wip, works for values < (1<<62)

arith/src/lib.rs

@@ -17,6 +17,7 @@ pub mod tuple_ring;
 
 // mod naive_ntt; // note: for dev only
 pub mod ntt;
+pub mod ntt_u64;
 
 // expose objects
 pub use complex::C;

arith/src/ntt.rs

@@ -51,18 +51,21 @@ impl NTT {
                 let S: u64 = roots_of_unity[m + i];
                 for j in k..k + t {
                     let U: u64 = r[j];
-                    let V: u64 = (r[j + t] * S) % q;
+                    // let V: u64 = (r[j + t] * S) % q;
+                    let V: u64 = ((r[j + t] as u128 * S as u128) % q as u128) as u64;
                     // compute r[j] = (U + V) % q:
-                    r[j] = U + V;
-                    if r[j] >= q {
-                        r[j] -= q;
-                    }
-                    // compute r[j + t] = (U - V) % q:
-                    if U >= V {
-                        r[j + t] = U - V;
-                    } else {
-                        r[j + t] = (q + U) - V;
-                    }
+                    r[j] = ((U as u128 + V as u128) % q as u128) as u64;
+                    r[j + t] = (((q as u128 + U as u128) - V as u128) % q as u128) as u64;
+                    // r[j] = U + V;
+                    // if r[j] >= q {
+                    //     r[j] -= q;
+                    // }
+                    // // compute r[j + t] = (U - V) % q:
+                    // if U >= V {
+                    //     r[j + t] = U - V;
+                    // } else {
+                    //     r[j + t] = (q + U) - V;
+                    // }
                 }
                 k = k + 2 * t;
             }
@@ -90,17 +93,20 @@ impl NTT {
                 for j in k..k + t {
                     let U: u64 = r[j];
                     let V: u64 = r[j + t];
+                    r[j] = ((U as u128 + V as u128) % q as u128) as u64;
+                    r[j + t] =
+                        (((q as u128 + U as u128) - V as u128) * S as u128 % q as u128) as u64;
                     // compute r[j] = (U + V) % q:
-                    r[j] = U + V;
-                    if r[j] >= q {
-                        r[j] -= q;
-                    }
-                    // compute r[j + t] = ((U - V) * S) % q;
-                    if U >= V {
-                        r[j + t] = ((U - V) * S) % q;
-                    } else {
-                        r[j + t] = ((q + U - V) * S) % q;
-                    }
+                    // r[j] = U + V;
+                    // if r[j] >= q {
+                    //     r[j] -= q;
+                    // }
+                    // // compute r[j + t] = ((U - V) * S) % q;
+                    // if U >= V {
+                    //     r[j + t] = ((U - V) * S) % q;
+                    // } else {
+                    //     r[j + t] = ((q + U - V) * S) % q;
+                    // }
                 }
                 k += 2 * t;
             }
@@ -108,7 +114,8 @@ impl NTT {
             m /= 2;
         }
         for i in 0..n {
-            r[i] = (r[i] * n_inv) % q;
+            // r[i] = (r[i] * n_inv) % q;
+            r[i] = ((r[i] as u128 * n_inv as u128) % q as u128) as u64;
         }
         r
     }

