librustzcash/bellman/src/groth16/tests/dummy_engine.rs

use pairing::{
    Engine,
    PrimeField,
    PrimeFieldRepr,
    Field,
    SqrtField,
    LegendreSymbol,
    CurveProjective,
    CurveAffine,
    PrimeFieldDecodingError,
    GroupDecodingError,
    EncodedPoint
};

use std::cmp::Ordering;
use std::fmt;
use rand::{Rand, Rng};
use std::num::Wrapping;

const MODULUS_R: Wrapping<u32> = Wrapping(64513);

#[derive(Copy, Clone, Debug, PartialEq, Eq)]
pub struct Fr(Wrapping<u32>);

impl fmt::Display for Fr {
    fn fmt(&self, f: &mut fmt::Formatter) -> Result<(), fmt::Error> {
        write!(f, "{}", (self.0).0)
    }
}

impl Rand for Fr {
    fn rand<R: Rng>(rng: &mut R) -> Self {
        Fr(Wrapping(rng.gen()) % MODULUS_R)
    }
}

impl Field for Fr {
    fn zero() -> Self {
        Fr(Wrapping(0))
    }

    fn one() -> Self {
        Fr(Wrapping(1))
    }

    fn is_zero(&self) -> bool {
        (self.0).0 == 0
    }

    fn square(&mut self) {
        self.0 = (self.0 * self.0) % MODULUS_R;
    }

    fn double(&mut self) {
        self.0 = (self.0 << 1) % MODULUS_R;
    }

    fn negate(&mut self) {
        if !<Fr as Field>::is_zero(self) {
            self.0 = MODULUS_R - self.0;
        }
    }

    fn add_assign(&mut self, other: &Self) {
        self.0 = (self.0 + other.0) % MODULUS_R;
    }

    fn sub_assign(&mut self, other: &Self) {
        self.0 = ((MODULUS_R + self.0) - other.0) % MODULUS_R;
    }

    fn mul_assign(&mut self, other: &Self) {
        self.0 = (self.0 * other.0) % MODULUS_R;
    }

    fn inverse(&self) -> Option<Self> {
        if <Fr as Field>::is_zero(self) {
            None
        } else {
            Some(self.pow(&[(MODULUS_R.0 as u64) - 2]))
        }
    }

    fn frobenius_map(&mut self, _: usize) {
        // identity
    }
}

impl SqrtField for Fr {
    fn legendre(&self) -> LegendreSymbol {
        // s = self^((r - 1) // 2)
        let s = self.pow([32256]);
        if s == <Fr as Field>::zero() { LegendreSymbol::Zero }
        else if s == <Fr as Field>::one() { LegendreSymbol::QuadraticResidue }
        else { LegendreSymbol::QuadraticNonResidue }
    }

    fn sqrt(&self) -> Option<Self> {
        // Tonelli-Shank's algorithm for q mod 16 = 1
        // https://eprint.iacr.org/2012/685.pdf (page 12, algorithm 5)
        match self.legendre() {
            LegendreSymbol::Zero => Some(*self),
            LegendreSymbol::QuadraticNonResidue => None,
            LegendreSymbol::QuadraticResidue => {
                let mut c = Fr::root_of_unity();
                // r = self^((t + 1) // 2)
                let mut r = self.pow([32]);
                // t = self^t
                let mut t = self.pow([63]);
                let mut m = Fr::S;

                while t != <Fr as Field>::one() {
                let mut i = 1;
                    {
                        let mut t2i = t;
                        t2i.square();
                        loop {
                            if t2i == <Fr as Field>::one() {
                                break;
                            }
                            t2i.square();
                            i += 1;
                        }
                    }

                    for _ in 0..(m - i - 1) {
                        c.square();
                    }
                    <Fr as Field>::mul_assign(&mut r, &c);
                    c.square();
                    <Fr as Field>::mul_assign(&mut t, &c);
                    m = i;
                }

