phantom-zone/src/lwe.rs
src/lwe.rsRaw
1use std::{
2 cell::RefCell,
3 collections::btree_map::Values,
4 fmt::{Debug, Display},
5 marker::PhantomData,
6};
7
8use itertools::{izip, Itertools};
9use num_traits::{abs, PrimInt, ToPrimitive, Zero};
10
11use crate::{
12 backend::{ArithmeticOps, VectorOps},
13 decomposer::Decomposer,
14 lwe,
15 num::UnsignedInteger,
16 random::{DefaultSecureRng, NewWithSeed, RandomGaussianDist, RandomUniformDist, DEFAULT_RNG},
17 utils::{fill_random_ternary_secret_with_hamming_weight, TryConvertFrom, WithLocal},
18 Matrix, MatrixEntity, MatrixMut, Row, RowEntity, RowMut, Secret,
19};
20
21struct SeededLweKeySwitchingKey<Ro, S>
22where
23 Ro: Row,
24{
25 data: Ro,
26 seed: S,
27 to_lwe_n: usize,
28 modulus: Ro::Element,
29}
30
31impl<Ro: RowEntity, S> SeededLweKeySwitchingKey<Ro, S> {
32 pub(crate) fn empty(
33 from_lwe_n: usize,
34 to_lwe_n: usize,
35 d: usize,
36 seed: S,
37 modulus: Ro::Element,
38 ) -> Self {
39 let data = Ro::zeros(from_lwe_n * d);
40 SeededLweKeySwitchingKey {
41 data,
42 to_lwe_n,
43 seed,
44 modulus,
45 }
46 }
47}
48
49struct LweKeySwitchingKey<M, R> {
50 data: M,
51 _phantom: PhantomData<R>,
52}
53
54impl<
55 M: MatrixMut + MatrixEntity,
56 R: NewWithSeed + RandomUniformDist<[M::MatElement], Parameters = M::MatElement>,
57 > From<&SeededLweKeySwitchingKey<M::R, R::Seed>> for LweKeySwitchingKey<M, R>
58where
59 M::R: RowMut,
60 R::Seed: Clone,
61 M::MatElement: Copy,
62{
63 fn from(value: &SeededLweKeySwitchingKey<M::R, R::Seed>) -> Self {
64 let mut p_rng = R::new_with_seed(value.seed.clone());
65 let mut data = M::zeros(value.data.as_ref().len(), value.to_lwe_n + 1);
66 izip!(value.data.as_ref().iter(), data.iter_rows_mut()).for_each(|(bi, lwe_i)| {
67 RandomUniformDist::random_fill(&mut p_rng, &value.modulus, &mut lwe_i.as_mut()[1..]);
68 lwe_i.as_mut()[0] = *bi;
69 });
70 LweKeySwitchingKey {
71 data,
72 _phantom: PhantomData,
73 }
74 }
75}
76
77trait LweCiphertext<M: Matrix> {}
78
79#[derive(Clone)]
80pub struct LweSecret {
81 values: Vec<i32>,
82}
83
84impl Secret for LweSecret {
85 type Element = i32;
86 fn values(&self) -> &[Self::Element] {
87 &self.values
88 }
89}
90
91impl LweSecret {
92 pub(crate) fn random(hw: usize, n: usize) -> LweSecret {
93 DefaultSecureRng::with_local_mut(|rng| {
94 let mut out = vec![0i32; n];
95 fill_random_ternary_secret_with_hamming_weight(&mut out, hw, rng);
96
97 LweSecret { values: out }
98 })
99 }
100}
101
102pub(crate) fn lwe_key_switch<
103 M: Matrix,
104 Ro: AsMut<[M::MatElement]> + AsRef<[M::MatElement]>,
105 Op: VectorOps<Element = M::MatElement> + ArithmeticOps<Element = M::MatElement>,
106 D: Decomposer<Element = M::MatElement>,
107>(
108 lwe_out: &mut Ro,
109 lwe_in: &Ro,
110 lwe_ksk: &M,
111 operator: &Op,
112 decomposer: &D,
