1use ark_ec::{
  2    bls12::{Bls12Parameters, G1Prepared, G2Prepared, TwistType},
  3    short_weierstrass_jacobian::GroupAffine,
  4};
  5use ark_ff::{BitIteratorBE, Field, One};
  6use ark_relations::r1cs::{Namespace, SynthesisError};
  7
  8use crate::{
  9    fields::{fp::FpVar, fp2::Fp2Var, FieldVar},
 10    groups::curves::short_weierstrass::*,
 11    Vec,
 12};
 13use core::fmt::Debug;
 14
 15/// Represents a projective point in G1.
 16pub type G1Var<P> =
 17    ProjectiveVar<<P as Bls12Parameters>::G1Parameters, FpVar<<P as Bls12Parameters>::Fp>>;
 18
 19/// Represents an affine point on G1. Should be used only for comparison and
 20/// when a canonical representation of a point is required, and not for
 21/// arithmetic.
 22pub type G1AffineVar<P> =
 23    AffineVar<<P as Bls12Parameters>::G1Parameters, FpVar<<P as Bls12Parameters>::Fp>>;
 24
 25/// Represents a projective point in G2.
 26pub type G2Var<P> = ProjectiveVar<<P as Bls12Parameters>::G2Parameters, Fp2G<P>>;
 27/// Represents an affine point on G2. Should be used only for comparison and
 28/// when a canonical representation of a point is required, and not for
 29/// arithmetic.
 30pub type G2AffineVar<P> = AffineVar<<P as Bls12Parameters>::G2Parameters, Fp2G<P>>;
 31
 32/// Represents the cached precomputation that can be performed on a G1 element
 33/// which enables speeding up pairing computation.
 34#[derive(Derivative)]
 35#[derivative(Clone(bound = "G1Var<P>: Clone"), Debug(bound = "G1Var<P>: Debug"))]
 36pub struct G1PreparedVar<P: Bls12Parameters>(pub AffineVar<P::G1Parameters, FpVar<P::Fp>>);
 37
 38impl<P: Bls12Parameters> G1PreparedVar<P> {
 39    /// Returns the value assigned to `self` in the underlying constraint
 40    /// system.
 41    pub fn value(&self) -> Result<G1Prepared<P>, SynthesisError> {
 42        let x = self.0.x.value()?;
 43        let y = self.0.y.value()?;
 44        let infinity = self.0.infinity.value()?;
 45        let g = GroupAffine::new(x, y, infinity);
 46        Ok(g.into())
 47    }
 48
 49    /// Constructs `Self` from a `G1Var`.
 50    pub fn from_group_var(q: &G1Var<P>) -> Result<Self, SynthesisError> {
 51        let g = q.to_affine()?;
 52        Ok(Self(g))
 53    }
 54}
 55
 56impl<P: Bls12Parameters> AllocVar<G1Prepared<P>, P::Fp> for G1PreparedVar<P> {
 57    fn new_variable<T: Borrow<G1Prepared<P>>>(
 58        cs: impl Into<Namespace<P::Fp>>,
 59        f: impl FnOnce() -> Result<T, SynthesisError>,
 60        mode: AllocationMode,
 61    ) -> Result<Self, SynthesisError> {
 62        let ns = cs.into();
 63        let cs = ns.cs();
 64        let g1_prep = f().map(|b| b.borrow().0);
 65
 66        let x = FpVar::new_variable(ark_relations::ns!(cs, "x"), || g1_prep.map(|g| g.x), mode)?;
 67        let y = FpVar::new_variable(ark_relations::ns!(cs, "y"), || g1_prep.map(|g| g.y), mode)?;
 68        let infinity = Boolean::new_variable(
 69            ark_relations::ns!(cs, "inf"),
 70            || g1_prep.map(|g| g.infinity),
 71            mode,
 72        )?;
 73        let g = AffineVar::new(x, y, infinity);
 74        Ok(Self(g))
 75    }
 76}
 77
 78impl<P: Bls12Parameters> ToBytesGadget<P::Fp> for G1PreparedVar<P> {
 79    #[inline]
 80    #[tracing::instrument(target = "r1cs")]
 81    fn to_bytes(&self) -> Result<Vec<UInt8<P::Fp>>, SynthesisError> {
