.values(),
1788 &mut encoded_m_back,
1789 &ntt_op,
1790 &mod_op,
1791 );
1792 let m_back = encoded_m_back
1793 .iter()
1794 .map(|v| (((*v as f64 * p as f64) / q as f64).round() as u64) % p)
1795 .collect_vec();
1796 assert_eq!(m0, m_back);
1797
1798 // let noise = measure_noise(&rlwe_in_ct, &encoded_m, &ntt_op, &mod_op,
1799 // s.values()); println!("Noise: {noise}");
1800 }
1801
1802 #[test]
1803 fn rlwe_by_rgsw_works() {
1804 let logq = 50;
1805 let logp = 2;
1806 let ring_size = 1 << 9;
1807 let q = generate_prime(logq, ring_size, 1u64 << logq).unwrap();
1808 let p: u64 = 1u64 << logp;
1809
1810 let mut rng = DefaultSecureRng::new_seeded([0u8; 32]);
1811
1812 let s = RlweSecret::random((ring_size >> 1) as usize, ring_size as usize);
1813
1814 let mut m0 = vec![0u64; ring_size as usize];
1815 RandomFillUniformInModulus::<[u64], _>::random_fill(
1816 &mut rng,
1817 &(1u64 << logp),
1818 m0.as_mut_slice(),
1819 );
1820 let mut m1 = vec![0u64; ring_size as usize];
1821 m1[thread_rng().gen_range(0..ring_size) as usize] = 1;
1822
1823 let ntt_op = NttBackendU64::new(&q, ring_size as usize);
1824 let mod_op = ModularOpsU64::new(q);
1825 let d_rgsw = 10;
1826 let logb = 5;
1827 let decomposer = (
1828 DefaultDecomposer::new(q, logb, d_rgsw),
1829 DefaultDecomposer::new(q, logb, d_rgsw),
1830 );
1831
1832 // create public key
1833 let mut pk_seed = [0u8; 32];
1834 rng.fill_bytes(&mut pk_seed);
1835 let mut pk_prng = DefaultSecureRng::new_seeded(pk_seed);
1836 let mut seeded_pk =
1837 SeededRlwePublicKey::<Vec<u64>, _>::empty(ring_size as usize, pk_seed, q);
1838 gen_rlwe_public_key(
1839 &mut seeded_pk.data,
1840 s.values(),
1841 &ntt_op,
1842 &mod_op,
1843 &mut pk_prng,
1844 &mut rng,
1845 );
1846 let pk = RlwePublicKey::<Vec<Vec<u64>>, DefaultSecureRng>::from(&seeded_pk);
1847
1848 // Encrypt m1 as RGSW(m1)
1849 let rgsw_ct = {
1850 //TODO(Jay): Figure out better way to test secret key and public key variant of
1851 // RGSW ciphertext encryption within the same test
1852
1853 if true {
1854 // Encryption m1 as RGSW(m1) using secret key
1855 let seeded_rgsw_ct =
1856 _sk_encrypt_rgsw(&m1, s.values(), &decomposer, &mod_op, &ntt_op);
1857 RgswCiphertextEvaluationDomain::<Vec<Vec<u64>>, DefaultSecureRng, NttBackendU64>::from(&seeded_rgsw_ct)
1858 } else {
1859 // Encrypt m1 as RGSW(m1) using public key
1860 let rgsw_ct = _pk_encrypt_rgsw(&m1, &pk, &decomposer, &mod_op, &ntt_op);
1861 RgswCiphertextEvaluationDomain::<_, DefaultSecureRng, NttBackendU64>::from(&rgsw_ct)
1862 }
1863 };
1864
1865 // Encrypt m0 as RLWE(m0)
1866 let mut rlwe_in_ct = {
1867 let encoded_m = m0
1868 .iter()
1869 .map(|v| (((*v as f64) * q as f64) / (p as f64)).round() as u64)
1870 .collect_vec();
1871
1872 _sk_encrypt_rlwe(&encoded_m, s.values(), &ntt_op, &mod_op)
1873 };
1874
1875 // RLWE(m0m1) = RLWE(m0) x RGSW(m1)
