Enum Boolean

pub enum Boolean<F: Field> {
    Var(AllocatedBool<F>),
    Constant(bool),
}

Represents a boolean value in the constraint system which is guaranteed to be either zero or one.

Variants

Var(AllocatedBool<F>)

Constant(bool)

Implementations

impl<F: Field> Boolean<F>

pub fn nand(&self, other: &Self) -> Result<Self, SynthesisError>

Outputs !(self & other).

impl<F: PrimeField> Boolean<F>

pub fn kary_and(bits: &[Self]) -> Result<Self, SynthesisError>

Outputs bits[0] & bits[1] & ... & bits.last().unwrap().

// We'll use the BLS12-381 scalar field for our constraints.
use ark_test_curves::bls12_381::Fr;
use ark_relations::r1cs::*;
use ark_r1cs_std::prelude::*;

let cs = ConstraintSystem::<Fr>::new_ref();

let a = Boolean::new_witness(cs.clone(), || Ok(true))?;
let b = Boolean::new_witness(cs.clone(), || Ok(false))?;
let c = Boolean::new_witness(cs.clone(), || Ok(true))?;

Boolean::kary_and(&[a.clone(), b.clone(), c.clone()])?.enforce_equal(&Boolean::FALSE)?;
Boolean::kary_and(&[a.clone(), c.clone()])?.enforce_equal(&Boolean::TRUE)?;

assert!(cs.is_satisfied().unwrap());

pub fn kary_nand(bits: &[Self]) -> Result<Self, SynthesisError>

Outputs !(bits[0] & bits[1] & ... & bits.last().unwrap()).

// We'll use the BLS12-381 scalar field for our constraints.
use ark_test_curves::bls12_381::Fr;
use ark_relations::r1cs::*;
use ark_r1cs_std::prelude::*;

let cs = ConstraintSystem::<Fr>::new_ref();

let a = Boolean::new_witness(cs.clone(), || Ok(true))?;
let b = Boolean::new_witness(cs.clone(), || Ok(false))?;
let c = Boolean::new_witness(cs.clone(), || Ok(true))?;

Boolean::kary_nand(&[a.clone(), b.clone(), c.clone()])?.enforce_equal(&Boolean::TRUE)?;
Boolean::kary_nand(&[a.clone(), c.clone()])?.enforce_equal(&Boolean::FALSE)?;
Boolean::kary_nand(&[b.clone(), c.clone()])?.enforce_equal(&Boolean::TRUE)?;

assert!(cs.is_satisfied().unwrap());

pub fn enforce_kary_nand(bits: &[Self]) -> Result<(), SynthesisError>

Enforces that !(bits[0] & bits[1] & ... ) == Boolean::TRUE.

Informally, this means that at least one element in bits must be false.

impl<F: PrimeField> Boolean<F>

pub fn enforce_in_field_le(bits: &[Self]) -> Result<(), SynthesisError>

Enforces that bits, when interpreted as a integer, is less than F::characteristic(), That is, interpret bits as a little-endian integer, and enforce that this integer is “in the field Z_p”, where p = F::characteristic() .

pub fn enforce_smaller_or_equal_than_le( bits: &[Self], element: impl AsRef<[u64]>, ) -> Result<Vec<Self>, SynthesisError>

Enforces that bits is less than or equal to element, when both are interpreted as (little-endian) integers.

impl<F: Field> Boolean<F>

pub fn not_in_place(&mut self) -> Result<(), SynthesisError>

impl<F: PrimeField> Boolean<F>

pub fn kary_or(bits: &[Self]) -> Result<Self, SynthesisError>

Outputs bits[0] | bits[1] | ... | bits.last().unwrap().

// We'll use the BLS12-381 scalar field for our constraints.
use ark_test_curves::bls12_381::Fr;
use ark_relations::r1cs::*;
use ark_r1cs_std::prelude::*;

let cs = ConstraintSystem::<Fr>::new_ref();

let a = Boolean::new_witness(cs.clone(), || Ok(true))?;
let b = Boolean::new_witness(cs.clone(), || Ok(false))?;
let c = Boolean::new_witness(cs.clone(), || Ok(false))?;

Boolean::kary_or(&[a.clone(), b.clone(), c.clone()])?.enforce_equal(&Boolean::TRUE)?;
Boolean::kary_or(&[a.clone(), c.clone()])?.enforce_equal(&Boolean::TRUE)?;
Boolean::kary_or(&[b.clone(), c.clone()])?.enforce_equal(&Boolean::FALSE)?;

assert!(cs.is_satisfied().unwrap());

impl<F: PrimeField> Boolean<F>

pub fn select<T: CondSelectGadget<F>>( &self, first: &T, second: &T, ) -> Result<T, SynthesisError>

Conditionally selects one of first and second based on the value of self:

If self.is_eq(&Boolean::TRUE), this outputs first; else, it outputs second.