arith/src/ntt_u64.rs

@@ -0,0 +1,268 @@
+//! This file implements the wrapper on top of the ntt.rs to be able to compute
+//! the NTT for non-prime modulus, specifically for modulus 2^64 (for u64).
+
+use crate::ntt::NTT as NTT_p;
+
+// const P0: u64 = 17293822569241362433;
+
+// const P0: u64 = 4611686018427387905;
+// const P1: u64 = 4611686018326724609;
+const P0: u64 = 8070449433331580929;
+const P1: u64 = 8070450532384645121;
+// const P0: u64 = (1 << 60) - (1 << 28) + 1;
+// const P1: u64 = (1 << 60) - (1 << 27) + 1;
+// const P2: u64 = (1 << 60) - (1 << 26) + 1;
+
+#[derive(Debug)]
+pub struct NTT {}
+
+impl NTT {
+    pub fn ntt(
+        n: usize,
+        a: &Vec<u64>,
+    ) -> (
+        Vec<u64>,
+        Vec<u64>,
+        // Vec<u64>,
+        // Vec<u64>,
+        // Vec<u64>,
+        // Vec<u64>,
+        // Vec<u64>,
+    ) {
+        // TODO ensure that: a_i <P0
+
+        // apply modulus p_i
+        let a_0: Vec<u64> = a.iter().map(|a_i| (a_i % P0 + P0) % P0).collect();
+        let a_1: Vec<u64> = a.iter().map(|a_i| (a_i % P1 + P1) % P1).collect();
+        // let a_2: Vec<u64> = a.iter().map(|a_i| (a_i % P2 + P2) % P2).collect();
+        // let a_3: Vec<u64> = a.iter().map(|a_i| (a_i % P3 + P3) % P3).collect();
+        // let a_4: Vec<u64> = a.iter().map(|a_i| (a_i % P4 + P4) % P4).collect();
+        // let a_5: Vec<u64> = a.iter().map(|a_i| (a_i % P5 + P5) % P5).collect();
+        // let a_6: Vec<u64> = a.iter().map(|a_i| (a_i % P6 + P6) % P6).collect();
+
+        let r_0 = NTT_p::ntt(P0, n, &a_0);
+        let r_1 = NTT_p::ntt(P1, n, &a_1);
+        // let r_2 = NTT_p::ntt(P2, n, &a_2);
+        // let r_3 = NTT_p::ntt(P3, n, &a_3);
+        // let r_4 = NTT_p::ntt(P4, n, &a_4);
+        // let r_5 = NTT_p::ntt(P5, n, &a_5);
+        // let r_6 = NTT_p::ntt(P6, n, &a_6);
+
+        (r_0, r_1) //, r_2) //, r_3, r_4) //, r_5, r_6)
+    }
+
+    pub fn intt(
+        n: usize,
+        r: &(
+            Vec<u64>,
+            Vec<u64>,
+            // Vec<u64>,
+            // Vec<u64>,
+            // Vec<u64>,
+            // Vec<u64>,
+            // Vec<u64>,
+        ),
+    ) -> Vec<u64> {
+        let a_0 = NTT_p::intt(P0, n, &r.0);
+        let a_1 = NTT_p::intt(P1, n, &r.1);
+        // let a_2 = NTT_p::intt(P2, n, &r.2);
+        // let a_3 = NTT_p::intt(P3, n, &r.3);
+        // let a_4 = NTT_p::intt(P4, n, &r.4);
+        // let a_5 = NTT_p::intt(P5, n, &r.5);
+        // let a_6 = NTT_p::intt(P6, n, &r.6);
+
+        // Garner CRT for two moduli: combine (r1 mod p1, r2 mod p2) -> Z/(p1*p2)
+        // let inv_p1_mod_p2: u128 = inv_mod_u64(p1 % p2, p2) as u128;
+        // const INV_P1_MOD_P2: u128 = 4895217125691974194;
+
+        reconstruct(a_0, a_1) //, a_2) // , a_3, a_4) //, a_5, a_6)
+    }
+}
+
+fn reconstruct(
+    a0: Vec<u64>,
+    a1: Vec<u64>,
+    // a2: Vec<u64>,
+    // a_3: Vec<u64>,
+    // a_4: Vec<u64>,
+    // a_5: Vec<u64>,
+    // a_6: Vec<u64>,
+) -> Vec<u64> {
+    // let Q = P0 as u128 * P1 as u128;
+
+    // y_i = q/q_i
+    let y0 = ((u64::MAX as u128 + 1) / P0 as u128);
+    let y1 = ((u64::MAX as u128 + 1) / P1 as u128);
+    // let y2 = ((u64::MAX as u128 + 1) / P2 as u128) as u64;
