//! This module implements the R1CS equivalent of `crate`. //! //! It implements field variables for `crate::{Fq, Fq2, Fq6, Fq12}`, //! group variables for `crate::{G1, G2}`, and implements constraint //! generation for computing `Bls12_377::pairing`. //! //! The field underlying these constraints is `crate::Fq`. //! //! # Examples //! //! One can perform standard algebraic operations on `FqVar`: //! //! ``` //! # fn main() -> Result<(), ark_relations::r1cs::SynthesisError> { //! use ark_std::UniformRand; //! use ark_relations::r1cs::*; //! use ark_r1cs_std::prelude::*; //! use ark_bls12_377::{*, constraints::*}; //! //! let cs = ConstraintSystem::::new_ref(); //! // This rng is just for test purposes; do not use it //! // in real applications. //! let mut rng = ark_std::test_rng(); //! //! // Generate some random `Fq` elements. //! let a_native = Fq::rand(&mut rng); //! let b_native = Fq::rand(&mut rng); //! //! // Allocate `a_native` and `b_native` as witness variables in `cs`. //! let a = FqVar::new_witness(ark_relations::ns!(cs, "generate_a"), || Ok(a_native))?; //! let b = FqVar::new_witness(ark_relations::ns!(cs, "generate_b"), || Ok(b_native))?; //! //! // Allocate `a_native` and `b_native` as constants in `cs`. This does not add any //! // constraints or variables. //! let a_const = FqVar::new_constant(ark_relations::ns!(cs, "a_as_constant"), a_native)?; //! let b_const = FqVar::new_constant(ark_relations::ns!(cs, "b_as_constant"), b_native)?; //! //! let one = FqVar::one(); //! let zero = FqVar::zero(); //! //! // Sanity check one + one = two //! let two = &one + &one + &zero; //! two.enforce_equal(&one.double()?)?; //! //! assert!(cs.is_satisfied()?); //! //! // Check that the value of &a + &b is correct. //! assert_eq!((&a + &b).value()?, a_native + &b_native); //! //! // Check that the value of &a * &b is correct. //! assert_eq!((&a * &b).value()?, a_native * &b_native); //! //! // Check that operations on variables and constants are equivalent. //! (&a + &b).enforce_equal(&(&a_const + &b_const))?; //! assert!(cs.is_satisfied()?); //! # Ok(()) //! # } //! ``` //! //! One can also perform standard algebraic operations on `G1Var` and `G2Var`: //! //! ``` //! # fn main() -> Result<(), ark_relations::r1cs::SynthesisError> { //! # use ark_std::UniformRand; //! # use ark_relations::r1cs::*; //! # use ark_r1cs_std::prelude::*; //! # use ark_bls12_377::{*, constraints::*}; //! //! # let cs = ConstraintSystem::::new_ref(); //! # let mut rng = ark_std::test_rng(); //! //! // Generate some random `G1` elements. //! let a_native = G1Projective::rand(&mut rng); //! let b_native = G1Projective::rand(&mut rng); //! //! // Allocate `a_native` and `b_native` as witness variables in `cs`. //! let a = G1Var::new_witness(ark_relations::ns!(cs, "a"), || Ok(a_native))?; //! let b = G1Var::new_witness(ark_relations::ns!(cs, "b"), || Ok(b_native))?; //! //! // Allocate `a_native` and `b_native` as constants in `cs`. This does not add any //! // constraints or variables. //! let a_const = G1Var::new_constant(ark_relations::ns!(cs, "a_as_constant"), a_native)?; //! let b_const = G1Var::new_constant(ark_relations::ns!(cs, "b_as_constant"), b_native)?; //! //! // This returns the identity of `G1`. //! let zero = G1Var::zero(); //! //! // Sanity check one + one = two //! let two_a = &a + &a + &zero; //! two_a.enforce_equal(&a.double()?)?; //! //! assert!(cs.is_satisfied()?); //! //! // Check that the value of &a + &b is correct. //! assert_eq!((&a + &b).value()?, a_native + &b_native); //! //! // Check that operations on variables and constants are equivalent. //! (&a + &b).enforce_equal(&(&a_const + &b_const))?; //! assert!(cs.is_satisfied()?); //! # Ok(()) //! # } //! ``` //! //! Finally, one can check pairing computations as well: //! //! ``` //! # fn main() -> Result<(), ark_relations::r1cs::SynthesisError> { //! # use ark_std::UniformRand; //! # use ark_ec::PairingEngine; //! # use ark_relations::r1cs::*; //! # use ark_r1cs_std::prelude::*; //! # use ark_bls12_377::{*, constraints::*}; //! //! # let cs = ConstraintSystem::::new_ref(); //! # let mut rng = ark_std::test_rng(); //! //! // Generate random `G1` and `G2` elements. //! let a_native = G1Projective::rand(&mut rng); //! let b_native = G2Projective::rand(&mut rng); //! //! // Allocate `a_native` and `b_native` as witness variables in `cs`. //! let a = G1Var::new_witness(ark_relations::ns!(cs, "a"), || Ok(a_native))?; //! let b = G2Var::new_witness(ark_relations::ns!(cs, "b"), || Ok(b_native))?; //! //! // Allocate `a_native` and `b_native` as constants in `cs`. This does not add any //! // constraints or variables. //! let a_const = G1Var::new_constant(ark_relations::ns!(cs, "a_as_constant"), a_native)?; //! let b_const = G2Var::new_constant(ark_relations::ns!(cs, "b_as_constant"), b_native)?; //! //! let pairing_result_native = Bls12_377::pairing(a_native, b_native); //! //! // Prepare `a` and `b` for pairing. //! let a_prep = constraints::PairingVar::prepare_g1(&a)?; //! let b_prep = constraints::PairingVar::prepare_g2(&b)?; //! let pairing_result = constraints::PairingVar::pairing(a_prep, b_prep)?; //! //! // Check that the value of &a + &b is correct. //! assert_eq!(pairing_result.value()?, pairing_result_native); //! //! // Check that operations on variables and constants are equivalent. //! let a_prep_const = constraints::PairingVar::prepare_g1(&a_const)?; //! let b_prep_const = constraints::PairingVar::prepare_g2(&b_const)?; //! let pairing_result_const = constraints::PairingVar::pairing(a_prep_const, b_prep_const)?; //! println!("Done here 3"); //! //! pairing_result.enforce_equal(&pairing_result_const)?; //! assert!(cs.is_satisfied()?); //! # Ok(()) //! # } //! ``` mod fields; pub use fields::*; #[cfg(feature = "curve")] mod curves; #[cfg(feature = "curve")] mod pairing; #[cfg(feature = "curve")] pub use curves::*; #[cfg(feature = "curve")] pub use pairing::*;