1876 let mut scratch_space = vec![
1877 vec![0u64; ring_size as usize];
1878 std::cmp::max(
1879 decomposer.a().decomposition_count(),
1880 decomposer.b().decomposition_count()
1881 ) + 2
1882 ];
1883 rlwe_by_rgsw(
1884 &mut rlwe_in_ct,
1885 &rgsw_ct.data,
1886 &mut scratch_space,
1887 &decomposer,
1888 &ntt_op,
1889 &mod_op,
1890 );
1891
1892 // Decrypt RLWE(m0m1)
1893 let mut encoded_m0m1_back = vec![0u64; ring_size as usize];
1894 decrypt_rlwe(
1895 &rlwe_in_ct,
1896 s.values(),
1897 &mut encoded_m0m1_back,
1898 &ntt_op,
1899 &mod_op,
1900 );
1901 let m0m1_back = encoded_m0m1_back
1902 .iter()
1903 .map(|v| (((*v as f64 * p as f64) / (q as f64)).round() as u64) % p)
1904 .collect_vec();
1905
1906 let mul_mod = |v0: &u64, v1: &u64| (v0 * v1) % p;
1907 let m0m1 = negacyclic_mul(&m0, &m1, mul_mod, p);
1908
1909 // {
1910 // // measure noise
1911 // let encoded_m_ideal = m0m1
1912 // .iter()
1913 // .map(|v| (((*v as f64) * q as f64) / (p as f64)).round() as u64)
1914 // .collect_vec();
1915
1916 // let noise = measure_noise(&rlwe_in_ct, &encoded_m_ideal, &ntt_op,
1917 // &mod_op, s.values()); println!("Noise RLWE(m0m1)(=
1918 // RLWE(m0)xRGSW(m1)) : {noise}"); }
1919
1920 assert!(
1921 m0m1 == m0m1_back,
1922 "Expected {:?} \n Got {:?}",
1923 m0m1,
1924 m0m1_back
1925 );
1926 }
1927
1928 #[test]
1929 fn galois_auto_works() {
1930 let logq = 55;
1931 let ring_size = 1 << 11;
1932 let q = generate_prime(logq, 2 * ring_size, 1u64 << logq).unwrap();
1933 let logp = 3;
1934 let p = 1u64 << logp;
1935 let d_rgsw = 5;
1936 let logb = 11;
1937
1938 let mut rng = DefaultSecureRng::new();
1939 let s = RlweSecret::random((ring_size >> 1) as usize, ring_size as usize);
1940
1941 let mut m = vec![0u64; ring_size as usize];
1942 RandomFillUniformInModulus::random_fill(&mut rng, &p, m.as_mut_slice());
1943 let encoded_m = m
1944 .iter()
1945 .map(|v| (((*v as f64 * q as f64) / (p as f64)).round() as u64))
1946 .collect_vec();
1947
1948 let ntt_op = NttBackendU64::new(&q, ring_size as usize);
1949 let mod_op = ModularOpsU64::new(q);
1950
1951 // RLWE_{s}(m)
1952 let mut seed_rlwe = [0u8; 32];
1953 rng.fill_bytes(&mut seed_rlwe);
1954 let mut seeded_rlwe_m = SeededRlweCiphertext::empty(ring_size as usize, seed_rlwe, q);
1955 let mut p_rng = DefaultSecureRng::new_seeded(seed_rlwe);
1956 secret_key_encrypt_rlwe(
1957 &encoded_m,
1958 &mut seeded_rlwe_m.data,
1959 s.values(),
1960 &mod_op,
1961 &ntt_op,
1962 &mut p_rng,
1963 &mut rng,
1964 );
1965 let mut rlwe_m = RlweCiphertext::<Vec<Vec<u64>>, DefaultSecureRng>::from(&seeded_rlwe_m);
1966
1967 let auto_k = -125;
1968
1969 // Generate galois key to key switch from s^k to s
1970 let decomposer = DefaultDecomposer::new(q, logb, d_rgsw);
1971 let mut seed_auto = [0u8; 32];
1972 rng.fill_bytes(&mut seed_auto);
