phantom-zone/src/lwe.rs
src/lwe.rsRaw
1use std::fmt::Debug;
2
3use itertools::{izip, Itertools};
4use num_traits::{abs, Zero};
5
6use crate::{
7 backend::{ArithmeticOps, VectorOps},
8 decomposer::Decomposer,
9 lwe,
10 num::UnsignedInteger,
11 random::{DefaultSecureRng, RandomGaussianDist, RandomUniformDist, DEFAULT_RNG},
12 utils::{fill_random_ternary_secret_with_hamming_weight, TryConvertFrom, WithLocal},
13 Matrix, MatrixEntity, MatrixMut, Row, RowMut, Secret,
14};
15
16trait LweKeySwitchParameters {
17 fn n_in(&self) -> usize;
18 fn n_out(&self) -> usize;
19 fn d_ks(&self) -> usize;
20}
21
22trait LweCiphertext<M: Matrix> {}
23
24struct LweSecret {
25 values: Vec<i32>,
26}
27
28impl Secret for LweSecret {
29 type Element = i32;
30 fn values(&self) -> &[Self::Element] {
31 &self.values
32 }
33}
34
35impl LweSecret {
36 fn random(hw: usize, n: usize) -> LweSecret {
37 DefaultSecureRng::with_local_mut(|rng| {
38 let mut out = vec![0i32; n];
39 fill_random_ternary_secret_with_hamming_weight(&mut out, hw, rng);
40
41 LweSecret { values: out }
42 })
43 }
44}
45
46pub(crate) fn lwe_key_switch<
47 M: Matrix,
48 Ro: AsMut<[M::MatElement]> + AsRef<[M::MatElement]>,
49 Op: VectorOps<Element = M::MatElement> + ArithmeticOps<Element = M::MatElement>,
50 D: Decomposer<Element = M::MatElement>,
51>(
52 lwe_out: &mut Ro,
53 lwe_in: &Ro,
54 lwe_ksk: &M,
55 operator: &Op,
56 decomposer: &D,
57) {
58 assert!(lwe_ksk.dimension().0 == ((lwe_in.as_ref().len() - 1) * decomposer.d()));
59 assert!(lwe_out.as_ref().len() == lwe_ksk.dimension().1);
60
61 let lwe_in_a_decomposed = lwe_in
62 .as_ref()
63 .iter()
64 .skip(1)
65 .flat_map(|ai| decomposer.decompose(ai));
66 izip!(lwe_in_a_decomposed, lwe_ksk.iter_rows()).for_each(|(ai_j, beta_ij_lwe)| {
67 operator.elwise_fma_scalar_mut(lwe_out.as_mut(), beta_ij_lwe.as_ref(), &ai_j);
68 });
69
70 let out_b = operator.add(&lwe_out.as_ref()[0], &lwe_in.as_ref()[0]);
71 lwe_out.as_mut()[0] = out_b;
72}
73
74fn lwe_ksk_keygen<
75 Mmut: MatrixMut,
76 S: Secret,
77 Op: VectorOps<Element = Mmut::MatElement> + ArithmeticOps<Element = Mmut::MatElement>,
78 R: RandomGaussianDist<Mmut::MatElement, Parameters = Mmut::MatElement>
79 + RandomUniformDist<[Mmut::MatElement], Parameters = Mmut::MatElement>,
80>(
81 from_lwe_sk: &S,
82 to_lwe_sk: &S,
83 ksk_out: &mut Mmut,
84 gadget: &[Mmut::MatElement],
85 operator: &Op,
86 rng: &mut R,
87) where
88 <Mmut as Matrix>::R: RowMut,
89 Mmut::R: TryConvertFrom<[S::Element], Parameters = Mmut::MatElement>,
90 Mmut::MatElement: Zero + Debug,
91{
92 assert!(
93 ksk_out.dimension()
94 == (
95 from_lwe_sk.values().len() * gadget.len(),
96 to_lwe_sk.values().len() + 1,
97 )
98 );
99
100 let d = gadget.len();
101
