Struct FieldElement 

pub struct FieldElement { /* private fields */ }

素域Fp的域元素

这里我们规定一个有限域Fp

• 取大质数p，则有限域中有p-1个有限元：0，1，2…p-1
• 域元素的加法是整数的模p加法，即若a,b ∈ Fp，则a+b = (a+b) mod p；
• 域元素的乘法是整数的模p乘法，即若a,b ∈ Fp，则a · b = (a · b) mod p
• 域元素的减法是整数的模p减法，即若a,b ∈ Fp，则a - b = (a - b) mod p
• Fp上的除法就是乘除数的乘法逆元a÷b≡c(mod p)，即 a×b^(-1)≡c (mod p)
• Fp的乘法单位元是整数1
• Fp的加法单位元是整数0
• Fp域上满足交换律，结合律，分配律

Implementations

impl FieldElement

pub fn new(x: Fe) -> FieldElement

pub fn from_slice(x: &[u32]) -> FieldElement

pub fn from_number(x: u64) -> FieldElement

pub fn to_bytes_be(&self) -> Vec<u8>

pub fn from_bytes_be(bytes: &[u8]) -> Sm2Result<FieldElement>

pub fn to_biguint(&self) -> BigUint

pub fn from_biguint(bi: &BigUint) -> Sm2Result<FieldElement>

pub fn sqrt(&self) -> Sm2Result<FieldElement>

pub fn to_str_radix(&self, radix: u32) -> String

pub fn zero() -> FieldElement

pub fn one() -> FieldElement

pub fn is_even(&self) -> bool

pub fn is_zero(&self) -> bool

pub fn is_one(&self) -> bool

pub fn square(&self) -> FieldElement

pub fn double(&self) -> FieldElement

pub fn modpow(&self, exponent: &BigUint) -> Self

pub fn modinv(&self) -> FieldElement

Trait Implementations

impl<'a, 'b> Add<&'b FieldElement> for &'a FieldElement

type Output = FieldElement

The resulting type after applying the + operator.

fn add(self, other: &FieldElement) -> FieldElement

Performs the + operation.

impl<'a> Add<&'a FieldElement> for FieldElement

type Output = FieldElement

The resulting type after applying the + operator.

fn add(self, rhs: &FieldElement) -> Self::Output

Performs the + operation.

impl<'a> Add<FieldElement> for &'a FieldElement

type Output = FieldElement

The resulting type after applying the + operator.

fn add(self, other: FieldElement) -> FieldElement

Performs the + operation.

impl Add for FieldElement

type Output = FieldElement

The resulting type after applying the + operator.

fn add(self, other: FieldElement) -> FieldElement

Performs the + operation.

impl Clone for FieldElement

fn clone(&self) -> FieldElement

Returns a duplicate of the value.

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

Performs copy-assignment from source.

impl Debug for FieldElement

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

Formats the value using the given formatter.

impl Default for FieldElement

fn default() -> FieldElement

Returns the “default value” for a type.

impl<'a, 'b> Mul<&'b FieldElement> for &'a FieldElement

type Output = FieldElement

The resulting type after applying the * operator.

fn mul(self, other: &FieldElement) -> FieldElement

Performs the * operation.

impl<'a> Mul<&'a FieldElement> for FieldElement

type Output = FieldElement

The resulting type after applying the * operator.

fn mul(self, rhs: &'a FieldElement) -> Self::Output

Performs the * operation.

impl<'a> Mul<FieldElement> for &'a FieldElement

type Output = FieldElement

The resulting type after applying the * operator.

fn mul(self, other: FieldElement) -> FieldElement

Performs the * operation.

impl Mul for FieldElement

type Output = FieldElement

The resulting type after applying the * operator.

fn mul(self, other: FieldElement) -> FieldElement

Performs the * operation.

impl Ord for FieldElement

fn cmp(&self, other: &FieldElement) -> Ordering

This method returns an Ordering between self and other.

fn max(self, other: Self) -> Self

where Self: Sized,

Compares and returns the maximum of two values.

fn min(self, other: Self) -> Self

where Self: Sized,

Compares and returns the minimum of two values.

fn clamp(self, min: Self, max: Self) -> Self

where Self: Sized,

Restrict a value to a certain interval.

impl PartialEq for FieldElement

fn eq(&self, other: &FieldElement) -> 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 PartialOrd for FieldElement

fn partial_cmp(&self, other: &FieldElement) -> Option<Ordering>

This method returns an ordering between self and other values if one exists.

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

Tests less than (for self and other) and is used by the < operator.

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

Tests less than or equal to (for self and other) and is used by the <= operator.

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

Tests greater than (for self and other) and is used by the > operator.

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

Tests greater than or equal to (for self and other) and is used by the >= operator.

impl<'a, 'b> Sub<&'b FieldElement> for &'a FieldElement

type Output = FieldElement

The resulting type after applying the - operator.

fn sub(self, other: &FieldElement) -> FieldElement

Performs the - operation.

impl<'a> Sub<&'a FieldElement> for FieldElement

type Output = FieldElement

The resulting type after applying the - operator.

fn sub(self, rhs: &'a FieldElement) -> Self::Output

Performs the - operation.

impl<'a> Sub<FieldElement> for &'a FieldElement

type Output = FieldElement

The resulting type after applying the - operator.

fn sub(self, other: FieldElement) -> FieldElement

Performs the - operation.

impl Sub for FieldElement

type Output = FieldElement

The resulting type after applying the - operator.

fn sub(self, other: FieldElement) -> FieldElement

Performs the - operation.

impl Copy for FieldElement

impl Eq for FieldElement

impl StructuralPartialEq for FieldElement