Struct Fp2Chip

pub struct Fp2Chip<'a, F: BigPrimeField, FpChip: FieldChip<F>, Fp2>(pub FieldVectorChip<'a, F, FpChip>, _);

Represent Fp2 point as FieldVector with degree = 2 Fp2 = Fp[u] / (u^2 + 1) This implementation assumes p = 3 (mod 4) in order for the polynomial u^2 + 1 to be irreducible over Fp; i.e., in order for -1 to not be a square (quadratic residue) in Fp This means we store an Fp2 point as a_0 + a_1 * u where a_0, a_1 in Fp

Tuple Fields

0: FieldVectorChip<'a, F, FpChip>

Implementations

impl<'a, F: BigPrimeField, FpChip: PrimeFieldChip<F>, Fp2: Field> Fp2Chip<'a, F, FpChip, Fp2>

where FpChip::FieldType: BigPrimeField,

pub fn new(fp_chip: &'a FpChip) -> Self

User must construct an FpChip first using a config. This is intended so everything shares a single FlexGateChip, which is needed for the column allocation to work.

pub fn fp_chip(&self) -> &FpChip

pub fn conjugate( &self, ctx: &mut Context<F>, a: FieldVector<FpChip::FieldPoint>, ) -> FieldVector<FpChip::FieldPoint>

pub fn neg_conjugate( &self, ctx: &mut Context<F>, a: FieldVector<FpChip::FieldPoint>, ) -> FieldVector<FpChip::FieldPoint>

Trait Implementations

impl<'a, F: Clone + BigPrimeField, FpChip: Clone + FieldChip<F>, Fp2: Clone> Clone for Fp2Chip<'a, F, FpChip, Fp2>

fn clone(&self) -> Fp2Chip<'a, F, FpChip, Fp2>

Returns a copy of the value.

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

Performs copy-assignment from source.

impl<'a, F: Debug + BigPrimeField, FpChip: Debug + FieldChip<F>, Fp2: Debug> Debug for Fp2Chip<'a, F, FpChip, Fp2>

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

Formats the value using the given formatter.

impl<'a, F, FpChip, Fp2> FieldChip<F> for Fp2Chip<'a, F, FpChip, Fp2>

where F: BigPrimeField, FpChip::FieldType: BigPrimeField, FpChip: PrimeFieldChip<F>, Fp2: Field + FieldExtConstructor<FpChip::FieldType, 2>, FieldVector<FpChip::UnsafeFieldPoint>: From<FieldVector<FpChip::FieldPoint>>, FieldVector<FpChip::FieldPoint>: From<FieldVector<FpChip::ReducedFieldPoint>>,

fn range_check( &self, ctx: &mut Context<F>, a: impl Into<Self::FieldPoint>, max_bits: usize, )

Assumptions

• max_bits <= n * k where n = self.fp_chip.limb_bits and k = self.fp_chip.num_limbs
• a[i].truncation.limbs.len() = self.fp_chip.num_limbs for all i = 0..a.len()

const PRIME_FIELD_NUM_BITS: u32 = <FpChip::FieldType>::NUM_BITS

type UnsafeFieldPoint = FieldVector<<FpChip as FieldChip<F>>::UnsafeFieldPoint>

A representation of a field element that is used for intermediate computations. The representation can have “overflows” (e.g., overflow limbs or negative limbs).

type FieldPoint = FieldVector<<FpChip as FieldChip<F>>::FieldPoint>

The “proper” representation of a field element. Allowed to be a non-unique representation of a field element (e.g., can be greater than modulus)

type ReducedFieldPoint = FieldVector<<FpChip as FieldChip<F>>::ReducedFieldPoint>

A proper representation of field elements that guarantees a unique representation of each field element. Typically this means Uints that are less than the modulus.

type FieldType = Fp2

A type implementing Field trait to help with witness generation (for example with inverse)

type RangeChip = <FpChip as FieldChip<F>>::RangeChip

fn get_assigned_value(&self, x: &Self::UnsafeFieldPoint) -> Fp2

fn mul_no_carry( &self, ctx: &mut Context<F>, a: impl Into<Self::UnsafeFieldPoint>, b: impl Into<Self::UnsafeFieldPoint>, ) -> Self::UnsafeFieldPoint

fn native_modulus(&self) -> &BigUint

fn range(&self) -> &Self::RangeChip

fn limb_bits(&self) -> usize

fn load_private( &self, ctx: &mut Context<F>, fe: Self::FieldType, ) -> Self::FieldPoint

Assigns fe as private witness. Note that the witness may not be constrained to be a unique representation of the field element fe.

