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, GetModulus, Modulus, VectorOps},
13 decomposer::Decomposer,
14 random::{
15 DefaultSecureRng, NewWithSeed, RandomFillGaussianInModulus, RandomGaussianElementInModulus,
16 RandomFillUniformInModulus, DEFAULT_RNG,
17 },
18 utils::{fill_random_ternary_secret_with_hamming_weight, TryConvertFrom1, WithLocal},
19 Matrix, MatrixEntity, MatrixMut, Row, RowEntity, RowMut, Secret,
20};
21
22struct SeededLweKeySwitchingKey<Ro, S>
23where
24 Ro: Row,
25{
26 data: Ro,
27 seed: S,
28 to_lwe_n: usize,
29 modulus: Ro::Element,
30}
31
32impl<Ro: RowEntity, S> SeededLweKeySwitchingKey<Ro, S> {
33 pub(crate) fn empty(
34 from_lwe_n: usize,
35 to_lwe_n: usize,
36 d: usize,
37 seed: S,
38 modulus: Ro::Element,
39 ) -> Self {
40 let data = Ro::zeros(from_lwe_n * d);
41 SeededLweKeySwitchingKey {
42 data,
43 to_lwe_n,
44 seed,
45 modulus,
46 }
47 }
48}
49
50struct LweKeySwitchingKey<M, R> {
51 data: M,
52 _phantom: PhantomData<R>,
53}
54
55impl<
56 M: MatrixMut + MatrixEntity,
57 R: NewWithSeed + RandomFillUniformInModulus<[M::MatElement], M::MatElement>,
58 > From<&SeededLweKeySwitchingKey<M::R, R::Seed>> for LweKeySwitchingKey<M, R>
59where
60 M::R: RowMut,
61 R::Seed: Clone,
62 M::MatElement: Copy,
63{
64 fn from(value: &SeededLweKeySwitchingKey<M::R, R::Seed>) -> Self {
65 let mut p_rng = R::new_with_seed(value.seed.clone());
66 let mut data = M::zeros(value.data.as_ref().len(), value.to_lwe_n + 1);
67 izip!(value.data.as_ref().iter(), data.iter_rows_mut()).for_each(|(bi, lwe_i)| {
68 RandomFillUniformInModulus::random_fill(&mut p_rng, &value.modulus, &mut lwe_i.as_mut()[1..]);
69 lwe_i.as_mut()[0] = *bi;
70 });
71 LweKeySwitchingKey {
72 data,
73 _phantom: PhantomData,
74 }
75 }
76}
77
78trait LweCiphertext<M: Matrix> {}
79
80#[derive(Clone)]
81pub struct LweSecret {
82 pub(crate) values: Vec<i32>,
83}
84
85impl Secret for LweSecret {
86 type Element = i32;
87 fn values(&self) -> &[Self::Element] {
88 &self.values
89 }
90}
91
92impl LweSecret {
93 pub(crate) fn random(hw: usize, n: usize) -> LweSecret {
94 DefaultSecureRng::with_local_mut(|rng| {
95 let mut out = vec![0i32; n];
96 fill_random_ternary_secret_with_hamming_weight(&mut out, hw, rng);
97
98 LweSecret { values: out }
99 })
100 }
101}
102
103pub(crate) fn lwe_key_switch<
104 M: Matrix,
105 Ro: AsMut<[M::MatElement]> + AsRef<[M::MatElement]>,
106 Op: VectorOps<Element = M::MatElement> + ArithmeticOps<Element = M::MatElement>,
107 D: Decomposer<Element = M::MatElement>,
108>(
109 lwe_out: &mut Ro,
110 lwe_in: &Ro,
111 lwe_ksk: &M,
112 operator: &Op,
113 decomposer: &D,
114) {
115 assert!(
116 lwe_ksk.dimension().0 == ((lwe_in.as_ref().len() - 1) * decomposer.decomposition_count())
117 );