102 let modulus = VectorOps::modulus(operator);
103 let mut neg_sk_in_m = Mmut::R::try_convert_from(from_lwe_sk.values(), &modulus);
104 operator.elwise_neg_mut(neg_sk_in_m.as_mut());
105 let sk_out_m = Mmut::R::try_convert_from(to_lwe_sk.values(), &modulus);
106
107 izip!(
108 neg_sk_in_m.as_ref(),
109 ksk_out.iter_rows_mut().chunks(d).into_iter()
110 )
111 .for_each(|(neg_sk_in_si, d_ks_lwes)| {
112 izip!(gadget.iter(), d_ks_lwes.into_iter()).for_each(|(f, lwe)| {
113 // sample `a`
114 RandomUniformDist::random_fill(rng, &modulus, &mut lwe.as_mut()[1..]);
115
116 // a * z
117 let mut az = Mmut::MatElement::zero();
118 izip!(lwe.as_ref()[1..].iter(), sk_out_m.as_ref()).for_each(|(ai, si)| {
119 let ai_si = operator.mul(ai, si);
120 az = operator.add(&az, &ai_si);
121 });
122
123 // a*z + (-s_i)*\beta^j + e
124 let mut b = operator.add(&az, &operator.mul(f, neg_sk_in_si));
125 let mut e = Mmut::MatElement::zero();
126 RandomGaussianDist::random_fill(rng, &modulus, &mut e);
127 b = operator.add(&b, &e);
128
129 lwe.as_mut()[0] = b;
130
131 // dbg!(&lwe.as_mut(), &f);
132 })
133 });
134}
135
136/// Encrypts encoded message m as LWE ciphertext
137fn encrypt_lwe<
138 Ro: Row + RowMut,
139 R: RandomGaussianDist<Ro::Element, Parameters = Ro::Element>
140 + RandomUniformDist<[Ro::Element], Parameters = Ro::Element>,
141 S: Secret,
142 Op: ArithmeticOps<Element = Ro::Element>,
143>(
144 lwe_out: &mut Ro,
145 m: &Ro::Element,
146 s: &S,
147 operator: &Op,
148 rng: &mut R,
149) where
150 Ro: TryConvertFrom<[S::Element], Parameters = Ro::Element>,
151 Ro::Element: Zero,
152{
153 let s = Ro::try_convert_from(s.values(), &operator.modulus());
154 assert!(s.as_ref().len() == (lwe_out.as_ref().len() - 1));
155
156 // a*s
157 RandomUniformDist::random_fill(rng, &operator.modulus(), &mut lwe_out.as_mut()[1..]);
158 let mut sa = Ro::Element::zero();
159 izip!(lwe_out.as_mut().iter().skip(1), s.as_ref()).for_each(|(ai, si)| {
160 let tmp = operator.mul(ai, si);
161 sa = operator.add(&tmp, &sa);
162 });
163
164 // b = a*s + e + m
165 let mut e = Ro::Element::zero();
166 RandomGaussianDist::random_fill(rng, &operator.modulus(), &mut e);
167 let b = operator.add(&operator.add(&sa, &e), m);
168 lwe_out.as_mut()[0] = b;
169}
170
171fn decrypt_lwe<Ro: Row, Op: ArithmeticOps<Element = Ro::Element>, S: Secret>(
172 lwe_ct: &Ro,
173 s: &S,
174 operator: &Op,
175) -> Ro::Element
176where
177 Ro: TryConvertFrom<[S::Element], Parameters = Ro::Element>,
178 Ro::Element: Zero,
179{
180 let s = Ro::try_convert_from(s.values(), &operator.modulus());
181
182 let mut sa = Ro::Element::zero();
183 izip!(lwe_ct.as_ref().iter().skip(1), s.as_ref()).for_each(|(ai, si)| {
184 let tmp = operator.mul(ai, si);
