galois auto works

src/backend.rs

@@ -7,6 +7,7 @@ pub trait VectorOps {
     fn elwise_mul(&self, out: &mut [Self::Element], a: &[Self::Element], b: &[Self::Element]);
 
     fn elwise_add_mut(&self, a: &mut [Self::Element], b: &[Self::Element]);
+    fn elwise_sub_mut(&self, a: &mut [Self::Element], b: &[Self::Element]);
     fn elwise_mul_mut(&self, a: &mut [Self::Element], b: &[Self::Element]);
     fn elwise_neg_mut(&self, a: &mut [Self::Element]);
     /// inplace mutates `a`: a = a + b*c
@@ -21,6 +22,7 @@ pub trait ArithmeticOps {
     fn mul(&self, a: &Self::Element, b: &Self::Element) -> Self::Element;
     fn add(&self, a: &Self::Element, b: &Self::Element) -> Self::Element;
     fn sub(&self, a: &Self::Element, b: &Self::Element) -> Self::Element;
+    fn neg(&self, a: &Self::Element) -> Self::Element;
 
     fn modulus(&self) -> Self::Element;
 }
@@ -115,6 +117,10 @@ impl ArithmeticOps for ModularOpsU64 {
         self.sub_mod_fast(*a, *b)
     }
 
+    fn neg(&self, a: &Self::Element) -> Self::Element {
+        self.q - *a
+    }
+
     fn modulus(&self) -> Self::Element {
         self.q
     }
@@ -129,6 +135,12 @@ impl VectorOps for ModularOpsU64 {
         });
     }
 
+    fn elwise_sub_mut(&self, a: &mut [Self::Element], b: &[Self::Element]) {
+        izip!(a.iter_mut(), b.iter()).for_each(|(ai, bi)| {
+            *ai = self.sub_mod_fast(*ai, *bi);
+        });
+    }
+
     fn elwise_mul_mut(&self, a: &mut [Self::Element], b: &[Self::Element]) {
         izip!(a.iter_mut(), b.iter()).for_each(|(ai, bi)| {
             *ai = self.mul_mod_fast(*ai, *bi);

src/decomposer.rs

@@ -45,7 +45,7 @@ impl NumInfo for u128 {
 
 impl<T: PrimInt + NumInfo + Debug> DefaultDecomposer<T> {
     pub fn new(q: T, logb: usize, d: usize) -> DefaultDecomposer<T> {
-        // if q is power of 2, then BITS - leading zeros outputs logq + 1.
+        // if q is power of 2, then `BITS - leading_zeros` outputs logq + 1.
         let logq = if q & (q - T::one()) == T::zero() {
             (T::BITS - q.leading_zeros() - 1) as usize
         } else {
@@ -71,7 +71,6 @@ impl DefaultDecomposer {
         Op: ArithmeticOps<Element = T>,
     {
         let mut value = T::zero();
-        dbg!(self.ignore_limbs);
         for i in 0..self.d {
             value = modq_op.add(
                 &value,
@@ -88,10 +87,15 @@ impl DefaultDecomposer {
 impl<T: PrimInt + WrappingSub + Debug> Decomposer for DefaultDecomposer<T> {
     type Element = T;
     fn decompose(&self, value: &T) -> Vec<T> {
-        let value = round_value(*value, self.ignore_bits);
+        let mut value = round_value(*value, self.ignore_bits);
+
         let q = self.q;
+        if value >= (q >> 1) {
+            value = value.wrapping_sub(&q);
+        }
+
         let logb = self.logb;
-        // let b = T::one() << logb; // base
+        let b = T::one() << logb; // base
         let b_by2 = T::one() << (logb - 1);
         // let neg_b_by2_modq = q - b_by2;
         let full_mask = (T::one() << logb) - T::one();
@@ -100,15 +104,22 @@ impl Decomposer for DefaultDecomposer {
         let mut out = Vec::<T>::with_capacity(self.d);
         for i in 0..self.d {
             let mut limb = ((value >> (logb * i)) & full_mask) + carry;
-
-            carry = limb & b_by2;
-            limb = (q + limb) - (carry << 1);
-            if limb > q {
-                limb = limb - q;
+            carry = T::zero();
+            if limb > b_by2 {
+                limb = (q + limb) - b;
+                carry = T::one();
             }
+
+            // carry = ((q + g - limb) % q) >> logb;
+
+            // carry = limb & b_by2;
+            // limb = (q + limb) - (carry << 1);
+            // if limb > q {
+            //     limb = limb - q;
+            // }
             out.push(limb);
 