+    // let y0: u128 = P1 as u128 * P2 as u128; // N_i =Q/P0 = P1*P2
+    // let y1: u128 = P0 as u128 * P2 as u128;
+    // let y2: u128 = P0 as u128 * P1 as u128;
+    // let y0 = (Q / P0 as u128) as u64;
+    // let y1 = (Q / P1 as u128) as u64;
+    // let y2 = ((u64::MAX as u128 + 1) / P2 as u128) as u64;
+    // let y3 = ((u64::MAX as u128 + 1) / P3 as u128) as u64;
+    // let y4 = ((u64::MAX as u128 + 1) / P4 as u128) as u64;
+
+    // y_i^-1 mod q_i = z_i
+    let z0: u128 = inv_mod(P0 as u128, y0); // M_i = N_i^-1 mod q_i
+    let z1: u128 = inv_mod(P1 as u128, y1);
+    // let z2: u128 = inv_mod(P2 as u128, y2);
+    // let y2_inv = inv_mod(P2 as u128, y2);
+    // let y3_inv = inv_mod(P3 as u128, y3);
+    // let y4_inv = inv_mod(P4 as u128, y4);
+
+    // m1 = q1^-1 mod q2
+    // aux = (a2 - a1) * m1 mod q2
+    // a = a1 + (q1 * m1) * aux
+
+    let m1 = inv_mod(P1 as u128, P0 as u128) as u64; // P0^-1 mod P1
+    let aux: Vec<u64> = itertools::zip_eq(a0.clone(), a1.clone())
+        .map(|(a0_i, a1_i)| ((a1_i - a0_i) * m1) % P1)
+        .collect();
+    let a: Vec<u64> = itertools::zip_eq(a0, aux)
+        // .map(|(a1_i, aux_i)| a1_i + (P1 * m1) * aux_i)
+        // .map(|(a0_i, aux_i)| a0_i + (P0 * m1) * aux_i)
+        .map(|(a0_i, aux_i)| a0_i + ((P0 * m1) % P1) * aux_i)
+        .collect();
+    a
+    // dbg!(a0[0] as u128);
+    // dbg!(a0[0] as u128 * y0);
+    // dbg!(a0[0] as u128 * z0);
+    // dbg!(a0[0] as u128 * y0 * z0);
+    // let a: Vec<u128> = itertools::multizip((a0, a1, a2))
+    //     .map(|(a0_i, a1_i, a2_i)| {
+    //         a0_i as u128 * y0 * z0 + a1_i as u128 * y1 * z1 + a2_i as u128 * y2 * z2
+    //     })
+    //     .collect();
+    // dbg!(&a);
+    // let Q = y2 * P2 as u128;
+    // let a: Vec<u128> = a.iter().map(|a_i| a_i % Q).collect();
+    // dbg!(&a);
+    // let q64 = 1_u128 << 64;
+    // let a: Vec<u64> = a.iter().map(|a_i| (a_i % q64) as u64).collect();
+    // a
+
+    /*
+    // x_i*z_i mod q_i
+    let r0: Vec<u64> = a_0.iter().map(|a_i| ((a_i * z0) % P0) * y0).collect();
+    let r1: Vec<u64> = a_1.iter().map(|a_i| ((a_i * z1) % P1) * y1).collect();
+    // let r0: Vec<u64> = a_0.iter().map(|a_i| ((a_i * z0) % P0) * y0).collect();
+    // let r1: Vec<u64> = a_1.iter().map(|a_i| ((a_i * z1) % P1) * y1).collect();
+    // let r2: Vec<u64> = a_2.iter().map(|a_i| ((a_i * y2_inv) % P2) * y2).collect();
+    // let r3: Vec<u64> = a_3.iter().map(|a_i| ((a_i * y3_inv) % P3) * y3).collect();
+    // let r4: Vec<u64> = a_4.iter().map(|a_i| ((a_i * y4_inv) % P4) * y4).collect();
+
+    let r: Vec<u64> = itertools::multizip((r0.iter(), r1.iter()))
+        .map(|(a, b)| a + b)
+        .collect();
+    // let r = r0;
+    //
+    dbg!(&r);
+
+    let p1p2: u128 = (P0 as u128) * (P1 as u128);
+    // let p1p2_inv: u128 = inv_mod((P0 % P1) as u128, P1) as u128;
+    let p1p2_inv: u128 = inv_mod((P0) as u128, P1) as u128;
+    dbg!(&p1p2);
+    dbg!(&p1p2_inv);
+    // let p1p2: u128 = P0 as u128 / 2; // PIHALF
+    let r = r
+        .iter()
+        .map(|c_i_u64| {
+            let c_i = *c_i_u64 as u128;
+            if c_i * 2 >= p1p2 {
+                // if c_i >= p1p2 {
+                c_i.wrapping_sub(p1p2) as u64
