poulpy/poulpy-backend/examples/rlwe_encrypt.rs

use itertools::izip;
use poulpy_backend::cpu_spqlios::FFT64Spqlios;
use poulpy_hal::{
    api::{
        ModuleNew, ScratchOwnedAlloc, ScratchOwnedBorrow, SvpApplyDftToDftInplace, SvpPPolAlloc, SvpPrepare, VecZnxAddNormal,
        VecZnxBigAddSmallInplace, VecZnxBigAlloc, VecZnxBigNormalize, VecZnxBigNormalizeTmpBytes, VecZnxBigSubSmallNegateInplace,
        VecZnxDftAlloc, VecZnxDftApply, VecZnxFillUniform, VecZnxIdftApplyTmpA, VecZnxNormalizeInplace,
    },
    layouts::{Module, ScalarZnx, ScratchOwned, SvpPPol, VecZnx, VecZnxBig, VecZnxDft, ZnxInfos},
    source::Source,
};

fn main() {
    let n: usize = 16;
    let base2k: usize = 18;
    let ct_size: usize = 3;
    let msg_size: usize = 2;
    let log_scale: usize = msg_size * base2k - 5;
    let module: Module<FFT64Spqlios> = Module::<FFT64Spqlios>::new(n as u64);

    let mut scratch: ScratchOwned<FFT64Spqlios> = ScratchOwned::<FFT64Spqlios>::alloc(module.vec_znx_big_normalize_tmp_bytes());

    let seed: [u8; 32] = [0; 32];
    let mut source: Source = Source::new(seed);

    // s <- Z_{-1, 0, 1}[X]/(X^{N}+1)
    let mut s: ScalarZnx<Vec<u8>> = ScalarZnx::alloc(module.n(), 1);
    s.fill_ternary_prob(0, 0.5, &mut source);

    // Buffer to store s in the DFT domain
    let mut s_dft: SvpPPol<Vec<u8>, FFT64Spqlios> = module.svp_ppol_alloc(s.cols());

    // s_dft <- DFT(s)
    module.svp_prepare(&mut s_dft, 0, &s, 0);

    // Allocates a VecZnx with two columns: ct=(0, 0)
    let mut ct: VecZnx<Vec<u8>> = VecZnx::alloc(
        module.n(),
        2,       // Number of columns
        ct_size, // Number of small poly per column
    );

    // Fill the second column with random values: ct = (0, a)
    module.vec_znx_fill_uniform(base2k, &mut ct, 1, &mut source);

    let mut buf_dft: VecZnxDft<Vec<u8>, FFT64Spqlios> = module.vec_znx_dft_alloc(1, ct_size);

    module.vec_znx_dft_apply(1, 0, &mut buf_dft, 0, &ct, 1);

    // Applies DFT(ct[1]) * DFT(s)
    module.svp_apply_dft_to_dft_inplace(
        &mut buf_dft, // DFT(ct[1] * s)
        0,            // Selects the first column of res
        &s_dft,       // DFT(s)
        0,            // Selects the first column of s_dft
    );

    // Alias scratch space (VecZnxDft<B> is always at least as big as VecZnxBig<B>)

    // BIG(ct[1] * s) <- IDFT(DFT(ct[1] * s)) (not normalized)
    let mut buf_big: VecZnxBig<Vec<u8>, FFT64Spqlios> = module.vec_znx_big_alloc(1, ct_size);
    module.vec_znx_idft_apply_tmpa(&mut buf_big, 0, &mut buf_dft, 0);

    // Creates a plaintext: VecZnx with 1 column
    let mut m = VecZnx::alloc(
        module.n(),
        1,        // Number of columns
        msg_size, // Number of small polynomials
    );
    let mut want: Vec<i64> = vec![0; n];
    want.iter_mut()
        .for_each(|x| *x = source.next_u64n(16, 15) as i64);
    m.encode_vec_i64(base2k, 0, log_scale, &want);
    module.vec_znx_normalize_inplace(base2k, &mut m, 0, scratch.borrow());

    // m - BIG(ct[1] * s)
    module.vec_znx_big_sub_small_negate_inplace(
        &mut buf_big,
        0, // Selects the first column of the receiver
        &m,
        0, // Selects the first column of the message
    );

    // Normalizes back to VecZnx
    // ct[0] <- m - BIG(c1 * s)
    module.vec_znx_big_normalize(
        base2k,
        &mut ct,
        0, // Selects the first column of ct (ct[0])
        base2k,
        &buf_big,
        0, // Selects the first column of buf_big
        scratch.borrow(),
    );

    // Add noise to ct[0]
    // ct[0] <- ct[0] + e
    module.vec_znx_add_normal(
        base2k,
        &mut ct,
        0,                // Selects the first column of ct (ct[0])
        base2k * ct_size, // Scaling of the noise: 2^{-base2k * limbs}
        &mut source,
        3.2,       // Standard deviation
        3.2 * 6.0, // Truncatation bound
    );

    // Final ciphertext: ct = (-a * s + m + e, a)

    // Decryption

    // DFT(ct[1] * s)
    module.vec_znx_dft_apply(1, 0, &mut buf_dft, 0, &ct, 1);
    module.svp_apply_dft_to_dft_inplace(
        &mut buf_dft,
        0, // Selects the first column of res.
        &s_dft,
        0,
    );

    // BIG(c1 * s) = IDFT(DFT(c1 * s))
    module.vec_znx_idft_apply_tmpa(&mut buf_big, 0, &mut buf_dft, 0);

    // BIG(c1 * s) + ct[0]
    module.vec_znx_big_add_small_inplace(&mut buf_big, 0, &ct, 0);

    // m + e <- BIG(ct[1] * s + ct[0])
    let mut res = VecZnx::alloc(module.n(), 1, ct_size);
    module.vec_znx_big_normalize(base2k, &mut res, 0, base2k, &buf_big, 0, scratch.borrow());

    // have = m * 2^{log_scale} + e
    let mut have: Vec<i64> = vec![i64::default(); n];
    res.decode_vec_i64(base2k, 0, ct_size * base2k, &mut have);
    let scale: f64 = (1 << (res.size() * base2k - log_scale)) as f64;
    izip!(want.iter(), have.iter())
        .enumerate()
        .for_each(|(i, (a, b))| {
            println!("{}: {} {}", i, a, (*b as f64) / scale);
        });
}