-            carry = carry >> (logb - 1);
+            // carry = carry >> (logb - 1);
         }
 
         return out;
@@ -154,13 +165,13 @@ mod tests {
             };
             let decomposer = DefaultDecomposer::new(q, logb, d);
             let modq_op = ModularOpsU64::new(q);
-            for _ in 0..1 {
+            for _ in 0..100 {
                 let value = rng.gen_range(0..q);
                 let limbs = decomposer.decompose(&value);
                 let value_back = decomposer.recompose(&limbs, &modq_op);
                 let rounded_value =
                     round_value(value, decomposer.ignore_bits) << decomposer.ignore_bits;
-                dbg!(value, rounded_value, value_back, &limbs);
+                dbg!(rounded_value, value, value_back);
                 assert_eq!(
                     rounded_value, value_back,
                     "Expected {rounded_value} got {value_back} for q={q}"

src/rgsw.rs

@@ -1,9 +1,15 @@
-use itertools::izip;
+use std::{
+    fmt::Debug,
+    ops::{Neg, Sub},
+};
+
+use itertools::{izip, Itertools};
+use num_traits::{PrimInt, ToPrimitive};
 
 use crate::{
-    backend::VectorOps,
+    backend::{ArithmeticOps, VectorOps},
     decomposer::{self, Decomposer},
-    ntt::Ntt,
+    ntt::{self, Ntt},
     random::{DefaultSecureRng, RandomGaussianDist, RandomUniformDist},
     utils::{fill_random_ternary_secret_with_hamming_weight, TryConvertFrom, WithLocal},
     Matrix, MatrixEntity, MatrixMut, RowMut, Secret,
@@ -31,6 +37,219 @@ impl RlweSecret {
     }
 }
 