113) {
114 assert!(lwe_ksk.dimension().0 == ((lwe_in.as_ref().len() - 1) * decomposer.d()));
115 assert!(lwe_out.as_ref().len() == lwe_ksk.dimension().1);
116
117 let lwe_in_a_decomposed = lwe_in
118 .as_ref()
119 .iter()
120 .skip(1)
121 .flat_map(|ai| decomposer.decompose(ai));
122 izip!(lwe_in_a_decomposed, lwe_ksk.iter_rows()).for_each(|(ai_j, beta_ij_lwe)| {
123 operator.elwise_fma_scalar_mut(lwe_out.as_mut(), beta_ij_lwe.as_ref(), &ai_j);
124 });
125
126 let out_b = operator.add(&lwe_out.as_ref()[0], &lwe_in.as_ref()[0]);
127 lwe_out.as_mut()[0] = out_b;
128}
129
130pub fn lwe_ksk_keygen<
131 Ro: Row + RowMut + RowEntity,
132 S,
133 Op: VectorOps<Element = Ro::Element> + ArithmeticOps<Element = Ro::Element>,
134 R: RandomGaussianDist<Ro::Element, Parameters = Ro::Element>
135 + RandomUniformDist<[Ro::Element], Parameters = Ro::Element>
136 + NewWithSeed,
137>(
138 from_lwe_sk: &[S],
139 to_lwe_sk: &[S],
140 ksk_out: &mut Ro,
141 gadget: &[Ro::Element],
142 seed: R::Seed,
143 operator: &Op,
144 rng: &mut R,
145) where
146 Ro: TryConvertFrom<[S], Parameters = Ro::Element>,
147 Ro::Element: Zero + Debug,
148{
149 assert!(ksk_out.as_ref().len() == (from_lwe_sk.len() * gadget.len()));
150
151 let d = gadget.len();
152
153 let modulus = VectorOps::modulus(operator);
154 let mut neg_sk_in_m = Ro::try_convert_from(from_lwe_sk, &modulus);
155 operator.elwise_neg_mut(neg_sk_in_m.as_mut());
156 let sk_out_m = Ro::try_convert_from(to_lwe_sk, &modulus);
157
158 let mut scratch = Ro::zeros(to_lwe_sk.len());
159 let mut p_rng = R::new_with_seed(seed);
160
161 izip!(neg_sk_in_m.as_ref(), ksk_out.as_mut().chunks_mut(d)).for_each(
162 |(neg_sk_in_si, d_lwes_partb)| {
163 izip!(gadget.iter(), d_lwes_partb.into_iter()).for_each(|(f, lwe_b)| {
164 // sample `a`
165 RandomUniformDist::random_fill(&mut p_rng, &modulus, scratch.as_mut());
166
167 // a * z
168 let mut az = Ro::Element::zero();
169 izip!(scratch.as_ref().iter(), sk_out_m.as_ref()).for_each(|(ai, si)| {
170 let ai_si = operator.mul(ai, si);
171 az = operator.add(&az, &ai_si);
172 });
173
174 // a*z + (-s_i)*\beta^j + e
175 let mut b = operator.add(&az, &operator.mul(f, neg_sk_in_si));
176 let mut e = Ro::Element::zero();
177 RandomGaussianDist::random_fill(rng, &modulus, &mut e);
178 b = operator.add(&b, &e);
179
180 *lwe_b = b;
181
182 // dbg!(&lwe.as_mut(), &f);
183 })
184 },
185 );
186}
187
188/// Encrypts encoded message m as LWE ciphertext
189pub fn encrypt_lwe<
190 Ro: Row + RowMut,
191 R: RandomGaussianDist<Ro::Element, Parameters = Ro::Element>
192 + RandomUniformDist<[Ro::Element], Parameters = Ro::Element>,
193 S,
194 Op: ArithmeticOps<Element = Ro::Element>,
195>(
196 lwe_out: &mut Ro,
197 m: &Ro::Element,
198 s: &[S],
199 operator: &Op,
200 rng: &mut R,
201) where