1973 let mut seeded_auto_key =
1974 SeededAutoKey::empty(ring_size as usize, &decomposer, seed_auto, q);
1975 let mut p_rng = DefaultSecureRng::new_seeded(seed_auto);
1976 let gadget_vector = decomposer.gadget_vector();
1977 galois_key_gen(
1978 &mut seeded_auto_key.data,
1979 s.values(),
1980 auto_k,
1981 &gadget_vector,
1982 &mod_op,
1983 &ntt_op,
1984 &mut p_rng,
1985 &mut rng,
1986 );
1987 let auto_key =
1988 AutoKeyEvaluationDomain::<Vec<Vec<u64>>, DefaultSecureRng, NttBackendU64>::from(
1989 &seeded_auto_key,
1990 );
1991
1992 // Send RLWE_{s}(m) -> RLWE_{s}(m^k)
1993 let mut scratch_space = vec![vec![0u64; ring_size as usize]; d_rgsw + 2];
1994 let (auto_map_index, auto_map_sign) = generate_auto_map(ring_size as usize, auto_k);
1995 galois_auto(
1996 &mut rlwe_m,
1997 &auto_key.data,
1998 &mut scratch_space,
1999 &auto_map_index,
2000 &auto_map_sign,
2001 &mod_op,
2002 &ntt_op,
2003 &decomposer,
2004 );
2005
2006 let rlwe_m_k = rlwe_m;
2007
2008 // Decrypt RLWE_{s}(m^k) and check
2009 let mut encoded_m_k_back = vec![0u64; ring_size as usize];
2010 decrypt_rlwe(
2011 &rlwe_m_k,
2012 s.values(),
2013 &mut encoded_m_k_back,
2014 &ntt_op,
2015 &mod_op,
2016 );
2017 let m_k_back = encoded_m_k_back
2018 .iter()
2019 .map(|v| (((*v as f64 * p as f64) / q as f64).round() as u64) % p)
2020 .collect_vec();
2021
2022 let mut m_k = vec![0u64; ring_size as usize];
2023 // Send \delta m -> \delta m^k
2024 izip!(m.iter(), auto_map_index.iter(), auto_map_sign.iter()).for_each(
2025 |(v, to_index, sign)| {
2026 if !*sign {
2027 m_k[*to_index] = (p - *v) % p;
2028 } else {
2029 m_k[*to_index] = *v;
2030 }
2031 },
2032 );
2033
2034 {
2035 let encoded_m_k = m_k
2036 .iter()
2037 .map(|v| ((*v as f64 * q as f64) / p as f64).round() as u64)
2038 .collect_vec();
2039
2040 let noise = measure_noise(&rlwe_m_k, &encoded_m_k, &ntt_op, &mod_op, s.values());
2041 println!("Ksk noise: {noise}");
2042 }
2043
2044 assert_eq!(m_k_back, m_k);
2045 }
2046
2047 #[test]
2048 fn sk_rgsw_by_rgsw() {
2049 let logq = 60;
2050 let logp = 2;
2051 let ring_size = 1 << 11;
2052 let q = generate_prime(logq, ring_size, 1u64 << logq).unwrap();
2053 let p = 1u64 << logp;
2054 let d_rgsw = 5;
2055 let logb = 12;
2056
2057 let s = RlweSecret::random((ring_size >> 1) as usize, ring_size as usize);
2058
2059 let mut rng = DefaultSecureRng::new();
2060 let ntt_op = NttBackendU64::new(&q, ring_size as usize);
2061 let mod_op = ModularOpsU64::new(q);
2062 let decomposer = (
2063 DefaultDecomposer::new(q, logb, d_rgsw),
2064 DefaultDecomposer::new(q, logb, d_rgsw),
2065 );
2066
2067 let mul_mod = |a: &u64, b: &u64| ((*a as u128 * *b as u128) % q as u128) as u64;
2068
2069 let mut carry_m = vec![0u64; ring_size as usize];
2070 carry_m[thread_rng().gen_range(0..ring_size) as usize] = 1;
2071
2072 // RGSW(carry_m)