118 assert!(lwe_out.as_ref().len() == lwe_ksk.dimension().1);
119
120 let lwe_in_a_decomposed = lwe_in
121 .as_ref()
122 .iter()
123 .skip(1)
124 .flat_map(|ai| decomposer.decompose(ai));
125 izip!(lwe_in_a_decomposed, lwe_ksk.iter_rows()).for_each(|(ai_j, beta_ij_lwe)| {
126 operator.elwise_fma_scalar_mut(lwe_out.as_mut(), beta_ij_lwe.as_ref(), &ai_j);
127 });
128
129 let out_b = operator.add(&lwe_out.as_ref()[0], &lwe_in.as_ref()[0]);
130 lwe_out.as_mut()[0] = out_b;
131}
132
133pub fn lwe_ksk_keygen<
134 Ro: Row + RowMut + RowEntity,
135 S,
136 Op: VectorOps<Element = Ro::Element>
137 + ArithmeticOps<Element = Ro::Element>
138 + GetModulus<Element = Ro::Element>,
139 R: RandomGaussianElementInModulus<Ro::Element, Op::M>,
140 PR: RandomFillUniformInModulus<[Ro::Element], Op::M>,
141>(
142 from_lwe_sk: &[S],
143 to_lwe_sk: &[S],
144 ksk_out: &mut Ro,
145 gadget: &[Ro::Element],
146 operator: &Op,
147 p_rng: &mut PR,
148 rng: &mut R,
149) where
150 Ro: TryConvertFrom1<[S], Op::M>,
151 Ro::Element: Zero + Debug,
152{
153 assert!(ksk_out.as_ref().len() == (from_lwe_sk.len() * gadget.len()));
154
155 let d = gadget.len();
156
157 let modulus = operator.modulus();
158 let mut neg_sk_in_m = Ro::try_convert_from(from_lwe_sk, modulus);
159 operator.elwise_neg_mut(neg_sk_in_m.as_mut());
160 let sk_out_m = Ro::try_convert_from(to_lwe_sk, modulus);
161
162 let mut scratch = Ro::zeros(to_lwe_sk.len());
163
164 izip!(neg_sk_in_m.as_ref(), ksk_out.as_mut().chunks_mut(d)).for_each(
165 |(neg_sk_in_si, d_lwes_partb)| {
166 izip!(gadget.iter(), d_lwes_partb.into_iter()).for_each(|(f, lwe_b)| {
167 // sample `a`
168 RandomFillUniformInModulus::random_fill(p_rng, &modulus, scratch.as_mut());
169
170 // a * z
171 let mut az = Ro::Element::zero();
172 izip!(scratch.as_ref().iter(), sk_out_m.as_ref()).for_each(|(ai, si)| {
173 let ai_si = operator.mul(ai, si);
174 az = operator.add(&az, &ai_si);
175 });
176
177 // a*z + (-s_i)*\beta^j + e
178 let mut b = operator.add(&az, &operator.mul(f, neg_sk_in_si));
179 let e = RandomGaussianElementInModulus::random(rng, &modulus);
180 b = operator.add(&b, &e);
181
182 *lwe_b = b;
183 })
184 },
185 );
186}
187
188/// Encrypts encoded message m as LWE ciphertext
189pub fn encrypt_lwe<
190 Ro: Row + RowMut,
191 Op: ArithmeticOps<Element = Ro::Element> + GetModulus<Element = Ro::Element>,
192 R: RandomGaussianElementInModulus<Ro::Element, Op::M> + RandomFillUniformInModulus<[Ro::Element], Op::M>,
193 S,
194>(
195 lwe_out: &mut Ro,
196 m: &Ro::Element,
197 s: &[S],
198 operator: &Op,
199 rng: &mut R,
200) where
201 Ro: TryConvertFrom1<[S], Op::M>,
202 Ro::Element: Zero,
203{
204 let s = Ro::try_convert_from(s, operator.modulus());
205 assert!(s.as_ref().len() == (lwe_out.as_ref().len() - 1));