+            } else {
+                c_i as u64
+            }
+        })
+        .collect();
+    // let r: Vec<u64> = itertools::multizip((r0.iter(), r1.iter(), r2.iter(), r3.iter(), r4.iter()))
+    //     .map(|(a, b, c, d, e)| a + b + c + d + e)
+    //     .collect();
+    // let mut r = a_0 + y0_inv + a_1 * y1_inv + a_2 * y2_inv + a_3 * y3_inv + a_4 * y4_inv;
+
+    r
+    */
+}
+
+fn exp_mod(q: u128, x: u128, k: u128) -> u128 {
+    // work on u128 to avoid overflow
+    let mut r = 1u128;
+    let mut x = x.clone();
+    let mut k = k.clone();
+    x = x % q;
+    // exponentiation by square strategy
+    while k > 0 {
+        if k % 2 == 1 {
+            r = (r * x) % q;
+        }
+        x = (x * x) % q;
+        k /= 2;
+    }
+    r
+}
+/// returns x^-1 mod Q
+fn inv_mod(q: u128, x: u128) -> u128 {
+    // by Fermat's Little Theorem, x^-1 mod q \equiv  x^{q-2} mod q
+    exp_mod(q, x, q - 2)
+}
+
+#[cfg(test)]
+mod tests {
+    use super::*;
+    use rand_distr::Distribution;
+
+    use anyhow::Result;
+
+    #[test]
+    fn test_dbg() -> Result<()> {
+        println!("{}", 1u128 << 64);
+        let n: usize = 16;
+
+        println!("{}", P0);
+        println!("{}", P1);
+        // let q = 1u128 << 64;
+        // assert!(P0 as u128 * P1 as u128 > (n as u128 * (q * q)) / 2);
+
+        // let a: Vec<u64> = vec![1u64, 2, 3, 4];
+        // let a: Vec<u64> = vec![1u64, 2, 3, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0];
+        // let a: Vec<u64> = vec![9u64, 8, 7, 6, 0, 9999, 0, 0, 0, 0, 0, 0, 6, 7, 8, 9];
+        use rand::Rng;
+        let mut rng = rand::thread_rng();
+        let a: Vec<u64> = (0..n)
+            // .map(|_| rng.gen_range(0..=(1u64 << 57) - 1) - (1u64 << 56))
+            .map(|_| rng.gen_range(0..(1 << 61)))
+            .collect();
+
+        dbg!(a.len());
+
+        let a_ntt = NTT::ntt(n, &a);
+        dbg!(&a_ntt);
+
+        let a_intt = NTT::intt(n, &a_ntt);
+
+        dbg!(&a_intt);
+        assert_eq!(a_intt, a);
+
+        // unnecessary:
+        // let a: Vec<u64> = vec![2u64, 4, 6, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0];
+        // let a_ntt = NTT_p::ntt(P0, n, &a);
+        // dbg!(&a_ntt);
+        // let a_intt = NTT_p::intt(P0, n, &a_ntt);
+        // dbg!(&a_intt);
+
+        // NOTE: *n_inv is already done in the intt method.
+
+        // Multiplies the values by the inverse of the polynomial modulo the NTT modulus
+        // let n_inv = inv_mod(P0 as u128, n as u64); // n^-1 mod p0
+        // let a_new: Vec<u64> = a_0_intt
+        //     .iter()
+        //     .map(|a_i| ((*a_i as u128 * n_inv as u128) % P0 as u128) as u64)
+        //     .collect();
+
+        // assert_eq!(a_intt, a);
+
+        Ok(())
+    }
+}

ckks/src/lib.rs

@@ -259,7 +259,7 @@ mod tests {
     #[test]
     fn test_sub() -> Result<()> {
         let q: u64 = 2u64.pow(16) + 1;
-        let n: usize = 16;
+        let n: usize = 8;
         let t: u64 = 2;
         let param = Param {
             ring: RingParam { q, n },

tfhe/src/tggsw.rs

@@ -41,7 +41,7 @@ impl TGGSW {
     }
 }
 
-/// External product tggsw x tglwe
+/// External product TGGSW x TGLWE
 impl Mul<TGLWE> for TGGSW {
     type Output = TGLWE;