fn load_constant( &self, ctx: &mut Context<F>, fe: Self::FieldType, ) -> Self::FieldPoint

Assigns fe as constant.

fn add_no_carry( &self, ctx: &mut Context<F>, a: impl Into<Self::UnsafeFieldPoint>, b: impl Into<Self::UnsafeFieldPoint>, ) -> Self::UnsafeFieldPoint

fn add_constant_no_carry( &self, ctx: &mut Context<F>, a: impl Into<Self::UnsafeFieldPoint>, c: Self::FieldType, ) -> Self::UnsafeFieldPoint

output: a + c

fn sub_no_carry( &self, ctx: &mut Context<F>, a: impl Into<Self::UnsafeFieldPoint>, b: impl Into<Self::UnsafeFieldPoint>, ) -> Self::UnsafeFieldPoint

fn negate(&self, ctx: &mut Context<F>, a: Self::FieldPoint) -> Self::FieldPoint

fn scalar_mul_no_carry( &self, ctx: &mut Context<F>, a: impl Into<Self::UnsafeFieldPoint>, c: i64, ) -> Self::UnsafeFieldPoint

a * c

fn scalar_mul_and_add_no_carry( &self, ctx: &mut Context<F>, a: impl Into<Self::UnsafeFieldPoint>, b: impl Into<Self::UnsafeFieldPoint>, c: i64, ) -> Self::UnsafeFieldPoint

a * c + b

fn check_carry_mod_to_zero( &self, ctx: &mut Context<F>, a: Self::UnsafeFieldPoint, )

fn carry_mod( &self, ctx: &mut Context<F>, a: Self::UnsafeFieldPoint, ) -> Self::FieldPoint

fn enforce_less_than( &self, ctx: &mut Context<F>, a: Self::FieldPoint, ) -> Self::ReducedFieldPoint

Constrains that a is a reduced representation and returns the wrapped a.

fn is_soft_zero( &self, ctx: &mut Context<F>, a: impl Into<Self::FieldPoint>, ) -> AssignedValue<F>

fn is_soft_nonzero( &self, ctx: &mut Context<F>, a: impl Into<Self::FieldPoint>, ) -> AssignedValue<F>

fn is_zero( &self, ctx: &mut Context<F>, a: impl Into<Self::FieldPoint>, ) -> AssignedValue<F>

fn is_equal_unenforced( &self, ctx: &mut Context<F>, a: Self::ReducedFieldPoint, b: Self::ReducedFieldPoint, ) -> AssignedValue<F>

fn assert_equal( &self, ctx: &mut Context<F>, a: impl Into<Self::FieldPoint>, b: impl Into<Self::FieldPoint>, )

fn gate(&self) -> &<Self::RangeChip as RangeInstructions<F>>::Gate

fn load_private_reduced( &self, ctx: &mut Context<F>, fe: Self::FieldType, ) -> Self::ReducedFieldPoint

Assigns fe as private witness and contrains the witness to be in reduced form.

fn is_equal( &self, ctx: &mut Context<F>, a: impl Into<Self::FieldPoint>, b: impl Into<Self::FieldPoint>, ) -> AssignedValue<F>

fn mul( &self, ctx: &mut Context<F>, a: impl Into<Self::UnsafeFieldPoint>, b: impl Into<Self::UnsafeFieldPoint>, ) -> Self::FieldPoint

If using UnsafeFieldPoint, make sure multiplication does not cause overflow.

fn divide( &self, ctx: &mut Context<F>, a: impl Into<Self::FieldPoint>, b: impl Into<Self::FieldPoint>, ) -> Self::FieldPoint

Constrains that b is nonzero as a field element and then returns a / b.

fn divide_unsafe( &self, ctx: &mut Context<F>, a: impl Into<Self::UnsafeFieldPoint>, b: impl Into<Self::UnsafeFieldPoint>, ) -> Self::FieldPoint

Returns a / b without constraining b to be nonzero.

fn neg_divide( &self, ctx: &mut Context<F>, a: impl Into<Self::FieldPoint>, b: impl Into<Self::FieldPoint>, ) -> Self::FieldPoint

Constrains that b is nonzero as a field element and then returns -a / b.

fn neg_divide_unsafe( &self, ctx: &mut Context<F>, a: impl Into<Self::UnsafeFieldPoint>, b: impl Into<Self::UnsafeFieldPoint>, ) -> Self::FieldPoint

impl<'a, F: Copy + BigPrimeField, FpChip: Copy + FieldChip<F>, Fp2: Copy> Copy for Fp2Chip<'a, F, FpChip, Fp2>