+fn generate_auto_map(ring_size: usize, k: usize) -> (Vec<usize>, Vec<bool>) {
+    assert!(k & 1 == 1, "Auto {k} must be odd");
+    let (auto_map_index, auto_sign_index): (Vec<usize>, Vec<bool>) = (0..ring_size)
+        .into_iter()
+        .map(|i| {
+            let mut to_index = (i * k) % (2 * ring_size);
+            let mut sign = true;
+
+            // wrap around. false implies negative
+            if to_index >= ring_size {
+                to_index = to_index - ring_size;
+                sign = false;
+            }
+
+            (to_index, sign)
+        })
+        .unzip();
+    (auto_map_index, auto_sign_index)
+}
+
+/// Generates RLWE Key switching key to key switch ciphertext RLWE_{from_s}(m)
+/// to RLWE_{to_s}(m).
+///
+/// Key switching equals
+///     \sum decompose(c_1)_i * RLWE_{to_s}(\beta^i -from_s)
+/// Hence, key switchin key equals RLWE'(-from_s) = RLWE(-from_s), RLWE(beta^1
+/// -from_s), ..., RLWE(beta^{d-1} -from_s).
+///
+/// - ksk_out: Output Key switching key. Key switching key stores RLWE
+///   ciphertexts as [RLWE'_A(-from_s) || RLWE'_B(-from_s)]
+/// - neg_from_s_eval: Negative of secret polynomial to key switch from in
+///   evaluation domain
+/// - to_s_eval: secret polynomial to key switch to in evalution domain.
+fn rlwe_ksk_gen<
+    Mmut: MatrixMut + MatrixEntity,
+    ModOp: ArithmeticOps<Element = Mmut::MatElement> + VectorOps<Element = Mmut::MatElement>,
+    NttOp: Ntt<Element = Mmut::MatElement>,
+    R: RandomGaussianDist<[Mmut::MatElement], Parameters = Mmut::MatElement>
+        + RandomUniformDist<[Mmut::MatElement], Parameters = Mmut::MatElement>,
+>(
+    ksk_out: &mut Mmut,
+    neg_from_s_eval: &Mmut,
+    to_s_eval: &Mmut,
+    gadget_vector: &[Mmut::MatElement],
+    mod_op: &ModOp,
+    ntt_op: &NttOp,
+    rng: &mut R,
+) where
+    <Mmut as Matrix>::R: RowMut,
+{
+    let ring_size = neg_from_s_eval.dimension().1;
+    let d = gadget_vector.len();
+    assert!(neg_from_s_eval.dimension().0 == 1);
+    assert!(ksk_out.dimension() == (d * 2, ring_size));
+    assert!(to_s_eval.dimension() == (1, ring_size));
+
+    let q = ArithmeticOps::modulus(mod_op);
+
+    let mut scratch_space = Mmut::zeros(1, ring_size);
+
+    // RLWE'_{to_s}(-from_s)
+    let (part_a, part_b) = ksk_out.split_at_row(d);
+    izip!(part_a.iter_mut(), part_b.iter_mut(), gadget_vector.iter()).for_each(
+        |(ai, bi, beta_i)| {
+            // sample ai and transform to evaluation
+            RandomUniformDist::random_fill(rng, &q, ai.as_mut());
+            ntt_op.forward(ai.as_mut());
+
+            // to_s * ai
+            mod_op.elwise_mul(
+                scratch_space.get_row_mut(0),
+                ai.as_ref(),
+                to_s_eval.get_row_slice(0),
+            );
+
+            // ei + to_s*ai
+            RandomGaussianDist::random_fill(rng, &q, bi.as_mut());
+            ntt_op.forward(bi.as_mut());
+            mod_op.elwise_add_mut(bi.as_mut(), scratch_space.get_row_slice(0));
+
+            // beta_i * -from_s
+            mod_op.elwise_scalar_mul(
+                scratch_space.get_row_mut(0),
+                neg_from_s_eval.get_row_slice(0),
+                beta_i,
+            );
+
+            // bi = ei + to_s*ai + beta_i*-from_s
+            mod_op.elwise_add_mut(bi.as_mut(), scratch_space.get_row_slice(0));
+        },
+    );
+}
+
+fn galois_key_gen<
+    Mmut: MatrixMut + MatrixEntity,
+    ModOp: ArithmeticOps<Element = Mmut::MatElement> + VectorOps<Element = Mmut::MatElement>,
+    NttOp: Ntt<Element = Mmut::MatElement>,
+    S: Secret,
+    R: RandomGaussianDist<[Mmut::MatElement], Parameters = Mmut::MatElement>
+        + RandomUniformDist<[Mmut::MatElement], Parameters = Mmut::MatElement>,
+>(
+    ksk_out: &mut Mmut,