206
207 // a*s
208 RandomFillUniformInModulus::random_fill(rng, operator.modulus(), &mut lwe_out.as_mut()[1..]);
209 let mut sa = Ro::Element::zero();
210 izip!(lwe_out.as_mut().iter().skip(1), s.as_ref()).for_each(|(ai, si)| {
211 let tmp = operator.mul(ai, si);
212 sa = operator.add(&tmp, &sa);
213 });
214
215 // b = a*s + e + m
216 let e = RandomGaussianElementInModulus::random(rng, operator.modulus());
217 let b = operator.add(&operator.add(&sa, &e), m);
218 lwe_out.as_mut()[0] = b;
219}
220
221pub fn decrypt_lwe<
222 Ro: Row,
223 Op: ArithmeticOps<Element = Ro::Element> + GetModulus<Element = Ro::Element>,
224 S,
225>(
226 lwe_ct: &Ro,
227 s: &[S],
228 operator: &Op,
229) -> Ro::Element
230where
231 Ro: TryConvertFrom1<[S], Op::M>,
232 Ro::Element: Zero,
233{
234 let s = Ro::try_convert_from(s, operator.modulus());
235
236 let mut sa = Ro::Element::zero();
237 izip!(lwe_ct.as_ref().iter().skip(1), s.as_ref()).for_each(|(ai, si)| {
238 let tmp = operator.mul(ai, si);
239 sa = operator.add(&tmp, &sa);
240 });
241
242 let b = &lwe_ct.as_ref()[0];
243 operator.sub(b, &sa)
244}
245
246/// Measures noise in input LWE ciphertext with reference of `ideal_m`
247///
248/// - ct: Input LWE ciphertext
249/// - s: corresponding secret
250/// - ideal_m: Ideal `encoded` message
251pub(crate) fn measure_noise_lwe<
252 Ro: Row,
253 Op: ArithmeticOps<Element = Ro::Element> + GetModulus<Element = Ro::Element>,
254 S,
255>(
256 ct: &Ro,
257 s: &[S],
258 operator: &Op,
259 ideal_m: &Ro::Element,
260) -> f64
261where
262 Ro: TryConvertFrom1<[S], Op::M>,
263 Ro::Element: Zero + ToPrimitive + PrimInt + Display,
264{
265 assert!(s.len() == ct.as_ref().len() - 1,);
266
267 let s = Ro::try_convert_from(s, &operator.modulus());
268 let mut sa = Ro::Element::zero();
269 izip!(s.as_ref().iter(), ct.as_ref().iter().skip(1)).for_each(|(si, ai)| {
270 sa = operator.add(&sa, &operator.mul(si, ai));
271 });
272 let m = operator.sub(&ct.as_ref()[0], &sa);
273
274 let mut diff = operator.sub(&m, ideal_m);
275 let q = operator.modulus();
276 return q.to_i64(&diff).to_f64().unwrap().abs().log2();
277}
278
279#[cfg(test)]
280mod tests {
281
282 use crate::{
283 backend::{ModInit, ModularOpsU64},
284 decomposer::{Decomposer, DefaultDecomposer},
285 lwe::{lwe_key_switch, measure_noise_lwe},
286 random::DefaultSecureRng,
287 rgsw::measure_noise,
288 Secret,
289 };
290
291 use super::{
292 decrypt_lwe, encrypt_lwe, lwe_ksk_keygen, LweKeySwitchingKey, LweSecret,
293 SeededLweKeySwitchingKey,
294 };
295
296 const K: usize = 50;
297
298 #[test]
299 fn encrypt_decrypt_works() {
300 let logq = 16;
301 let q = 1u64 << logq;
302 let lwe_n = 1024;
303 let logp = 3;
304
305 let modq_op = ModularOpsU64::new(q);
