pub struct Fp12Chip<'a, F: PrimeField, FpChip: FieldChip<F>, Fp12, const XI_0: i64>(pub FieldVectorChip<'a, F, FpChip>, _);
Expand description

Represent Fp12 point as FqPoint with degree = 12 Fp12 = Fp2[w] / (w^6 - u - xi) 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 Fp12 point as \sum_{i = 0}^6 (a_{i0} + a_{i1} * u) * w^i This is encoded in an FqPoint of degree 12 as (a_{00}, ..., a_{50}, a_{01}, ..., a_{51})

Tuple Fields

0: FieldVectorChip<'a, F, FpChip>

Implementations

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.

Assumptions
  • a is nonzero field point

in = g0 + g2 w + g4 w^2 + g1 w^3 + g3 w^4 + g5 w^5 where g_i = g_i0 + g_i1 * u are elements of Fp2 out = Compress(in) = [ g2, g3, g4, g5 ]

Input:

  • compression = [g2, g3, g4, g5] where g_i are proper elements of Fp2 Output:
  • Decompress(compression) = g0 + g2 w + g4 w^2 + g1 w^3 + g3 w^4 + g5 w^5 where
  • All elements of output are proper elements of Fp2 and: c = XI0 + u if g2 != 0: g1 = (g5^2 * c + 3 g4^2 - 2 g3)/(4g2) g0 = (2 g1^2 + g2 * g5 - 3 g3*g4) * c + 1 if g2 = 0: g1 = (2 g4 * g5)/g3 g0 = (2 g1^2 - 3 g3 * g4) * c + 1
Assumptions
  • a is a nonzero element in the cyclotomic subgroup
Assumptions
  • a is nonzero field point

Trait Implementations

Returns a copy of the value. Read more
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Formats the value using the given formatter. Read more
A representation of a field element that is used for intermediate computations. The representation can have “overflows” (e.g., overflow limbs or negative limbs). Read more
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)
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.
A type implementing Field trait to help with witness generation (for example with inverse)
Assigns fe as private witness. Note that the witness may not be constrained to be a unique representation of the field element fe.
Assigns fe as constant.
output: a + c
a * c
a * c + b
Constrains that a is a reduced representation and returns the wrapped a.
Assigns fe as private witness and contrains the witness to be in reduced form.
If using UnsafeFieldPoint, make sure multiplication does not cause overflow.
Constrains that b is nonzero as a field element and then returns a / b.
Returns a / b without constraining b to be nonzero. Read more
Constrains that b is nonzero as a field element and then returns -a / b.

Auto Trait Implementations

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