Trait halo2_proofs::arithmetic::SqrtRatio

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pub trait SqrtRatio: PrimeField {
    const T_MINUS1_OVER2: [u64; 4];

    fn get_lower_32(&self) -> u32;

    fn pow_by_t_minus1_over2(&self) -> Self { ... }
    fn sqrt_ratio(num: &Self, div: &Self) -> (Choice, Self) { ... }
    fn sqrt_alt(&self) -> (Choice, Self) { ... }
}

Expand description

A trait that exposes additional operations related to calculating square roots of prime-order finite fields.

Required Associated Constants

const T_MINUS1_OVER2: [u64; 4]

The value $(T-1)/2$ such that $2^S \cdot T = p - 1$ with $T$ odd.

Required Methods

fn get_lower_32(&self) -> u32

Gets the lower 32 bits of this field element when expressed canonically.

Provided Methods

fn pow_by_t_minus1_over2(&self) -> Self

Raise this field element to the power Self::T_MINUS1_OVER2.

Field implementations may override this to use an efficient addition chain.

fn sqrt_ratio(num: &Self, div: &Self) -> (Choice, Self)

Computes:

$(\textsf{true}, \sqrt{\textsf{num}/\textsf{div}})$, if $\textsf{num}$ and $\textsf{div}$ are nonzero and $\textsf{num}/\textsf{div}$ is a square in the field;
$(\textsf{true}, 0)$, if $\textsf{num}$ is zero;
$(\textsf{false}, 0)$, if $\textsf{num}$ is nonzero and $\textsf{div}$ is zero;
$(\textsf{false}, \sqrt{G_S \cdot \textsf{num}/\textsf{div}})$, if $\textsf{num}$ and $\textsf{div}$ are nonzero and $\textsf{num}/\textsf{div}$ is a nonsquare in the field;

where $G_S$ is a non-square.

For pasta_curves, $G_S$ is currently [ff::PrimeField::root_of_unity], a generator of the order $2^S$ subgroup. Users of this crate should not rely on this generator being fixed; it may be changed in future crate versions to simplify the implementation of the SSWU hash-to-curve algorithm.

The choice of root from sqrt is unspecified.

fn sqrt_alt(&self) -> (Choice, Self)

Equivalent to Self::sqrt_ratio(self, one()).