                Some(r)
            }
        }
    }
}

#[derive(Copy, Clone, Debug, Eq, PartialEq)]
pub struct FrRepr([u64; 1]);

impl Ord for FrRepr {
    fn cmp(&self, other: &FrRepr) -> Ordering {
        (self.0)[0].cmp(&(other.0)[0])
    }
}

impl PartialOrd for FrRepr {
    fn partial_cmp(&self, other: &FrRepr) -> Option<Ordering> {
        Some(self.cmp(other))
    }
}

impl Rand for FrRepr {
    fn rand<R: Rng>(rng: &mut R) -> Self {
        FrRepr([rng.gen()])
    }
}

impl fmt::Display for FrRepr {
    fn fmt(&self, f: &mut fmt::Formatter) -> Result<(), fmt::Error> {
        write!(f, "{}", (self.0)[0])
    }
}

impl From<u64> for FrRepr {
    fn from(v: u64) -> FrRepr {
        FrRepr([v])
    }
}

impl From<Fr> for FrRepr {
    fn from(v: Fr) -> FrRepr {
        FrRepr([(v.0).0 as u64])
    }
}

impl AsMut<[u64]> for FrRepr {
    fn as_mut(&mut self) -> &mut [u64] {
        &mut self.0[..]
    }
}

impl AsRef<[u64]> for FrRepr {
    fn as_ref(&self) -> &[u64] {
        &self.0[..]
    }
}

impl Default for FrRepr {
    fn default() -> FrRepr {
        FrRepr::from(0u64)
    }
}

impl PrimeFieldRepr for FrRepr {
    fn sub_noborrow(&mut self, other: &Self) {
        self.0[0] = self.0[0].wrapping_sub(other.0[0]);
    }
    fn add_nocarry(&mut self, other: &Self) {
        self.0[0] = self.0[0].wrapping_add(other.0[0]);
    }
    fn num_bits(&self) -> u32 {
        64 - self.0[0].leading_zeros()
    }
    fn is_zero(&self) -> bool {
        self.0[0] == 0
    }
    fn is_odd(&self) -> bool {
        !self.is_even()
    }
    fn is_even(&self) -> bool {
        self.0[0] % 2 == 0
    }
    fn div2(&mut self) {
        self.shr(1)
    }
    fn shr(&mut self, amt: u32) {
        self.0[0] >>= amt;
    }
    fn mul2(&mut self) {
        self.shl(1)
    }
    fn shl(&mut self, amt: u32) {
        self.0[0] <<= amt;
    }
}

impl PrimeField for Fr {
    type Repr = FrRepr;

    const NUM_BITS: u32 = 16;
    const CAPACITY: u32 = 15;
    const S: u32 = 10;

    fn from_repr(repr: FrRepr) -> Result<Self, PrimeFieldDecodingError> {
        if repr.0[0] >= (MODULUS_R.0 as u64) {
            Err(PrimeFieldDecodingError::NotInField(format!("{}", repr)))
        } else {
            Ok(Fr(Wrapping(repr.0[0] as u32)))
        }
    }

    fn into_repr(&self) -> FrRepr {
        FrRepr::from(*self)
    }

    fn char() -> FrRepr {
        Fr(MODULUS_R).into()
    }

    fn multiplicative_generator() -> Fr {
        Fr(Wrapping(5))
    }

    fn root_of_unity() -> Fr {
        Fr(Wrapping(57751))
    }
}

#[derive(Clone)]
pub struct DummyEngine;

impl Engine for DummyEngine {
    type Fr = Fr;
    type G1 = Fr;
    type G1Affine = Fr;
    type G2 = Fr;
    type G2Affine = Fr;
    type Fq = Fr;
    type Fqe = Fr;
    