+    s: &S,
+    auto_k: usize,
+    gadget_vector: &[Mmut::MatElement],
+    mod_op: &ModOp,
+    ntt_op: &NttOp,
+    rng: &mut R,
+) where
+    <Mmut as Matrix>::R: RowMut,
+    Mmut: TryConvertFrom<[S::Element], Parameters = Mmut::MatElement>,
+    Mmut::MatElement: Copy + Sub<Output = Mmut::MatElement>,
+{
+    let ring_size = s.values().len();
+    let (auto_map_index, auto_map_sign) = generate_auto_map(ring_size, auto_k);
+
+    let q = ArithmeticOps::modulus(mod_op);
+
+    // s(X) -> -s(X^k)
+    let mut s = Mmut::try_convert_from(s.values(), &q);
+    let mut neg_s_auto = Mmut::zeros(1, s.dimension().1);
+    izip!(s.get_row(0), auto_map_index.iter(), auto_map_sign.iter()).for_each(
+        |(el, to_index, sign)| {
+            // if sign is +ve (true), then negate because we need -s(X) (i.e. do the
+            // opposite than the usual case)
+            if *sign {
+                neg_s_auto.set(0, *to_index, q - *el)
+            } else {
+                neg_s_auto.set(0, *to_index, *el)
+            }
+        },
+    );
+
+    // send both s(X) and -s(X^k) to evaluation domain
+    ntt_op.forward(s.get_row_mut(0));
+    ntt_op.forward(neg_s_auto.get_row_mut(0));
+
+    // Ksk from -s(X^k) to s(X)
+    rlwe_ksk_gen(ksk_out, &neg_s_auto, &s, gadget_vector, mod_op, ntt_op, rng);
+}
+
+/// Sends RLWE_{s}(X) -> RLWE_{s}(X^k) where k is some galois element
+fn galois_auto<
+    M: Matrix,
+    Mmut: MatrixMut<MatElement = M::MatElement>,
+    ModOp: ArithmeticOps<Element = M::MatElement> + VectorOps<Element = M::MatElement>,
+    NttOp: Ntt<Element = M::MatElement>,
+    D: Decomposer<Element = M::MatElement>,
+>(
+    rlwe_in: &M,
+    ksk: &M,
+    rlwe_out: &mut Mmut,
+    a_rlwe_decomposed: &mut Mmut,
+    auto_map_index: &[usize],
+    auto_map_sign: &[bool],
+    mod_op: &ModOp,
+    ntt_op: &NttOp,
+    decomposer: &D,
+) where
+    <Mmut as Matrix>::R: RowMut,
+    M::MatElement: Copy,
+{
+    let d = decomposer.d();
+
+    // send b(X) -> b(X^k)
+    izip!(
+        rlwe_in.get_row(1),
+        auto_map_index.iter(),
+        auto_map_sign.iter()
+    )
+    .for_each(|(el_in, to_index, sign)| {
+        if !*sign {
+            rlwe_out.set(1, *to_index, mod_op.neg(el_in));
+        } else {
+            rlwe_out.set(1, *to_index, *el_in);
+        }
+    });
+
+    // send a(X) -> a(X^k) and decompose a(X^k)
+    izip!(
+        rlwe_in.get_row(0),
+        auto_map_index.iter(),
+        auto_map_sign.iter()
+    )
+    .for_each(|(el_in, to_index, sign)| {
+        let el_out = if !*sign { mod_op.neg(el_in) } else { *el_in };
+
+        let el_out_decomposed = decomposer.decompose(&el_out);
+        for j in 0..d {
+            a_rlwe_decomposed.set(j, *to_index, el_out_decomposed[j]);
+        }
+    });
+
+    // transform decomposed a(X^k) to evaluation domain
+    a_rlwe_decomposed.iter_rows_mut().for_each(|r| {
+        ntt_op.forward(r.as_mut());
+    });
+
+    // key switch (a(X^k) * RLWE'(s(X^k)))
+    izip!(a_rlwe_decomposed.iter_rows(), ksk.iter_rows().take(d)).for_each(|(a, b)| {
+        mod_op.elwise_fma_mut(rlwe_out.get_row_mut(0), a.as_ref(), b.as_ref());
+    });
+    ntt_op.forward(rlwe_out.get_row_mut(1));
+    izip!(a_rlwe_decomposed.iter_rows(), ksk.iter_rows().skip(d)).for_each(|(a, b)| {
+        mod_op.elwise_fma_mut(rlwe_out.get_row_mut(1), a.as_ref(), b.as_ref());
+    });
+
+    // transform RLWE(-s(X^k) * a(X^k)) to coefficient domain
+    rlwe_out
+        .iter_rows_mut()
+        .for_each(|r| ntt_op.backward(r.as_mut()));
+}
+
 /// Encrypts message m as a RGSW ciphertext.
 ///
 /// - m_eval: is `m` is evaluation domain
@@ -366,11 +585,71 @@ fn decrypt_rlwe<
     mod_op.elwise_add_mut(m_out.get_row_mut(0), rlwe_ct.get_row_slice(1));
 }
 
