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//! `bellperson` is a crate for building zk-SNARK circuits. It provides circuit //! traits and and primitive structures, as well as basic gadget implementations //! such as booleans and number abstractions. //! //! # Example circuit //! //! Say we want to write a circuit that proves we know the preimage to some hash //! computed using SHA-256d (calling SHA-256 twice). The preimage must have a //! fixed length known in advance (because the circuit parameters will depend on //! it), but can otherwise have any value. We take the following strategy: //! //! - Witness each bit of the preimage. //! - Compute `hash = SHA-256d(preimage)` inside the circuit. //! - Expose `hash` as a public input using multiscalar packing. //! //! ``` //! use bellperson::{ //! gadgets::{ //! boolean::{AllocatedBit, Boolean}, //! multipack, //! sha256::sha256, //! }, //! groth16, Circuit, ConstraintSystem, SynthesisError, //! }; //! use paired::{bls12_381::Bls12, Engine}; //! use rand::rngs::OsRng; //! use sha2::{Digest, Sha256}; //! //! /// Our own SHA-256d gadget. Input and output are in little-endian bit order. //! fn sha256d<E: Engine, CS: ConstraintSystem<E>>( //! mut cs: CS, //! data: &[Boolean], //! ) -> Result<Vec<Boolean>, SynthesisError> { //! // Flip endianness of each input byte //! let input: Vec<_> = data //! .chunks(8) //! .map(|c| c.iter().rev()) //! .flatten() //! .cloned() //! .collect(); //! //! let mid = sha256(cs.namespace(|| "SHA-256(input)"), &input)?; //! let res = sha256(cs.namespace(|| "SHA-256(mid)"), &mid)?; //! //! // Flip endianness of each output byte //! Ok(res //! .chunks(8) //! .map(|c| c.iter().rev()) //! .flatten() //! .cloned() //! .collect()) //! } //! //! struct MyCircuit { //! /// The input to SHA-256d we are proving that we know. Set to `None` when we //! /// are verifying a proof (and do not have the witness data). //! preimage: Option<[u8; 80]>, //! } //! //! impl<E: Engine> Circuit<E> for MyCircuit { //! fn synthesize<CS: ConstraintSystem<E>>(self, cs: &mut CS) -> Result<(), SynthesisError> { //! // Compute the values for the bits of the preimage. If we are verifying a proof, //! // we still need to create the same constraints, so we return an equivalent-size //! // Vec of None (indicating that the value of each bit is unknown). //! let bit_values = if let Some(preimage) = self.preimage { //! preimage //! .iter() //! .map(|byte| (0..8).map(move |i| (byte >> i) & 1u8 == 1u8)) //! .flatten() //! .map(|b| Some(b)) //! .collect() //! } else { //! vec![None; 80 * 8] //! }; //! assert_eq!(bit_values.len(), 80 * 8); //! //! // Witness the bits of the preimage. //! let preimage_bits = bit_values //! .into_iter() //! .enumerate() //! // Allocate each bit. //! .map(|(i, b)| { //! AllocatedBit::alloc(cs.namespace(|| format!("preimage bit {}", i)), b) //! }) //! // Convert the AllocatedBits into Booleans (required for the sha256 gadget). //! .map(|b| b.map(Boolean::from)) //! .collect::<Result<Vec<_>, _>>()?; //! //! // Compute hash = SHA-256d(preimage). //! let hash = sha256d(cs.namespace(|| "SHA-256d(preimage)"), &preimage_bits)?; //! //! // Expose the vector of 32 boolean variables as compact public inputs. //! multipack::pack_into_inputs(cs.namespace(|| "pack hash"), &hash) //! } //! } //! //! // Create parameters for our circuit. In a production deployment these would //! // be generated securely using a multiparty computation. //! let params = { //! let c = MyCircuit { preimage: None }; //! groth16::generate_random_parameters::<Bls12, _, _>(c, &mut OsRng).unwrap() //! }; //! //! // Prepare the verification key (for proof verification). //! let pvk = groth16::prepare_verifying_key(¶ms.vk); //! //! // Pick