// We'll use the BLS12-381 scalar field for our constraints.
use ark_test_curves::bls12_381::Fr;
use ark_relations::r1cs::*;
use ark_r1cs_std::prelude::*;

let cs = ConstraintSystem::<Fr>::new_ref();

let a = Boolean::new_witness(cs.clone(), || Ok(true))?;
let b = Boolean::new_witness(cs.clone(), || Ok(false))?;

let cond = Boolean::new_witness(cs.clone(), || Ok(true))?;

cond.select(&a, &b)?.enforce_equal(&Boolean::TRUE)?;
cond.select(&b, &a)?.enforce_equal(&Boolean::FALSE)?;

assert!(cs.is_satisfied().unwrap());

impl<F: Field> Boolean<F>

pub const TRUE: Self = _

The constant true.

pub const FALSE: Self = _

The constant false.

pub fn constant_vec_from_bytes(values: &[u8]) -> Vec<Self>

Constructs a Boolean vector from a slice of constant u8. The u8s are decomposed in little-endian manner.

This does not create any new variables or constraints.

// We'll use the BLS12-381 scalar field for our constraints.
use ark_test_curves::bls12_381::Fr;
use ark_relations::r1cs::*;
use ark_r1cs_std::prelude::*;

let cs = ConstraintSystem::<Fr>::new_ref();
let t = Boolean::<Fr>::TRUE;
let f = Boolean::<Fr>::FALSE;

let bits = vec![f, t];
let generated_bits = Boolean::constant_vec_from_bytes(&[2]);
bits[..2].enforce_equal(&generated_bits[..2])?;
assert!(cs.is_satisfied().unwrap());

pub fn constant(b: bool) -> Self

Constructs a constant Boolean with value b.

This does not create any new variables or constraints.

// We'll use the BLS12-381 scalar field for our constraints.
use ark_test_curves::bls12_381::Fr;
use ark_r1cs_std::prelude::*;

let true_var = Boolean::<Fr>::TRUE;
let false_var = Boolean::<Fr>::FALSE;

true_var.enforce_equal(&Boolean::TRUE)?;
false_var.enforce_equal(&Boolean::constant(false))?;

pub fn lc(&self) -> LinearCombination<F>

Constructs a LinearCombination from Self’s variables according to the following map.

• Boolean::TRUE => lc!() + Variable::One
• Boolean::FALSE => lc!()
• Boolean::Var(v) => lc!() + v.variable()

pub fn le_bits_to_fp(bits: &[Self]) -> Result<FpVar<F>, SynthesisError>

where F: PrimeField,

Convert a little-endian bitwise representation of a field element to FpVar<F>

Wraps around if the bit representation is larger than the field modulus.

Trait Implementations

impl<F: Field> AllocVar<bool, F> for Boolean<F>

fn new_variable<T: Borrow<bool>>( cs: impl Into<Namespace<F>>, f: impl FnOnce() -> Result<T, SynthesisError>, mode: AllocationMode, ) -> Result<Self, SynthesisError>

Allocates a new variable of type Self in the ConstraintSystem cs. The mode of allocation is decided by mode.

fn new_constant( cs: impl Into<Namespace<F>>, t: impl Borrow<V>, ) -> Result<Self, SynthesisError>

Allocates a new constant of type Self in the ConstraintSystem cs.

fn new_input<T: Borrow<V>>( cs: impl Into<Namespace<F>>, f: impl FnOnce() -> Result<T, SynthesisError>, ) -> Result<Self, SynthesisError>

Allocates a new public input of type Self in the ConstraintSystem cs.

fn new_witness<T: Borrow<V>>( cs: impl Into<Namespace<F>>, f: impl FnOnce() -> Result<T, SynthesisError>, ) -> Result<Self, SynthesisError>

Allocates a new private witness of type Self in the ConstraintSystem cs.

fn new_variable_with_inferred_mode<T: Borrow<V>>( cs: impl Into<Namespace<F>>, f: impl FnOnce() -> Result<T, SynthesisError>, ) -> Result<Self, SynthesisError>