    // TODO: This should be F_645131 or something. Doesn't matter for now.
    type Fqk = Fr;

    fn miller_loop<'a, I>(i: I) -> Self::Fqk
        where I: IntoIterator<Item=&'a (
                                    &'a <Self::G1Affine as CurveAffine>::Prepared,
                                    &'a <Self::G2Affine as CurveAffine>::Prepared
                               )>
    {
        let mut acc = <Fr as Field>::zero();

        for &(a, b) in i {
            let mut tmp = *a;
            <Fr as Field>::mul_assign(&mut tmp, b);
            <Fr as Field>::add_assign(&mut acc, &tmp);
        }

        acc
    }

    /// Perform final exponentiation of the result of a miller loop.
    fn final_exponentiation(this: &Self::Fqk) -> Option<Self::Fqk>
    {
        Some(*this)
    }
}

impl CurveProjective for Fr {
    type Affine = Fr;
    type Base = Fr;
    type Scalar = Fr;
    type Engine = DummyEngine;

    fn zero() -> Self {
        <Fr as Field>::zero()
    }

    fn one() -> Self {
        <Fr as Field>::one()
    }

    fn is_zero(&self) -> bool {
        <Fr as Field>::is_zero(self)
    }

    fn batch_normalization(_: &mut [Self]) {
        
    }

    fn is_normalized(&self) -> bool {
        true
    }

    fn double(&mut self) {
        <Fr as Field>::double(self);
    }

    fn add_assign(&mut self, other: &Self) {
        <Fr as Field>::add_assign(self, other);
    }

    fn add_assign_mixed(&mut self, other: &Self) {
        <Fr as Field>::add_assign(self, other);
    }

    fn negate(&mut self) {
        <Fr as Field>::negate(self);
    }

    fn mul_assign<S: Into<<Self::Scalar as PrimeField>::Repr>>(&mut self, other: S)
    {
        let tmp = Fr::from_repr(other.into()).unwrap();

        <Fr as Field>::mul_assign(self, &tmp);
    }

    fn into_affine(&self) -> Fr {
        *self
    }

    fn recommended_wnaf_for_scalar(_: <Self::Scalar as PrimeField>::Repr) -> usize {
        3
    }

    fn recommended_wnaf_for_num_scalars(_: usize) -> usize {
        3
    }
}

#[derive(Copy, Clone)]
pub struct FakePoint;

impl AsMut<[u8]> for FakePoint {
    fn as_mut(&mut self) -> &mut [u8] {
        unimplemented!()
    }
}

impl AsRef<[u8]> for FakePoint {
    fn as_ref(&self) -> &[u8] {
        unimplemented!()
    }
}

impl EncodedPoint for FakePoint {
    type Affine = Fr;

    fn empty() -> Self {
        unimplemented!()
    }

    fn size() -> usize {
        unimplemented!()
    }

    fn into_affine(&self) -> Result<Self::Affine, GroupDecodingError> {
        unimplemented!()
    }

    fn into_affine_unchecked(&self) -> Result<Self::Affine, GroupDecodingError> {
        unimplemented!()
    }

    fn from_affine(_: Self::Affine) -> Self {
        unimplemented!()
    }
}

impl CurveAffine for Fr {
    type Pair = Fr;
    type PairingResult = Fr;
    type Compressed = FakePoint;
    type Uncompressed = FakePoint;
    type Prepared = Fr;
    type Projective = Fr;
    type Base = Fr;
    type Scalar = Fr;
    type Engine = DummyEngine;

    fn zero() -> Self {
        <Fr as Field>::zero()
    }

    fn one() -> Self {
        <Fr as Field>::one()
    }

    fn is_zero(&self) -> bool {
        <Fr as Field>::is_zero(self)
    }

    fn negate(&mut self) {
        <Fr as Field>::negate(self);
    }

    fn mul<S: Into<<Self::Scalar as PrimeField>::Repr>>(&self, other: S) -> Self::Projective
    {
        let mut res = *self;
        let tmp = Fr::from_repr(other.into()).unwrap();

        <Fr as Field>::mul_assign(&mut res, &tmp);

        res
    }

    fn prepare(&self) -> Self::Prepared {
        *self
    }

    fn pairing_with(&self, other: &Self::Pair) -> Self::PairingResult {
        self.mul(*other)
    }

    fn into_projective(&self) -> Self::Projective {
        *self
    }
}