2073 let mut rgsw_carrym = {
2074 let seeded_rgsw = _sk_encrypt_rgsw(&carry_m, s.values(), &decomposer, &mod_op, &ntt_op);
2075 let mut rgsw_eval =
2076 RgswCiphertextEvaluationDomain::<_, DefaultSecureRng, NttBackendU64>::from(
2077 &seeded_rgsw,
2078 );
2079 rgsw_eval
2080 .data
2081 .iter_mut()
2082 .for_each(|ri| ntt_op.backward(ri.as_mut()));
2083 rgsw_eval.data
2084 };
2085
2086 let mut scratch_matrix = vec![
2087 vec![0u64; ring_size as usize];
2088 decomposer.a().decomposition_count() * 2
2089 + decomposer.b().decomposition_count() * 2
2090 + std::cmp::max(
2091 decomposer.a().decomposition_count(),
2092 decomposer.b().decomposition_count()
2093 )
2094 ];
2095
2096 _measure_noise_rgsw(&rgsw_carrym, &carry_m, s.values(), &decomposer, &q);
2097
2098 for i in 0..2 {
2099 let mut m = vec![0u64; ring_size as usize];
2100 m[thread_rng().gen_range(0..ring_size) as usize] = if (i & 1) == 1 { q - 1 } else { 1 };
2101 let rgsw_m = RgswCiphertextEvaluationDomain::<_, DefaultSecureRng, NttBackendU64>::from(
2102 &_sk_encrypt_rgsw(&m, s.values(), &decomposer, &mod_op, &ntt_op),
2103 );
2104 rgsw_by_rgsw_inplace(
2105 &mut rgsw_carrym,
2106 &rgsw_m.data,
2107 &decomposer,
2108 &mut scratch_matrix,
2109 &ntt_op,
2110 &mod_op,
2111 );
2112
2113 // measure noise
2114 carry_m = negacyclic_mul(&carry_m, &m, mul_mod, q);
2115 println!("########### Noise RGSW(carrym) in {i}^th loop ###########");
2116 _measure_noise_rgsw(&rgsw_carrym, &carry_m, s.values(), &decomposer, &q);
2117 }
2118 {
2119 // RLWE(m) x RGSW(carry_m)
2120 let mut m = vec![0u64; ring_size as usize];
2121 RandomFillUniformInModulus::random_fill(&mut rng, &q, m.as_mut_slice());
2122 let mut rlwe_ct = _sk_encrypt_rlwe(&m, s.values(), &ntt_op, &mod_op);
2123
2124 // send rgsw to evaluation domain
2125 rgsw_carrym
2126 .iter_mut()
2127 .for_each(|ri| ntt_op.forward(ri.as_mut_slice()));
2128
2129 rlwe_by_rgsw(
2130 &mut rlwe_ct,
2131 &rgsw_carrym,
2132 &mut scratch_matrix,
2133 &decomposer,
2134 &ntt_op,
2135 &mod_op,
2136 );
2137 let m_expected = negacyclic_mul(&carry_m, &m, mul_mod, q);
2138 let noise = measure_noise(&rlwe_ct, &m_expected, &ntt_op, &mod_op, s.values());
2139 println!("RLWE(m) x RGSW(carry_m): {noise}");
2140 }
2141 }
2142
2143 #[test]
2144 fn some_work() {
2145 let logq = 50;
2146 let ring_size = 1 << 11;
2147 let q = generate_prime(logq, ring_size, 1u64 << logq).unwrap();
2148 let d_rgsw = 10;
2149 let logb = 5;
2150 let decomposer = (
2151 DefaultDecomposer::new(q, logb, d_rgsw),
2152 DefaultDecomposer::new(q, logb, d_rgsw),
2153 );
2154
2155 let ntt_op = NttBackendU64::new(&q, ring_size as usize);
2156 let mod_op = ModularOpsU64::new(q);
2157 let mut rng = DefaultSecureRng::new_seeded([0u8; 32]);
2158
2159 let s = RlweSecret::random((ring_size >> 1) as usize, ring_size as usize);
2160
