//! Implementation of CKKS https://eprint.iacr.org/2016/421.pdf
#![allow(non_snake_case)]
#![allow(non_upper_case_globals)]
#![allow(non_camel_case_types)]
#![allow(clippy::upper_case_acronyms)]
#![allow(dead_code)] // TMP

use arith::{Rq, C, R};

use anyhow::Result;
use rand::Rng;
use rand_distr::{Normal, Uniform};

pub mod encoder;
pub use encoder::Encoder;

// error deviation for the Gaussian(Normal) distribution
// sigma=3.2 from: https://eprint.iacr.org/2016/421.pdf page 17
const ERR_SIGMA: f64 = 3.2;

#[derive(Debug)]
pub struct PublicKey<const Q: u64, const N: usize>(Rq<Q, N>, Rq<Q, N>);

pub struct SecretKey<const Q: u64, const N: usize>(Rq<Q, N>);

pub struct CKKS<const Q: u64, const N: usize> {
    encoder: Encoder<Q, N>,
}

impl<const Q: u64, const N: usize> CKKS<Q, N> {
    pub fn new(delta: C<f64>) -> Self {
        let encoder = Encoder::<Q, N>::new(delta);
        Self { encoder }
    }
    /// generate a new key pair (privK, pubK)
    pub fn new_key(&self, mut rng: impl Rng) -> Result<(SecretKey<Q, N>, PublicKey<Q, N>)> {
        let Xi_key = Uniform::new(-1_f64, 1_f64);
        let Xi_err = Normal::new(0_f64, ERR_SIGMA)?;

        let e = Rq::<Q, N>::rand_f64(&mut rng, Xi_err)?;

        let mut s = Rq::<Q, N>::rand_f64(&mut rng, Xi_key)?;
        // since s is going to be multiplied by other Rq elements, already
        // compute its NTT
        s.compute_evals();

        let a = Rq::<Q, N>::rand_f64(&mut rng, Xi_key)?;

        let pk: PublicKey<Q, N> = PublicKey((&(-a) * &s) + e, a.clone());
        Ok((SecretKey(s), pk))
    }

    // encrypts a plaintext \in R=Z_Q[X]/(X^N+1)
    fn encrypt(
        &self, // TODO maybe rm?
        mut rng: impl Rng,
        pk: &PublicKey<Q, N>,
        m: &R<N>,
    ) -> Result<(Rq<Q, N>, Rq<Q, N>)> {
        let Xi_key = Uniform::new(-1_f64, 1_f64);
        let Xi_err = Normal::new(0_f64, ERR_SIGMA)?;

        let e_0 = Rq::<Q, N>::rand_f64(&mut rng, Xi_err)?;
        let e_1 = Rq::<Q, N>::rand_f64(&mut rng, Xi_err)?;

        let v = Rq::<Q, N>::rand_f64(&mut rng, Xi_key)?;

        let m: Rq<Q, N> = Rq::<Q, N>::from(*m);

        Ok((m + e_0 + v * pk.0.clone(), v * pk.1.clone() + e_1))
    }

    fn decrypt(
        &self, // TODO maybe rm?
        sk: SecretKey<Q, N>,
        c: (Rq<Q, N>, Rq<Q, N>),
    ) -> Result<R<N>> {
        let m = c.0.clone() + c.1 * sk.0;
        Ok(m.mod_centered_q())
    }

    pub fn encode_and_encrypt(
        &self,
        mut rng: impl Rng,
        pk: &PublicKey<Q, N>,
        z: &[C<f64>],
    ) -> Result<(Rq<Q, N>, Rq<Q, N>)> {
        let m: R<N> = self.encoder.encode(&z)?; // polynomial (encoded vec) \in R

        self.encrypt(&mut rng, pk, &m)
    }

    pub fn decrypt_and_decode(
        &self,
        sk: SecretKey<Q, N>,
        c: (Rq<Q, N>, Rq<Q, N>),
    ) -> Result<Vec<C<f64>>> {
        let d = self.decrypt(sk, c)?;

        self.encoder.decode(&d)
    }
}

#[cfg(test)]
mod tests {
    use super::*;

    #[test]
    fn test_encrypt_decrypt() -> Result<()> {
        const Q: u64 = 2u64.pow(16) + 1;
        const T: u64 = 16;
        const N: usize = 8;
        let scale_factor_u64 = 512_u64; // delta
        let scale_factor = C::<f64>::new(512.0, 0.0); // delta

        let mut rng = rand::thread_rng();

        for _ in 0..1000 {
            let ckks = CKKS::<Q, N>::new(scale_factor);

            let (sk, pk) = ckks.new_key(&mut rng)?;

            let m_raw: R<N> = Rq::<Q, N>::rand_f64(&mut rng, Uniform::new(0_f64, T as f64))?.to_r();
            let m = m_raw * scale_factor_u64;

            let ct = ckks.encrypt(&mut rng, &pk, &m)?;
            let m_decrypted = ckks.decrypt(sk, ct)?;

            let m_decrypted: Vec<u64> = m_decrypted
                .coeffs()
                .iter()
                .map(|e| (*e as f64 / (scale_factor_u64 as f64)).round() as u64)
                .collect();
            let m_decrypted = Rq::<Q, N>::from_vec_u64(m_decrypted);
            assert_eq!(m_decrypted, Rq::<Q, N>::from(m_raw));
        }

        Ok(())
    }

    #[test]
    fn test_encode_encrypt_decrypt_decode() -> Result<()> {
        const Q: u64 = 2u64.pow(16) + 1;
        const T: u64 = 16;
        const N: usize = 4;
        let scale_factor = C::<f64>::new(512.0, 0.0); // delta

        let mut rng = rand::thread_rng();

        for _ in 0..1000 {
            let ckks = CKKS::<Q, N>::new(scale_factor);
            let (sk, pk) = ckks.new_key(&mut rng)?;

            let z: Vec<C<f64>> = std::iter::repeat_with(|| C::<f64>::rand(&mut rng, T))
                .take(N / 2)
                .collect();
            let m: R<N> = ckks.encoder.encode(&z)?;

            // sanity check
            {
                let z_decoded = ckks.encoder.decode(&m)?;
                let rounded_z_decoded: Vec<C<f64>> = z_decoded
                    .iter()
                    .map(|c| C::<f64>::new(c.re.round(), c.im.round()))
                    .collect();
                assert_eq!(rounded_z_decoded, z);
            }

            let ct = ckks.encrypt(&mut rng, &pk, &m)?;
            let m_decrypted = ckks.decrypt(sk, ct)?;

            let z_decrypted = ckks.encoder.decode(&m_decrypted)?;

            let rounded_z_decrypted: Vec<C<f64>> = z_decrypted
                .iter()
                .map(|&c| C::<f64>::new(c.re.round(), c.im.round()))
                .collect();
            assert_eq!(rounded_z_decrypted, z);
        }

        Ok(())
    }
}