a preimage and compute its hash. //! let preimage = [42; 80]; //! let hash = Sha256::digest(&Sha256::digest(&preimage)); //! //! // Create an instance of our circuit (with the preimage as a witness). //! let c = MyCircuit { //! preimage: Some(preimage), //! }; //! //! // Create a Groth16 proof with our parameters. //! let proof = groth16::create_random_proof(c, ¶ms, &mut OsRng).unwrap(); //! //! // Pack the hash as inputs for proof verification. //! let hash_bits = multipack::bytes_to_bits_le(&hash); //! let inputs = multipack::compute_multipacking::<Bls12>(&hash_bits); //! //! // Check the proof! //! assert!(groth16::verify_proof(&pvk, &proof, &inputs).unwrap()); //! ``` //! //! # Roadmap //! //! `bellperson` is being refactored into a generic proving library. Currently it //! is pairing-specific, and different types of proving systems need to be //! implemented as sub-modules. After the refactor, `bellperson` will be generic //! using the [`ff`] and [`group`] crates, while specific proving systems will //! be separate crates that pull in the dependencies they require. // Catch documentation errors caused by code changes. #![deny(intra_doc_link_resolution_failure)] #[cfg(test)] #[macro_use] extern crate hex_literal; pub mod domain; pub mod gadgets; pub mod gpu; #[cfg(feature = "groth16")] pub mod groth16; pub mod multicore; pub mod multiexp; pub mod util_cs; #[cfg(feature = "gpu")] pub use gpu::GPU_NVIDIA_DEVICES; use ff::{Field, ScalarEngine}; use ahash::AHashMap as HashMap; use std::io; use std::marker::PhantomData; use std::ops::{Add, Sub}; const BELLMAN_VERSION: &'static str = env!("CARGO_PKG_VERSION"); /// Computations are expressed in terms of arithmetic circuits, in particular /// rank-1 quadratic constraint systems. The `Circuit` trait represents a /// circuit that can be synthesized. The `synthesize` method is called during /// CRS generation and during proving. pub trait Circuit<E: ScalarEngine> { /// Synthesize the circuit into a rank-1 quadratic constraint system. fn synthesize<CS: ConstraintSystem<E>>(self, cs: &mut CS) -> Result<(), SynthesisError>; } /// Represents a variable in our constraint system. #[derive(Copy, Clone, Debug, PartialEq, Eq, Hash)] pub struct Variable(Index); impl Variable { /// This constructs a variable with an arbitrary index. /// Circuit implementations are not recommended to use this. pub fn new_unchecked(idx: Index) -> Variable { Variable(idx) } /// This returns the index underlying the variable. /// Circuit implementations are not recommended to use this. pub fn get_unchecked(&self) -> Index { self.0 } } /// Represents the index of either an input variable or /// auxiliary variable. #[derive(Copy, Clone, PartialEq, Debug, Eq, Hash)] pub enum Index { Input(usize), Aux(usize), } /// This represents a linear combination of some variables, with coefficients /// in the scalar field of a pairing-friendly elliptic curve group. #[derive(Clone)] pub struct LinearCombination<E: ScalarEngine>(HashMap<Variable, E::Fr>); impl<E: ScalarEngine> Default for LinearCombination<E> { fn default() -> Self { Self::zero() } } impl<E: ScalarEngine> LinearCombination<E> { pub fn zero() -> LinearCombination<E> { LinearCombination(HashMap::new()) } pub fn iter(&self) -> impl Iterator<Item = (&Variable, &E::Fr)> + '_ { self.0.iter() } pub fn add_unsimplified(mut self, (coeff, var): (E::Fr, Variable)) -> LinearCombination<E> { self.0 .entry(var) .or_insert(E::Fr::zero()) .add_assign(&coeff); self } } impl<E: ScalarEngine> Add<(E::Fr, Variable)> for LinearCombination<E> { type Output = LinearCombination<E>; fn add(mut self, (coeff, var): (E::Fr, Variable)) -> LinearCombination<E> { self.0 .entry(var) .or_insert(E::Fr::zero()) .add_assign(&coeff); self } } impl<E: ScalarEngine> Sub<(E::Fr, Variable)> for LinearCombination<E> { type Output = LinearCombination<E>; #[allow(clippy::suspicious_arithmetic_impl)] fn sub(self, (mut coeff, var): (E::Fr, Variable)) -> LinearCombination<E> { coeff.negate(); self + (coeff, var) } } impl<E: ScalarEngine> Add<Variable> for LinearCombination<E> { type Output = LinearCombination<E>; fn add(self, other: Variable) -> LinearCombination<E> { self + (E::Fr::one(), other) } } impl<E: ScalarEngine> Sub<Variable> for LinearCombination<E> { type Output = LinearCombination<E>; fn sub(self, other: Variable) -> LinearCombination<E> { self - (E::Fr::one(), other) } } impl<'a, E: ScalarEngine> Add<&'a LinearCombination<E>> for LinearCombination<E> { type Output = LinearCombination<E>; fn add(mut self, other: &'a LinearCombination<E>) -> LinearCombination<E> { for (var, val) in &other.0 { self.0.entry(*var).or_insert(E::Fr::zero()).add_assign(val); } self } } impl<'a, E: ScalarEngine> Sub<&'a LinearCombination<E>> for LinearCombination<E> { type Output = LinearCombination<E>; fn sub(mut self, other: &'a LinearCombination<E>) -> LinearCombination<E> { for (var, val) in &other.0 { self = self - (*val, *var); } self } } impl<'a, E: ScalarEngine> Add<(E::Fr, &'a LinearCombination<E>)> for LinearCombination<E> { type Output = LinearCombination<E>; fn add(mut self, (coeff, other): (E::Fr, &'a LinearCombination<E>)) -> LinearCombination<E> { for s in &other.0 { let mut tmp = *s.1; tmp.mul_assign(&coeff); self = self + (tmp, *s.0); } self } } impl<'a, E: ScalarEngine> Sub<(E::Fr, &'a LinearCombination<E>)> for LinearCombination<E> { type Output = LinearCombination<E>; fn sub(mut self, (coeff, other): (E::Fr, &'a LinearCombination<E>)) -> LinearCombination<E> { for s in &other.0 { let mut tmp = *s.1; tmp.mul_assign(&coeff); self = self - (tmp, *s.0); } self } } /// This is an error that could occur during circuit synthesis contexts, /// such as CRS generation, proving or verification. #[derive(thiserror::Error, Debug)] pub enum SynthesisError { /// During synthesis, we lacked knowledge of a variable assignment. #[error("an assignment for a variable could not be computed")] AssignmentMissing, /// During synthesis, we divided by zero. #[error("division by zero")] DivisionByZero, /// During synthesis, we constructed an unsatisfiable constraint system. #[error("unsatisfiable constraint system")] Unsatisfiable, /// During synthesis, our polynomials ended up being too high of degree #[error("polynomial degree is too large")] PolynomialDegreeTooLarge, /// During proof generation, we encountered an identity in the CRS #[error("encountered an identity element in the CRS")] UnexpectedIdentity, /// During proof generation, we encountered an I/O error with the CRS #[error("encountered an I/O error: {0}")] IoError(#[from] io::Error), /// During verification, our verifying key was malformed. #[error("malformed verifying key")] MalformedVerifyingKey, /// During CRS generation, we observed an unconstrained auxiliary variable #[error("auxiliary variable was unconstrained")] UnconstrainedVariable, /// During GPU multiexp/fft, some GPU related error happened #[error("encountered a GPU error: {0}")] GPUError(#[from] gpu::GPUError), } /// Represents a constraint system which can have new variables /// allocated and constrains between them formed. pub trait ConstraintSystem<E: ScalarEngine>: Sized + Send { /// Represents the type of the "root" of this constraint system /// so that nested namespaces can minimize indirection. type Root: ConstraintSystem<E>; fn new() -> Self { unimplemented!