2161 let mut check = Stats { samples: vec![] };
2162
2163 for _ in 0..100 {
2164 let mut m0 = vec![0u64; ring_size as usize];
2165 m0[thread_rng().gen_range(0..ring_size) as usize] = 1;
2166 let mut m1 = vec![0u64; ring_size as usize];
2167 m1[thread_rng().gen_range(0..ring_size) as usize] = 1;
2168
2169 let mut rgsw_ct0 = {
2170 let seeded_rgsw_ct =
2171 _sk_encrypt_rgsw(&m0, s.values(), &decomposer, &mod_op, &ntt_op);
2172 RgswCiphertextEvaluationDomain::<Vec<Vec<u64>>, DefaultSecureRng, NttBackendU64>::from(&seeded_rgsw_ct)
2173 };
2174 let rgsw_ct1 = {
2175 let seeded_rgsw_ct =
2176 _sk_encrypt_rgsw(&m1, s.values(), &decomposer, &mod_op, &ntt_op);
2177 RgswCiphertextEvaluationDomain::<Vec<Vec<u64>>, DefaultSecureRng, NttBackendU64>::from(&seeded_rgsw_ct)
2178 };
2179
2180 // RGSW x RGSW
2181 // send RGSW(m0) to coefficient domain
2182 rgsw_ct0
2183 .data
2184 .iter_mut()
2185 .for_each(|r| ntt_op.backward(r.as_mut_slice()));
2186 let mut scratch_matrix = vec![
2187 vec![0u64; ring_size as usize];
2188 std::cmp::max(
2189 decomposer.a().decomposition_count(),
2190 decomposer.b().decomposition_count()
2191 ) + decomposer.a().decomposition_count() * 2
2192 + decomposer.b().decomposition_count() * 2
2193 ];
2194 rgsw_by_rgsw_inplace(
2195 &mut rgsw_ct0.data,
2196 &rgsw_ct1.data,
2197 &decomposer,
2198 &mut scratch_matrix,
2199 &ntt_op,
2200 &mod_op,
2201 );
2202 let mut rgsw_m0m1 = rgsw_ct0;
2203 // Back to Evaluation for RLWExRGSW
2204 rgsw_m0m1
2205 .data
2206 .iter_mut()
2207 .for_each(|r| ntt_op.forward(r.as_mut_slice()));
2208
2209 // Sample m2, encrypt it as RLWE(m2) and multiply RLWE(m2)xRGSW(m0m1)
2210 let mut m2 = vec![0u64; ring_size as usize];
2211 RandomFillUniformInModulus::random_fill(&mut rng, &q, m2.as_mut_slice());
2212 let mut rlwe_in_ct = { _sk_encrypt_rlwe(&m2, s.values(), &ntt_op, &mod_op) };
2213 let mut scratch_space = vec![
2214 vec![0u64; ring_size as usize];
2215 std::cmp::max(
2216 decomposer.a().decomposition_count(),
2217 decomposer.b().decomposition_count()
2218 ) + 2
2219 ];
2220 rlwe_by_rgsw(
2221 &mut rlwe_in_ct,
2222 &rgsw_m0m1.data,
2223 &mut scratch_space,
2224 &decomposer,
2225 &ntt_op,
2226 &mod_op,
2227 );
2228
2229 // Decrypt RLWE(m0m1m2)
2230 let mut m0m1m2_back = vec![0u64; ring_size as usize];
2231 decrypt_rlwe(&rlwe_in_ct, s.values(), &mut m0m1m2_back, &ntt_op, &mod_op);
2232
2233 // Calculate m0m1m2
2234 let mul_mod = |v0: &u64, v1: &u64| ((*v0 as u128 * *v1 as u128) % q as u128) as u64;
2235 let m0m1 = negacyclic_mul(&m0, &m1, mul_mod, q);
2236 let m0m1m2 = negacyclic_mul(&m2, &m0m1, mul_mod, q);
2237
2238 // diff
2239 mod_op.elwise_sub_mut(m0m1m2_back.as_mut_slice(), m0m1m2.as_ref());
2240
2241 check.add_more(&Vec::<i64>::try_convert_from(&m0m1m2_back, &q));
2242 }
2243
2244 println!("Std: {}", check.std_dev().abs().log2());
2245 }
2246}