202 Ro: TryConvertFrom<[S], Parameters = Ro::Element>,
203 Ro::Element: Zero,
204{
205 let s = Ro::try_convert_from(s, &operator.modulus());
206 assert!(s.as_ref().len() == (lwe_out.as_ref().len() - 1));
207
208 // a*s
209 RandomUniformDist::random_fill(rng, &operator.modulus(), &mut lwe_out.as_mut()[1..]);
210 let mut sa = Ro::Element::zero();
211 izip!(lwe_out.as_mut().iter().skip(1), s.as_ref()).for_each(|(ai, si)| {
212 let tmp = operator.mul(ai, si);
213 sa = operator.add(&tmp, &sa);
214 });
215
216 // b = a*s + e + m
217 let mut e = Ro::Element::zero();
218 RandomGaussianDist::random_fill(rng, &operator.modulus(), &mut e);
219 let b = operator.add(&operator.add(&sa, &e), m);
220 lwe_out.as_mut()[0] = b;
221}
222
223pub fn decrypt_lwe<Ro: Row, Op: ArithmeticOps<Element = Ro::Element>, S>(
224 lwe_ct: &Ro,
225 s: &[S],
226 operator: &Op,
227) -> Ro::Element
228where
229 Ro: TryConvertFrom<[S], Parameters = Ro::Element>,
230 Ro::Element: Zero,
231{
232 let s = Ro::try_convert_from(s, &operator.modulus());
233
234 let mut sa = Ro::Element::zero();
235 izip!(lwe_ct.as_ref().iter().skip(1), s.as_ref()).for_each(|(ai, si)| {
236 let tmp = operator.mul(ai, si);
237 sa = operator.add(&tmp, &sa);
238 });
239
240 let b = &lwe_ct.as_ref()[0];
241 operator.sub(b, &sa)
242}
243
244/// Measures noise in input LWE ciphertext with reference of `ideal_m`
245///
246/// - ct: Input LWE ciphertext
247/// - s: corresponding secret
248/// - ideal_m: Ideal `encoded` message
249pub(crate) fn measure_noise_lwe<Ro: Row, Op: ArithmeticOps<Element = Ro::Element>, S>(
250 ct: &Ro,
251 s: &[S],
252 operator: &Op,
253 ideal_m: &Ro::Element,
254) -> f64
255where
256 Ro: TryConvertFrom<[S], Parameters = Ro::Element>,
257 Ro::Element: Zero + ToPrimitive + PrimInt + Display,
258{
259 assert!(s.len() == ct.as_ref().len() - 1,);
260
261 let s = Ro::try_convert_from(s, &operator.modulus());
262 let mut sa = Ro::Element::zero();
263 izip!(s.as_ref().iter(), ct.as_ref().iter().skip(1)).for_each(|(si, ai)| {
264 sa = operator.add(&sa, &operator.mul(si, ai));
265 });
266 let m = operator.sub(&ct.as_ref()[0], &sa);
267
268 let mut diff = operator.sub(&m, ideal_m);
269 let q = operator.modulus();
270 if diff > (q >> 1) {
271 diff = q - diff;
272 }
273 return diff.to_f64().unwrap().log2();
274}
275
276#[cfg(test)]
277mod tests {
278
279 use crate::{
280 backend::{ModInit, ModularOpsU64},
281 decomposer::{gadget_vector, DefaultDecomposer},
282 lwe::{lwe_key_switch, measure_noise_lwe},
283 random::DefaultSecureRng,
284 rgsw::measure_noise,
285 Secret,
286 };
287
288 use super::{
289 decrypt_lwe, encrypt_lwe, lwe_ksk_keygen, LweKeySwitchingKey, LweSecret,
290 SeededLweKeySwitchingKey,
291 };
292
293 const K: usize = 50;
294
295 #[test]
296 fn encrypt_decrypt_works() {