+// Measures noise in degree 1 RLWE ciphertext against encoded ideal message
+// encoded_m
+fn measure_noise<
+    Mmut: MatrixMut + Matrix + MatrixEntity,
+    ModOp: VectorOps<Element = Mmut::MatElement>,
+    NttOp: Ntt<Element = Mmut::MatElement>,
+    S: Secret,
+>(
+    rlwe_ct: &Mmut,
+    encoded_m_ideal: &Mmut,
+    ntt_op: &NttOp,
+    mod_op: &ModOp,
+    s: &S,
+) -> f64
+where
+    <Mmut as Matrix>::R: RowMut,
+    Mmut: TryConvertFrom<[S::Element], Parameters = Mmut::MatElement>,
+    Mmut::MatElement: PrimInt + ToPrimitive + Debug,
+{
+    let ring_size = s.values().len();
+    assert!(rlwe_ct.dimension() == (2, ring_size));
+    assert!(encoded_m_ideal.dimension() == (1, ring_size));
+
+    // -(s * a)
+    let q = VectorOps::modulus(mod_op);
+    let mut s = Mmut::try_convert_from(s.values(), &q);
+    ntt_op.forward(s.get_row_mut(0));
+    let mut a = Mmut::zeros(1, ring_size);
+    a.get_row_mut(0).copy_from_slice(rlwe_ct.get_row_slice(0));
+    ntt_op.forward(a.get_row_mut(0));
+    mod_op.elwise_mul_mut(s.get_row_mut(0), a.get_row_slice(0));
+    mod_op.elwise_neg_mut(s.get_row_mut(0));
+    ntt_op.backward(s.get_row_mut(0));
+
+    // m+e = b - s*a
+    let mut m_plus_e = s;
+    mod_op.elwise_add_mut(m_plus_e.get_row_mut(0), rlwe_ct.get_row_slice(1));
+
+    // difference
+    mod_op.elwise_sub_mut(m_plus_e.get_row_mut(0), encoded_m_ideal.get_row_slice(0));
+
+    let mut max_diff_bits = f64::MIN;
+    m_plus_e.get_row_slice(0).iter().for_each(|v| {
+        let mut v = *v;
+
+        if v >= (q >> 1) {
+            // v is -ve
+            v = q - v;
+        }
+
+        let bits = (v.to_f64().unwrap()).log2();
+
+        if max_diff_bits < bits {
+            max_diff_bits = bits;
+        }
+    });
+
+    return max_diff_bits;
+}
+
 #[cfg(test)]
 mod tests {
     use std::vec;
 