 82        let mut bytes = self.0.x.to_bytes()?;
 83        let y_bytes = self.0.y.to_bytes()?;
 84        let inf_bytes = self.0.infinity.to_bytes()?;
 85        bytes.extend_from_slice(&y_bytes);
 86        bytes.extend_from_slice(&inf_bytes);
 87        Ok(bytes)
 88    }
 89
 90    #[tracing::instrument(target = "r1cs")]
 91    fn to_non_unique_bytes(&self) -> Result<Vec<UInt8<P::Fp>>, SynthesisError> {
 92        let mut bytes = self.0.x.to_non_unique_bytes()?;
 93        let y_bytes = self.0.y.to_non_unique_bytes()?;
 94        let inf_bytes = self.0.infinity.to_non_unique_bytes()?;
 95        bytes.extend_from_slice(&y_bytes);
 96        bytes.extend_from_slice(&inf_bytes);
 97        Ok(bytes)
 98    }
 99}
100
101type Fp2G<P> = Fp2Var<<P as Bls12Parameters>::Fp2Config>;
102type LCoeff<P> = (Fp2G<P>, Fp2G<P>);
103/// Represents the cached precomputation that can be performed on a G2 element
104/// which enables speeding up pairing computation.
105#[derive(Derivative)]
106#[derivative(
107    Clone(bound = "Fp2Var<P::Fp2Config>: Clone"),
108    Debug(bound = "Fp2Var<P::Fp2Config>: Debug")
109)]
110pub struct G2PreparedVar<P: Bls12Parameters> {
111    #[doc(hidden)]
112    pub ell_coeffs: Vec<LCoeff<P>>,
113}
114
115impl<P: Bls12Parameters> AllocVar<G2Prepared<P>, P::Fp> for G2PreparedVar<P> {
116    #[tracing::instrument(target = "r1cs", skip(cs, f, mode))]
117    fn new_variable<T: Borrow<G2Prepared<P>>>(
118        cs: impl Into<Namespace<P::Fp>>,
119        f: impl FnOnce() -> Result<T, SynthesisError>,
120        mode: AllocationMode,
121    ) -> Result<Self, SynthesisError> {
122        let ns = cs.into();
123        let cs = ns.cs();
124        let g2_prep = f().map(|b| {
125            let projective_coeffs = &b.borrow().ell_coeffs;
126            match P::TWIST_TYPE {
127                TwistType::M => {
128                    let mut z_s = projective_coeffs
129                        .iter()
130                        .map(|(_, _, z)| *z)
131                        .collect::<Vec<_>>();
132                    ark_ff::fields::batch_inversion(&mut z_s);
133                    projective_coeffs
134                        .iter()
135                        .zip(z_s)
136                        .map(|((x, y, _), z_inv)| (*x * &z_inv, *y * &z_inv))
137                        .collect::<Vec<_>>()
138                },
139                TwistType::D => {
140                    let mut z_s = projective_coeffs
141                        .iter()
142                        .map(|(z, _, _)| *z)
143                        .collect::<Vec<_>>();
144                    ark_ff::fields::batch_inversion(&mut z_s);
145                    projective_coeffs
146                        .iter()
147                        .zip(z_s)
148                        .map(|((_, x, y), z_inv)| (*x * &z_inv, *y * &z_inv))
149                        .collect::<Vec<_>>()
150                },
151            }
152        });
153
154        let l = Vec::new_variable(
155            ark_relations::ns!(cs, "l"),
156            || {
157                g2_prep
158                    .clone()
159                    .map(|c| c.iter().map(|(l, _)| *l).collect::<Vec<_>>())
160            },
161            mode,
162        )?;
163        let r = Vec::new_variable(
164            ark_relations::ns!(cs, "r"),