Allocates a new constant or private witness of type Self in the ConstraintSystem cs with the allocation mode inferred from cs. A constant is allocated if cs is None, and a private witness is allocated otherwise.

impl<'a, F: Field> BitAnd<&'a Boolean<F>> for Boolean<F>

type Output = Boolean<F>

The resulting type after applying the & operator.

fn bitand(self, other: &Self) -> Self::Output

Performs the & operation.

impl<'a, F: Field> BitAnd<Boolean<F>> for &'a Boolean<F>

type Output = Boolean<F>

The resulting type after applying the & operator.

fn bitand(self, other: Boolean<F>) -> Self::Output

Performs the & operation.

impl<'a, F: Field> BitAnd for &'a Boolean<F>

fn bitand(self, other: Self) -> Self::Output

Outputs self & other.

If at least one of self and other are constants, then this method does not create any constraints or variables.

// We'll use the BLS12-381 scalar field for our constraints.
use ark_test_curves::bls12_381::Fr;
use ark_relations::r1cs::*;
use ark_r1cs_std::prelude::*;

let cs = ConstraintSystem::<Fr>::new_ref();

let a = Boolean::new_witness(cs.clone(), || Ok(true))?;
let b = Boolean::new_witness(cs.clone(), || Ok(false))?;

(&a & &a).enforce_equal(&Boolean::TRUE)?;

(&a & &b).enforce_equal(&Boolean::FALSE)?;
(&b & &a).enforce_equal(&Boolean::FALSE)?;
(&b & &b).enforce_equal(&Boolean::FALSE)?;

assert!(cs.is_satisfied().unwrap());

type Output = Boolean<F>

The resulting type after applying the & operator.

impl<F: Field> BitAnd for Boolean<F>

type Output = Boolean<F>

The resulting type after applying the & operator.

fn bitand(self, other: Self) -> Self::Output

Performs the & operation.

impl<'a, F: Field> BitAndAssign<&'a Boolean<F>> for Boolean<F>

fn bitand_assign(&mut self, other: &'a Self)

Sets self = self & other.

impl<F: Field> BitAndAssign for Boolean<F>

fn bitand_assign(&mut self, other: Self)

Sets self = self & other.

impl<'a, F: PrimeField> BitOr<&'a Boolean<F>> for Boolean<F>

type Output = Boolean<F>

The resulting type after applying the | operator.

fn bitor(self, other: &Self) -> Self::Output

Performs the | operation.

impl<'a, F: PrimeField> BitOr<Boolean<F>> for &'a Boolean<F>

type Output = Boolean<F>

The resulting type after applying the | operator.

fn bitor(self, other: Boolean<F>) -> Self::Output

Performs the | operation.

impl<'a, F: PrimeField> BitOr for &'a Boolean<F>

fn bitor(self, other: Self) -> Self::Output

Outputs self | other.

If at least one of self and other are constants, then this method does not create any constraints or variables.

// We'll use the BLS12-381 scalar field for our constraints.
use ark_test_curves::bls12_381::Fr;
use ark_relations::r1cs::*;
use ark_r1cs_std::prelude::*;

let cs = ConstraintSystem::<Fr>::new_ref();

let a = Boolean::new_witness(cs.clone(), || Ok(true))?;
let b = Boolean::new_witness(cs.clone(), || Ok(false))?;

(&a | &b).enforce_equal(&Boolean::TRUE)?;
(&b | &a).enforce_equal(&Boolean::TRUE)?;

(&a | &a).enforce_equal(&Boolean::TRUE)?;
(&b | &b).enforce_equal(&Boolean::FALSE)?;

assert!(cs.is_satisfied().unwrap());

type Output = Boolean<F>

The resulting type after applying the | operator.

impl<F: PrimeField> BitOr for Boolean<F>

type Output = Boolean<F>

The resulting type after applying the | operator.

fn bitor(self, other: Self) -> Self::Output

Performs the | operation.

impl<'a, F: PrimeField> BitOrAssign<&'a Boolean<F>> for Boolean<F>

fn bitor_assign(&mut self, other: &'a Self)

Sets self = self | other.

impl<F: PrimeField> BitOrAssign for Boolean<F>

fn bitor_assign(&mut self, other: Self)

Sets self = self | other.

impl<'a, F: Field> BitXor<&'a Boolean<F>> for Boolean<F>

type Output = Boolean<F>

The resulting type after applying the ^ operator.

fn bitxor(self, other: &Self) -> Self::Output

Performs the ^ operation.

impl<'a, F: Field> BitXor<Boolean<F>> for &'a Boolean<F>

type Output = Boolean<F>

The resulting type after applying the ^ operator.

fn bitxor(self, other: Boolean<F>) -> Self::Output

Performs the ^ operation.

impl<'a, F: Field> BitXor for &'a Boolean<F>

fn bitxor(self, other: Self) -> Self::Output

Outputs self ^ other.