-    use itertools::Itertools;
+    use itertools::{izip, Itertools};
     use rand::{thread_rng, Rng};
 
     use crate::{
@@ -378,10 +657,14 @@ mod tests {
         decomposer::{gadget_vector, DefaultDecomposer},
         ntt::{self, Ntt, NttBackendU64},
         random::{DefaultSecureRng, RandomUniformDist},
+        rgsw::measure_noise,
         utils::{generate_prime, negacyclic_mul},
     };
 
-    use super::{decrypt_rlwe, encrypt_rgsw, encrypt_rlwe, rlwe_by_rgsw, RlweSecret};
+    use super::{
+        decrypt_rlwe, encrypt_rgsw, encrypt_rlwe, galois_auto, galois_key_gen, generate_auto_map,
+        rlwe_by_rgsw, RlweSecret,
+    };
 
     #[test]
     fn rlwe_by_rgsw_works() {
@@ -463,4 +746,106 @@ mod tests {
         assert_eq!(m0m1, m0m1_back, "Expected {:?} got {:?}", m0m1, m0m1_back);
         // dbg!(&m0m1_back, m0m1, q);
     }
+
+    #[test]
+    fn galois_auto_works() {
+        let logq = 50;
+        let ring_size = 1 << 5;
+        let q = generate_prime(logq, 2 * ring_size, 1u64 << logq).unwrap();
+        let logp = 3;
+        let p = 1u64 << logp;
+        let d_rgsw = 10;
+        let logb = 5;
+
+        let mut rng = DefaultSecureRng::new();
+        let s = RlweSecret::random((ring_size >> 1) as usize, ring_size as usize);
+
+        let mut m = vec![0u64; ring_size as usize];
+        RandomUniformDist::random_fill(&mut rng, &p, m.as_mut_slice());
+        let encoded_m = m
+            .iter()
+            .map(|v| (((*v as f64 * q as f64) / (p as f64)).round() as u64))
+            .collect_vec();
+
+        let ntt_op = NttBackendU64::new(q, ring_size as usize);
+        let mod_op = ModularOpsU64::new(q);
+
+        // RLWE_{s}(m)
+        let mut rlwe_m = vec![vec![0u64; ring_size as usize]; 2];
+        encrypt_rlwe(
+            &vec![encoded_m.clone()],
+            &mut rlwe_m,
+            &s,
+            &mod_op,
+            &ntt_op,
+            &mut rng,
+        );
+
+        let auto_k = 25;
+
+        // Generate galois key to key switch from s^k to s
+        let mut ksk_out = vec![vec![0u64; ring_size as usize]; d_rgsw * 2];
+        let gadget_vector = gadget_vector(logq, logb, d_rgsw);
+        galois_key_gen(
+            &mut ksk_out,
+            &s,
+            auto_k,
+            &gadget_vector,
+            &mod_op,
+            &ntt_op,
+            &mut rng,
+        );
+
+        // Send RLWE_{s}(m) -> RLWE_{s}(m^k)
+        let mut rlwe_m_k = vec![vec![0u64; ring_size as usize]; 2];
+        let mut scratch_space = vec![vec![0u64; ring_size as usize]; d_rgsw];
+        let (auto_map_index, auto_map_sign) = generate_auto_map(ring_size as usize, auto_k);
+        let decomposer = DefaultDecomposer::new(q, logb, d_rgsw);
+        galois_auto(
+            &rlwe_m,
+            &ksk_out,
+            &mut rlwe_m_k,
+            &mut scratch_space,
+            &auto_map_index,
+            &auto_map_sign,
+            &mod_op,
+            &ntt_op,
+            &decomposer,
+        );
+
+        // Decrypt RLWE_{s}(m^k) and check
+        let mut encoded_m_k_back = vec![vec![0u64; ring_size as usize]];
+        decrypt_rlwe(&rlwe_m_k, &s, &mut encoded_m_k_back, &ntt_op, &mod_op);
+        let m_k_back = encoded_m_k_back[0]
+            .iter()
+            .map(|v| (((*v as f64 * p as f64) / q as f64).round() as u64) % p)
+            .collect_vec();
+
+        let mut m_k = vec![0u64; ring_size as usize];
+        // Send \delta m -> \delta m^k
+        izip!(m.iter(), auto_map_index.iter(), auto_map_sign.iter()).for_each(
+            |(v, to_index, sign)| {
+                if !*sign {
+                    m_k[*to_index] = (p - *v) % p;
+                } else {
+                    m_k[*to_index] = *v;
+                }
+            },
+        );
+
+        {
+            let encoded_m_k = m_k
+                .iter()
+                .map(|v| ((*v as f64 * q as f64) / p as f64).round() as u64)
+                .collect_vec();
+
+            let noise = measure_noise(&rlwe_m_k, &vec![encoded_m_k], &ntt_op, &mod_op, &s);
+            println!("Ksk noise: {noise}");
+        }
+
+        // FIXME(Jay): Galios autormophism will incur high error unless we fix in
+        // accurate decomoposition of Decomposer when q is prime
+        assert_eq!(m_k_back, m_k);
+        // dbg!(m_k_back, m_k, q);
+    }
 }