185 sa = operator.add(&tmp, &sa);
186 });
187
188 let b = &lwe_ct.as_ref()[0];
189 operator.sub(b, &sa)
190}
191
192#[cfg(test)]
193mod tests {
194
195 use crate::{
196 backend::ModularOpsU64,
197 decomposer::{gadget_vector, DefaultDecomposer},
198 lwe::lwe_key_switch,
199 random::DefaultSecureRng,
200 };
201
202 use super::{decrypt_lwe, encrypt_lwe, lwe_ksk_keygen, LweSecret};
203
204 #[test]
205 fn encrypt_decrypt_works() {
206 let logq = 20;
207 let q = 1u64 << logq;
208 let lwe_n = 1024;
209 let logp = 3;
210
211 let modq_op = ModularOpsU64::new(q);
212 let lwe_sk = LweSecret::random(lwe_n >> 1, lwe_n);
213
214 let mut rng = DefaultSecureRng::new();
215
216 // encrypt
217 for m in 0..1u64 << logp {
218 let encoded_m = m << (logq - logp);
219 let mut lwe_ct = vec![0u64; lwe_n + 1];
220 encrypt_lwe(&mut lwe_ct, &encoded_m, &lwe_sk, &modq_op, &mut rng);
221 let encoded_m_back = decrypt_lwe(&lwe_ct, &lwe_sk, &modq_op);
222 let m_back = ((((encoded_m_back as f64) * ((1 << logp) as f64)) / q as f64).round()
223 as u64)
224 % (1u64 << logp);
225 assert_eq!(m, m_back, "Expected {m} but got {m_back}");
226 }
227 }
228
229 #[test]
230 fn key_switch_works() {
231 let logq = 16;
232 let logp = 3;
233 let q = 1u64 << logq;
234 let lwe_in_n = 1024;
235 let lwe_out_n = 470;
236 let d_ks = 3;
237 let logb = 4;
238
239 let lwe_sk_in = LweSecret::random(lwe_in_n >> 1, lwe_in_n);
240 let lwe_sk_out = LweSecret::random(lwe_out_n >> 1, lwe_out_n);
241
242 let mut rng = DefaultSecureRng::new();
243 let modq_op = ModularOpsU64::new(q);
244
245 // genrate ksk
246 for _ in 0..10 {
247 let mut ksk = vec![vec![0u64; lwe_out_n + 1]; d_ks * lwe_in_n];
248 let gadget = gadget_vector(logq, logb, d_ks);
249 lwe_ksk_keygen(
250 &lwe_sk_in,
251 &lwe_sk_out,
252 &mut ksk,
253 &gadget,
254 &modq_op,
255 &mut rng,
256 );
257 // println!("{:?}", ksk);
258
259 for m in 0..(1 << logp) {
260 // encrypt using lwe_sk_in
261 let encoded_m = m << (logq - logp);
262 let mut lwe_in_ct = vec![0u64; lwe_in_n + 1];
263 encrypt_lwe(&mut lwe_in_ct, &encoded_m, &lwe_sk_in, &modq_op, &mut rng);
264
265 // key switch from lwe_sk_in to lwe_sk_out
266 let decomposer = DefaultDecomposer::new(1u64 << logq, logb, d_ks);
267 let mut lwe_out_ct = vec![0u64; lwe_out_n + 1];
268 lwe_key_switch(&mut lwe_out_ct, &lwe_in_ct, &ksk, &modq_op, &decomposer);
269
270 // decrypt lwe_out_ct using lwe_sk_out
271 let encoded_m_back = decrypt_lwe(&lwe_out_ct, &lwe_sk_out, &modq_op);
272 let m_back = ((((encoded_m_back as f64) * ((1 << logp) as f64)) / q as f64).round()
273 as u64)
274 % (1u64 << logp);
275 assert_eq!(m, m_back, "Expected {m} but got {m_back}");
276 // dbg!(m, m_back);
277 // dbg!(encoded_m, encoded_m_back);
278 }
279 }
280 }
281}