Struct Coset

pub struct Coset {
    pub log_2_size: u32,
    pub shift: CirclePoint<Mersenne31Field>,
}

Given g_n, a generator of the subgroup of size n of the circle, i.e. <g_n>, and given a shift, that is a another point of the circle, we define the coset shift + <g_n> which is the set of all the points in <g_n> plus the shift. For example, if <g_4> = {p1, p2, p3, p4}, then g_8 + <g_4> = {g_8 + p1, g_8 + p2, g_8 + p3, g_8 + p4}.

Fields

log_2_size: u32

shift: CirclePoint<Mersenne31Field>

Implementations

impl Coset

pub fn new(log_2_size: u32, shift: CirclePoint<Mersenne31Field>) -> Self

pub fn new_standard(log_2_size: u32) -> Self

Returns the coset g_2n + <g_n>

pub fn get_generator(&self) -> CirclePoint<Mersenne31Field>

Returns g_n, the generator of the subgroup of order n = 2^log_2_size.

pub fn half_coset(coset: Self) -> Self

Given a standard coset g_2n + <g_n>, returns the subcoset with half size g_2n + <g_{n/2}>

pub fn conjugate(coset: Self) -> Self

Given a coset shift + G returns the coset -shift + G. Note that (g_2n + <g_{n/2}>) U (-g_2n + <g_{n/2}>) = g_2n + <g_n>.

pub fn get_coset_points(coset: &Self) -> Vec<CirclePoint<Mersenne31Field>>

Returns the vector of shift + g for every g in <g_n>. where g = i * g_n for i = 0, …, n-1.

Trait Implementations

impl Clone for Coset

fn clone(&self) -> Coset

Returns a duplicate of the value.

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

Performs copy-assignment from source.

impl Debug for Coset

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

Formats the value using the given formatter.