If at least one of self and other are constants, then this method does not create any constraints or variables.

// We'll use the BLS12-381 scalar field for our constraints.
use ark_test_curves::bls12_381::Fr;
use ark_relations::r1cs::*;
use ark_r1cs_std::prelude::*;

let cs = ConstraintSystem::<Fr>::new_ref();

let a = Boolean::new_witness(cs.clone(), || Ok(true))?;
let b = Boolean::new_witness(cs.clone(), || Ok(false))?;

(&a ^ &b).enforce_equal(&Boolean::TRUE)?;
(&b ^ &a).enforce_equal(&Boolean::TRUE)?;

(&a ^ &a).enforce_equal(&Boolean::FALSE)?;
(&b ^ &b).enforce_equal(&Boolean::FALSE)?;

assert!(cs.is_satisfied().unwrap());

type Output = Boolean<F>

The resulting type after applying the ^ operator.

impl<F: Field> BitXor for Boolean<F>

type Output = Boolean<F>

The resulting type after applying the ^ operator.

fn bitxor(self, other: Self) -> Self::Output

Performs the ^ operation.

impl<'a, F: Field> BitXorAssign<&'a Boolean<F>> for Boolean<F>

fn bitxor_assign(&mut self, other: &'a Self)

Sets self = self ^ other.

impl<F: Field> BitXorAssign for Boolean<F>

fn bitxor_assign(&mut self, other: Self)

Sets self = self ^ other.

impl<F: Clone + Field> Clone for Boolean<F>

fn clone(&self) -> Boolean<F>

Returns a copy of the value.

fn clone_from(&mut self, source: &Self)

Performs copy-assignment from source.

impl<F: PrimeField> CmpGadget<F> for Boolean<F>

fn is_ge(&self, other: &Self) -> Result<Boolean<F>, SynthesisError>

fn is_gt(&self, other: &Self) -> Result<Boolean<F>, SynthesisError>

fn is_lt(&self, other: &Self) -> Result<Boolean<F>, SynthesisError>

fn is_le(&self, other: &Self) -> Result<Boolean<F>, SynthesisError>

impl<F: PrimeField> CondSelectGadget<F> for Boolean<F>

fn conditionally_select( cond: &Boolean<F>, true_val: &Self, false_val: &Self, ) -> Result<Self, SynthesisError>

If cond == &Boolean::TRUE, then this returns true_value; else, returns false_value.

fn conditionally_select_power_of_two_vector( position: &[Boolean<ConstraintF>], values: &[Self], ) -> Result<Self, SynthesisError>

Returns an element of values whose index in represented by position. position is an array of boolean that represents an unsigned integer in big endian order.

impl<F: Debug + Field> Debug for Boolean<F>

fn fmt(&self, f: &mut Formatter<'_>) -> Result

Formats the value using the given formatter.

impl<F: Field> EqGadget<F> for Boolean<F>

fn is_eq(&self, other: &Self) -> Result<Boolean<F>, SynthesisError>

Output a Boolean value representing whether self.value() == other.value().

fn conditional_enforce_equal( &self, other: &Self, condition: &Boolean<F>, ) -> Result<(), SynthesisError>

If should_enforce == true, enforce that self and other are equal; else, enforce a vacuously true statement.

fn conditional_enforce_not_equal( &self, other: &Self, should_enforce: &Boolean<F>, ) -> Result<(), SynthesisError>

If should_enforce == true, enforce that self and other are not equal; else, enforce a vacuously true statement.

fn is_neq(&self, other: &Self) -> Result<Boolean<F>, SynthesisError>

Output a Boolean value representing whether self.value() != other.value().

fn enforce_equal(&self, other: &Self) -> Result<(), SynthesisError>

Enforce that self and other are equal.

fn enforce_not_equal(&self, other: &Self) -> Result<(), SynthesisError>

Enforce that self and other are not equal.