306 let lwe_sk = LweSecret::random(lwe_n >> 1, lwe_n);
307
308 let mut rng = DefaultSecureRng::new();
309
310 // encrypt
311 for m in 0..1u64 << logp {
312 let encoded_m = m << (logq - logp);
313 let mut lwe_ct = vec![0u64; lwe_n + 1];
314 encrypt_lwe(
315 &mut lwe_ct,
316 &encoded_m,
317 &lwe_sk.values(),
318 &modq_op,
319 &mut rng,
320 );
321 let encoded_m_back = decrypt_lwe(&lwe_ct, &lwe_sk.values(), &modq_op);
322 let m_back = ((((encoded_m_back as f64) * ((1 << logp) as f64)) / q as f64).round()
323 as u64)
324 % (1u64 << logp);
325 assert_eq!(m, m_back, "Expected {m} but got {m_back}");
326 }
327 }
328
329 #[test]
330 fn key_switch_works() {
331 let logq = 18;
332 let logp = 2;
333 let q = 1u64 << logq;
334 let lwe_in_n = 2048;
335 let lwe_out_n = 493;
336 let d_ks = 3;
337 let logb = 6;
338
339 let lwe_sk_in = LweSecret::random(lwe_in_n >> 1, lwe_in_n);
340 let lwe_sk_out = LweSecret::random(lwe_out_n >> 1, lwe_out_n);
341
342 let mut rng = DefaultSecureRng::new();
343 let modq_op = ModularOpsU64::new(q);
344
345 // genrate ksk
346 for _ in 0..K {
347 let mut ksk_seed = [0u8; 32];
348 rng.fill_bytes(&mut ksk_seed);
349 let mut seeded_ksk =
350 SeededLweKeySwitchingKey::empty(lwe_in_n, lwe_out_n, d_ks, ksk_seed, q);
351 let mut p_rng = DefaultSecureRng::new_seeded(ksk_seed);
352 let decomposer = DefaultDecomposer::new(q, logb, d_ks);
353 let gadget = decomposer.gadget_vector();
354 lwe_ksk_keygen(
355 &lwe_sk_in.values(),
356 &lwe_sk_out.values(),
357 &mut seeded_ksk.data,
358 &gadget,
359 &modq_op,
360 &mut p_rng,
361 &mut rng,
362 );
363 // println!("{:?}", ksk);
364 let ksk = LweKeySwitchingKey::<Vec<Vec<u64>>, DefaultSecureRng>::from(&seeded_ksk);
365
366 for m in 0..(1 << logp) {
367 // encrypt using lwe_sk_in
368 let encoded_m = m << (logq - logp);
369 let mut lwe_in_ct = vec![0u64; lwe_in_n + 1];
370 encrypt_lwe(
371 &mut lwe_in_ct,
372 &encoded_m,
373 lwe_sk_in.values(),
374 &modq_op,
375 &mut rng,
376 );
377
378 // key switch from lwe_sk_in to lwe_sk_out
379 let decomposer = DefaultDecomposer::new(1u64 << logq, logb, d_ks);
380 let mut lwe_out_ct = vec![0u64; lwe_out_n + 1];
381 lwe_key_switch(
382 &mut lwe_out_ct,
383 &lwe_in_ct,
384 &ksk.data,
385 &modq_op,
386 &decomposer,
387 );
388
389 // decrypt lwe_out_ct using lwe_sk_out
390 let encoded_m_back = decrypt_lwe(&lwe_out_ct, &lwe_sk_out.values(), &modq_op);
391 let m_back = ((((encoded_m_back as f64) * ((1 << logp) as f64)) / q as f64).round()
392 as u64)
393 % (1u64 << logp);
394 let noise =
395 measure_noise_lwe(&lwe_out_ct, lwe_sk_out.values(), &modq_op, &encoded_m);
396 println!("Noise: {noise}");
397 assert_eq!(m, m_back, "Expected {m} but got {m_back}");
398 // dbg!(m, m_back);
399 // dbg!(encoded_m, encoded_m_back);
400 }
401 }
402 }
403}