297 let logq = 16;
298 let q = 1u64 << logq;
299 let lwe_n = 1024;
300 let logp = 3;
301
302 let modq_op = ModularOpsU64::new(q);
303 let lwe_sk = LweSecret::random(lwe_n >> 1, lwe_n);
304
305 let mut rng = DefaultSecureRng::new();
306
307 // encrypt
308 for m in 0..1u64 << logp {
309 let encoded_m = m << (logq - logp);
310 let mut lwe_ct = vec![0u64; lwe_n + 1];
311 encrypt_lwe(
312 &mut lwe_ct,
313 &encoded_m,
314 &lwe_sk.values(),
315 &modq_op,
316 &mut rng,
317 );
318 let encoded_m_back = decrypt_lwe(&lwe_ct, &lwe_sk.values(), &modq_op);
319 let m_back = ((((encoded_m_back as f64) * ((1 << logp) as f64)) / q as f64).round()
320 as u64)
321 % (1u64 << logp);
322 assert_eq!(m, m_back, "Expected {m} but got {m_back}");
323 }
324 }
325
326 #[test]
327 fn key_switch_works() {
328 let logq = 16;
329 let logp = 2;
330 let q = 1u64 << logq;
331 let lwe_in_n = 2048;
332 let lwe_out_n = 493;
333 let d_ks = 3;
334 let logb = 4;
335
336 let lwe_sk_in = LweSecret::random(lwe_in_n >> 1, lwe_in_n);
337 let lwe_sk_out = LweSecret::random(lwe_out_n >> 1, lwe_out_n);
338
339 let mut rng = DefaultSecureRng::new();
340 let modq_op = ModularOpsU64::new(q);
341
342 // genrate ksk
343 for _ in 0..K {
344 let mut ksk_seed = [0u8; 32];
345 rng.fill_bytes(&mut ksk_seed);
346 let mut seeded_ksk =
347 SeededLweKeySwitchingKey::empty(lwe_in_n, lwe_out_n, d_ks, ksk_seed, q);
348 let gadget = gadget_vector(logq, logb, d_ks);
349 lwe_ksk_keygen(
350 &lwe_sk_in.values(),
351 &lwe_sk_out.values(),
352 &mut seeded_ksk.data,
353 &gadget,
354 seeded_ksk.seed,
355 &modq_op,
356 &mut rng,
357 );
358 // println!("{:?}", ksk);
359 let ksk = LweKeySwitchingKey::<Vec<Vec<u64>>, DefaultSecureRng>::from(&seeded_ksk);
360
361 for m in 0..(1 << logp) {
362 // encrypt using lwe_sk_in
363 let encoded_m = m << (logq - logp);
364 let mut lwe_in_ct = vec![0u64; lwe_in_n + 1];
365 encrypt_lwe(
366 &mut lwe_in_ct,
367 &encoded_m,
368 lwe_sk_in.values(),
369 &modq_op,
370 &mut rng,
371 );
372
373 // key switch from lwe_sk_in to lwe_sk_out
374 let decomposer = DefaultDecomposer::new(1u64 << logq, logb, d_ks);
375 let mut lwe_out_ct = vec![0u64; lwe_out_n + 1];
376 lwe_key_switch(
377 &mut lwe_out_ct,
378 &lwe_in_ct,
379 &ksk.data,
380 &modq_op,
381 &decomposer,
382 );
383
384 // decrypt lwe_out_ct using lwe_sk_out
385 let encoded_m_back = decrypt_lwe(&lwe_out_ct, &lwe_sk_out.values(), &modq_op);
386 let m_back = ((((encoded_m_back as f64) * ((1 << logp) as f64)) / q as f64).round()
387 as u64)
388 % (1u64 << logp);
389 let noise =
390 measure_noise_lwe(&lwe_out_ct, lwe_sk_out.values(), &modq_op, &encoded_m);
391 println!("Noise: {noise}");
392 assert_eq!(m, m_back, "Expected {m} but got {m_back}");
393 // dbg!(m, m_back);
394 // dbg!(encoded_m, encoded_m_back);
395 }
396 }
397 }
398}