impl<F: Field> From<AllocatedBool<F>> for Boolean<F>

fn from(b: AllocatedBool<F>) -> Self

Converts to this type from the input type.

impl<BF, P> From<Boolean<<P as CubicExtConfig>::BasePrimeField>> for CubicExtVar<BF, P>

where BF: FieldVar<P::BaseField, P::BasePrimeField>, for<'a> &'a BF: FieldOpsBounds<'a, P::BaseField, BF>, P: CubicExtVarConfig<BF>,

fn from(other: Boolean<P::BasePrimeField>) -> Self

Converts to this type from the input type.

impl<BF, P> From<Boolean<<P as QuadExtConfig>::BasePrimeField>> for QuadExtVar<BF, P>

where BF: FieldVar<P::BaseField, P::BasePrimeField>, for<'a> &'a BF: FieldOpsBounds<'a, P::BaseField, BF>, P: QuadExtVarConfig<BF>,

fn from(other: Boolean<P::BasePrimeField>) -> Self

Converts to this type from the input type.

impl<TargetF: PrimeField, BaseF: PrimeField> From<Boolean<BaseF>> for EmulatedFpVar<TargetF, BaseF>

fn from(other: Boolean<BaseF>) -> Self

Converts to this type from the input type.

impl<F: PrimeField> From<Boolean<F>> for FpVar<F>

fn from(other: Boolean<F>) -> Self

Converts to this type from the input type.

impl<'a, F: Field> Not for &'a Boolean<F>

fn not(self) -> Self::Output

Negates self.

This does not create any new variables or constraints.

// We'll use the BLS12-381 scalar field for our constraints.
use ark_test_curves::bls12_381::Fr;
use ark_relations::r1cs::*;
use ark_r1cs_std::prelude::*;

let cs = ConstraintSystem::<Fr>::new_ref();

let a = Boolean::new_witness(cs.clone(), || Ok(true))?;
let b = Boolean::new_witness(cs.clone(), || Ok(false))?;

(!&a).enforce_equal(&b)?;
(!&b).enforce_equal(&a)?;

(!&a).enforce_equal(&Boolean::FALSE)?;
(!&b).enforce_equal(&Boolean::TRUE)?;

assert!(cs.is_satisfied().unwrap());

type Output = Boolean<F>

The resulting type after applying the ! operator.

impl<'a, F: Field> Not for &'a mut Boolean<F>

type Output = Boolean<F>

The resulting type after applying the ! operator.

fn not(self) -> Self::Output

Performs the unary ! operation.

impl<F: Field> Not for Boolean<F>

type Output = Boolean<F>

The resulting type after applying the ! operator.

fn not(self) -> Self::Output

Performs the unary ! operation.

impl<F: PartialEq + Field> PartialEq for Boolean<F>

fn eq(&self, other: &Boolean<F>) -> bool

Tests for self and other values to be equal, and is used by ==.

fn ne(&self, other: &Rhs) -> bool

Tests for !=. The default implementation is almost always sufficient, and should not be overridden without very good reason.

impl<F: Field> ToBitsGadget<F> for Boolean<F>

fn to_bits_le(&self) -> Result<Vec<Boolean<F>>, SynthesisError>

Outputs the canonical little-endian bit-wise representation of self.

fn to_non_unique_bits_le(&self) -> Result<Vec<Boolean<F>>, SynthesisError>

Outputs a possibly non-unique little-endian bit-wise representation of self.

fn to_bits_be(&self) -> Result<Vec<Boolean<F>>, SynthesisError>

Outputs the canonical big-endian bit-wise representation of self.

fn to_non_unique_bits_be(&self) -> Result<Vec<Boolean<F>>, SynthesisError>

Outputs a possibly non-unique big-endian bit-wise representation of self.

impl<F: Field> ToBytesGadget<F> for Boolean<F>

fn to_bytes_le(&self) -> Result<Vec<UInt8<F>>, SynthesisError>

Outputs 1u8 if self is true, and 0u8 otherwise.

fn to_non_unique_bytes_le(&self) -> Result<Vec<UInt8<F>>, SynthesisError>

Outputs a possibly non-unique byte decomposition of self.

impl<F: PrimeField> ToConstraintFieldGadget<F> for Boolean<F>

fn to_constraint_field(&self) -> Result<Vec<FpVar<F>>, SynthesisError>

Converts self to FpVar<ConstraintF> variables.

impl<F: Eq + Field> Eq for Boolean<F>

impl<F: Field> StructuralPartialEq for Boolean<F>