结构

工作空间组织如下

• src/curves/: 包含椭圆曲线和曲线上的点的实现。
• src/galois_field/: 包含伽罗瓦域的实现，用于椭圆曲线运算。
• src/mod_math/: 包含模运算函数。
• src/num_mod/: 包含对某些模数的数字实现。

用法

首先，将以下内容添加到您的Cargo.toml

[dependencies]
modular_math = "0.1.6"

ModMath

use modular_math::ModMath;
use primitive_types::U256;

let modulus = "101";
let mod_math = ModMath::new(modulus);

// Addition
let sum = mod_math.add(8, 12);
assert_eq!(sum, U256::from(3));

// Subtraction
let sub = mod_math.sub(8, 12);
assert_eq!(sub, U256::from(97));

// Multiplication
let mul = mod_math.mul(8, 12);
assert_eq!(mul, U256::from(96));

// Multiplicative Inverse
let inv = mod_math.inv(8);
assert_eq!(inv, U256::from(77));

// Exponentiation
let exp = mod_math.exp(8, 12);
assert_eq!(exp, U256::from(64));

// FromStr
let mod_math = ModMath::new("115792089237316195423570985008687907852837564279074904382605163141518161494337");
let div = mod_math.div("32670510020758816978083085130507043184471273380659243275938904335757337482424" , "55066263022277343669578718895168534326250603453777594175500187360389116729240");
assert_eq!(div, U256::from_dec_str("13499648161236477938760301359943791721062504425530739546045302818736391397630"));

椭圆曲线

创建椭圆曲线

use primitive_types::U256;
use modular_math::elliptical_curve::{Curve, ECPoint};

fn BN128() -> Curve {
  let a = U256::zero();
  let b = U256::from(3);
  let field_modulus = U256::from_dec_str("21888242871839275222246405745257275088696311157297823662689037894645226208583").unwrap();
  let curve_order = U256::from_dec_str("21888242871839275222246405745257275088548364400416034343698204186575808495617").unwrap();
  let G = ECPoint::new(U256::from(1), U256::from(2));
  
  let bn128 = Curve::new(a, b, field_modulus, curve_order, G);

  bn128
}

BN128用法

use modular_math::curves::BN128;
use primitive_types::U256;

let bn128 = BN128();
let G = bn128.G;

// Scalar Multiplication
let double_G = bn128.point_multiplication_scalar(2, &G);

// Point Addition
let triple_G = bn128.point_addition(&double_G, &G);

// Point Doubling
let quad_G = bn128.point_doubling(&double_G);

模数下的数字

use modular_math::number_mod::NumberUnderMod as NM;
use primitive_types::U256;
use modular_math::num_mod;

// Add
let a = num_mod!(10, 13);
let b = num_mod!(6, 13);
let sum = a + b;
assert_eq!(sum, U256::from(3));

// Sub
let sub = a - b;
assert_eq!(sub, U256::from(4));

// Mul
let mul = a * b;
assert_eq!(mul, U256::from(8));

// Div
let div = a / b;
assert_eq!(div, U256::from(11));

// Neg
let neg = -a;
assert_eq!(neg, U256::from(3));

let c = num_mod!(10, 13);
assert!(a == c);

待办事项

• 模数下的平方根
• 加法逆元
• 大数字测试
• 椭圆曲线
• 伽罗瓦域
• 双线性配对

许可证

本项目采用MIT许可协议 - 有关详细信息，请参阅LICENSE文件。