Trait FeOperation

pub trait FeOperation {
    // Required methods
    fn mod_add(&self, other: &Self, modulus: &Self) -> Self;
    fn mod_sub(&self, other: &Self, modulus: &Self) -> Self;
    fn mod_mul(&self, other: &Self, modulus: &Self) -> Self;
    fn inv(&self, modulus: &Self) -> Self;
    fn right_shift(&self, carry: u32) -> Self;
}

Fp 的加法，减法，乘法并不是简单的四则运算。其运算结果的值必须在Fp的有限域中，这样保证椭圆曲线变成离散的点

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
• Fp上的加法为模p加法a+b≡c(mod p)
• Fp上的乘法为模p乘法a×b≡c(mod p)
• Fp上的减法为模p减法a-b≡c(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的乘法单位元为1，零元为0
• Fp域上满足交换律，结合律，分配律

Required Methods

fn mod_add(&self, other: &Self, modulus: &Self) -> Self

Returns (self + other) % modulus.

Panics if the modulus is zero.

fn mod_sub(&self, other: &Self, modulus: &Self) -> Self

Returns (self - other) % modulus.

Panics if the modulus is zero.

fn mod_mul(&self, other: &Self, modulus: &Self) -> Self

Returns (self * other) % modulus.

Panics if the modulus is zero.

fn inv(&self, modulus: &Self) -> Self

Extended Eulidean Algorithm(EEA) to calculate x^(-1) mod p

fn right_shift(&self, carry: u32) -> Self

Self >>= carry

Dyn Compatibility

This trait is not dyn compatible.

In older versions of Rust, dyn compatibility was called "object safety", so this trait is not object safe.

Implementations on Foreign Types

impl FeOperation for BigUint

fn mod_add(&self, other: &Self, modulus: &Self) -> BigUint

fn mod_sub(&self, other: &Self, modulus: &Self) -> BigUint

fn mod_mul(&self, other: &Self, modulus: &Self) -> BigUint

fn inv(&self, modulus: &Self) -> BigUint

fn right_shift(&self, carry: u32) -> BigUint

Implementors

impl FeOperation for Fe