165            || g2_prep.map(|c| c.iter().map(|(_, r)| *r).collect::<Vec<_>>()),
166            mode,
167        )?;
168        let ell_coeffs = l.into_iter().zip(r).collect();
169        Ok(Self { ell_coeffs })
170    }
171}
172
173impl<P: Bls12Parameters> ToBytesGadget<P::Fp> for G2PreparedVar<P> {
174    #[inline]
175    #[tracing::instrument(target = "r1cs")]
176    fn to_bytes(&self) -> Result<Vec<UInt8<P::Fp>>, SynthesisError> {
177        let mut bytes = Vec::new();
178        for coeffs in &self.ell_coeffs {
179            bytes.extend_from_slice(&coeffs.0.to_bytes()?);
180            bytes.extend_from_slice(&coeffs.1.to_bytes()?);
181        }
182        Ok(bytes)
183    }
184
185    #[tracing::instrument(target = "r1cs")]
186    fn to_non_unique_bytes(&self) -> Result<Vec<UInt8<P::Fp>>, SynthesisError> {
187        let mut bytes = Vec::new();
188        for coeffs in &self.ell_coeffs {
189            bytes.extend_from_slice(&coeffs.0.to_non_unique_bytes()?);
190            bytes.extend_from_slice(&coeffs.1.to_non_unique_bytes()?);
191        }
192        Ok(bytes)
193    }
194}
195
196impl<P: Bls12Parameters> G2PreparedVar<P> {
197    /// Constructs `Self` from a `G2Var`.
198    #[tracing::instrument(target = "r1cs")]
199    pub fn from_group_var(q: &G2Var<P>) -> Result<Self, SynthesisError> {
200        let q = q.to_affine()?;
201        let two_inv = P::Fp::one().double().inverse().unwrap();
202        // Enforce that `q` is not the point at infinity.
203        q.infinity.enforce_not_equal(&Boolean::Constant(true))?;
204        let mut ell_coeffs = vec![];
205        let mut r = q.clone();
206
207        for i in BitIteratorBE::new(P::X).skip(1) {
208            ell_coeffs.push(Self::double(&mut r, &two_inv)?);
209
210            if i {
211                ell_coeffs.push(Self::add(&mut r, &q)?);
212            }
213        }
214
215        Ok(Self { ell_coeffs })
216    }
217
218    #[tracing::instrument(target = "r1cs")]
219    fn double(r: &mut G2AffineVar<P>, two_inv: &P::Fp) -> Result<LCoeff<P>, SynthesisError> {
220        let a = r.y.inverse()?;
221        let mut b = r.x.square()?;
222        let b_tmp = b.clone();
223        b.mul_assign_by_base_field_constant(*two_inv);
224        b += &b_tmp;
225
226        let c = &a * &b;
227        let d = r.x.double()?;
228        let x3 = c.square()? - &d;
229        let e = &c * &r.x - &r.y;
230        let c_x3 = &c * &x3;
231        let y3 = &e - &c_x3;
232        let mut f = c;
233        f.negate_in_place()?;
234        r.x = x3;
235        r.y = y3;
236        match P::TWIST_TYPE {
237            TwistType::M => Ok((e, f)),
238            TwistType::D => Ok((f, e)),
239        }
240    }
241
242    #[tracing::instrument(target = "r1cs")]
243    fn add(r: &mut G2AffineVar<P>, q: &G2AffineVar<P>) -> Result<LCoeff<P>, SynthesisError> {
244        let a = (&q.x - &r.x).inverse()?;
245        let b = &q.y - &r.y;
246        let c = &a * &b;
247        let d = &r.x + &q.x;
248        let x3 = c.square()? - &d;
249
250        let e = (&r.x - &x3) * &c;
251        let y3 = e - &r.y;
252        let g = &c * &r.x - &r.y;
253        let mut f = c;
254        f.negate_in_place()?;
255        r.x = x3;
256        r.y = y3;
257        match P::TWIST_TYPE {
258            TwistType::M => Ok((g, f)),
259            TwistType::D => Ok((f, g)),
260        }
261    }
262}