( "ConstraintSystem::new must be implemented for extensible types implementing ConstraintSystem" ); } /// Return the "one" input variable fn one() -> Variable { Variable::new_unchecked(Index::Input(0)) } /// Allocate a private variable in the constraint system. The provided function is used to /// determine the assignment of the variable. The given `annotation` function is invoked /// in testing contexts in order to derive a unique name for this variable in the current /// namespace. fn alloc<F, A, AR>(&mut self, annotation: A, f: F) -> Result<Variable, SynthesisError> where F: FnOnce() -> Result<E::Fr, SynthesisError>, A: FnOnce() -> AR, AR: Into<String>; /// Allocate a public variable in the constraint system. The provided function is used to /// determine the assignment of the variable. fn alloc_input<F, A, AR>(&mut self, annotation: A, f: F) -> Result<Variable, SynthesisError> where F: FnOnce() -> Result<E::Fr, SynthesisError>, A: FnOnce() -> AR, AR: Into<String>; /// Enforce that `A` * `B` = `C`. The `annotation` function is invoked in testing contexts /// in order to derive a unique name for the constraint in the current namespace. fn enforce<A, AR, LA, LB, LC>(&mut self, annotation: A, a: LA, b: LB, c: LC) where A: FnOnce() -> AR, AR: Into<String>, LA: FnOnce(LinearCombination<E>) -> LinearCombination<E>, LB: FnOnce(LinearCombination<E>) -> LinearCombination<E>, LC: FnOnce(LinearCombination<E>) -> LinearCombination<E>; /// Create a new (sub)namespace and enter into it. Not intended /// for downstream use; use `namespace` instead. fn push_namespace<NR, N>(&mut self, name_fn: N) where NR: Into<String>, N: FnOnce() -> NR; /// Exit out of the existing namespace. Not intended for /// downstream use; use `namespace` instead. fn pop_namespace(&mut self); /// Gets the "root" constraint system, bypassing the namespacing. /// Not intended for downstream use; use `namespace` instead. fn get_root(&mut self) -> &mut Self::Root; /// Begin a namespace for this constraint system. fn namespace<NR, N>(&mut self, name_fn: N) -> Namespace<'_, E, Self::Root> where NR: Into<String>, N: FnOnce() -> NR, { self.get_root().push_namespace(name_fn); Namespace(self.get_root(), Default::default()) } /// Most implementations of ConstraintSystem are not 'extensible': they won't implement a specialized /// version of `extend` and should therefore also keep the default implementation of `is_extensible` /// so callers which optionally make use of `extend` can know to avoid relying on it when unimplemented. fn is_extensible() -> bool { false } /// Extend concatenates thew `other` constraint systems to the receiver, modifying the receiver, whose /// inputs, allocated variables, and constraints will precede those of the `other` constraint system. /// The primary use case for this is parallel synthesis of circuits which can be decomposed into /// entirely independent sub-circuits. Each can be synthesized in its own thread, then the /// original `ConstraintSystem` can be extended with each, in the same order they would have /// been synthesized sequentially. fn extend(&mut self, _other: Self) { unimplemented!( "ConstraintSystem::extend must be implemented for types implementing ConstraintSystem" ); } } /// This is a "namespaced" constraint system which borrows a constraint system (pushing /// a namespace context) and, when dropped, pops out of the namespace context. pub struct Namespace<'a, E: ScalarEngine, CS: ConstraintSystem<E>>(&'a mut CS, SendMarker<E>); struct SendMarker<E: ScalarEngine>(PhantomData<E>); impl<E: ScalarEngine> Default for SendMarker<E> { fn default() -> Self { Self(PhantomData) } } // Safety: ScalarEngine is static and this is only a marker unsafe impl<E: ScalarEngine> Send for SendMarker<E> {} impl<'cs, E: ScalarEngine, CS: ConstraintSystem<E>> ConstraintSystem<E> for Namespace<'cs, E, CS> { type Root = CS::Root; fn one() -> Variable { CS::one() } fn alloc<F, A, AR>(&mut self, annotation: A, f: F) -> Result<Variable, SynthesisError> where F: FnOnce() -> Result<E::Fr, SynthesisError>, A: FnOnce() -> AR, AR: Into<String>, { self.0.alloc(annotation, f) } fn alloc_input<F, A, AR>(&mut self, annotation: A, f: F) -> Result<Variable, SynthesisError> where F: FnOnce() -> Result<E::Fr, SynthesisError>, A: FnOnce() -> AR, AR: Into<String>, { self.0.alloc_input(annotation, f) } fn enforce<A, AR, LA, LB, LC>(&mut self, annotation: A, a: LA, b: LB, c: LC) where A: FnOnce() -> AR, AR: Into<String>, LA: FnOnce(LinearCombination<E>) -> LinearCombination<E>, LB: FnOnce(LinearCombination<E>) -> LinearCombination<E>, LC: FnOnce(LinearCombination<E>) -> LinearCombination<E>, { self.0.enforce(annotation, a, b, c) } // Downstream users who use `namespace` will never interact with these // functions and they will never be invoked because the namespace is // never a root constraint system. fn push_namespace<NR, N>(&mut self, _: N) where NR: Into<String>, N: FnOnce() -> NR, { panic!("only the root's push_namespace should be called"); } fn pop_namespace(&mut self) { panic!("only the root's pop_namespace should be called"); } fn get_root(&mut self) -> &mut Self::Root { self.0.get_root() } } impl<'a, E: ScalarEngine, CS: ConstraintSystem<E>> Drop for Namespace<'a, E, CS> { fn drop(&mut self) { self.get_root().pop_namespace() } } /// Convenience implementation of ConstraintSystem<E> for mutable references to /// constraint systems. impl<'cs, E: ScalarEngine, CS: ConstraintSystem<E>> ConstraintSystem<E> for &'cs mut CS { type Root = CS::Root; fn one() -> Variable { CS::one() } fn alloc<F, A, AR>(&mut self, annotation: A, f: F) -> Result<Variable, SynthesisError> where F: FnOnce() -> Result<E::Fr, SynthesisError>, A: FnOnce() -> AR, AR: Into<String>, { (**self).alloc(annotation, f) } fn alloc_input<F, A, AR>(&mut self, annotation: A, f: F) -> Result<Variable, SynthesisError> where F: FnOnce() -> Result<E::Fr, SynthesisError>, A: FnOnce() -> AR, AR: Into<String>, { (**self).alloc_input(annotation, f) } fn enforce<A, AR, LA, LB, LC>(&mut self, annotation: A, a: LA, b: LB, c: LC) where A: FnOnce() -> AR, AR: Into<String>, LA: FnOnce(LinearCombination<E>) -> LinearCombination<E>, LB: FnOnce(LinearCombination<E>) -> LinearCombination<E>, LC: FnOnce(LinearCombination<E>) -> LinearCombination<E>, { (**self).enforce(annotation, a, b, c) } fn push_namespace<NR, N>(&mut self, name_fn: N) where NR: Into<String>, N: FnOnce() -> NR, { (**self).push_namespace(name_fn) } fn pop_namespace(&mut self) { (**self).pop_namespace() } fn get_root(&mut self) -> &mut Self::Root { (**self).get_root() } } #[cfg(test)] mod tests { use super::*; #[test] fn test_add_simplify() { use paired::bls12_381::Bls12; let n = 5; let mut lc = LinearCombination::<Bls12>::zero(); let mut expected_sums = vec![<Bls12 as ScalarEngine>::Fr::zero(); n]; let mut total_additions = 0; for i in 0..n { for _ in 0..i + 1 { let coeff = <Bls12 as ScalarEngine>::Fr::one(); lc = lc + (coeff, Variable::new_unchecked(Index::Aux(i))); let mut tmp = expected_sums[i]; tmp.add_assign(&coeff); expected_sums[i] = tmp; total_additions += 1; } } // There are only as many terms as distinct variable Indexes — not one per addition operation. assert_eq!(n, lc.0.len()); assert!(lc.0.len() != total_additions); // Each variable has the expected coefficient, the sume of those added by its Index. lc.0.iter().for_each(|(var, coeff)| match var.0 { Index::Aux(i) => assert_eq!(expected_sums[i], *coeff), _ => panic!("unexpected variable type"), }); } }