https://github.com/trivo25/istar

A composition of algebra finite fields, polynomials and elliptic curves.
https://github.com/trivo25/istar

Last synced: about 1 month ago
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A composition of algebra finite fields, polynomials and elliptic curves.

• Host: GitHub
• URL: https://github.com/trivo25/istar
• Owner: Trivo25
• Created: 2023-05-07T20:33:24.000Z (almost 2 years ago)
• Default Branch: main
• Last Pushed: 2023-10-14T21:01:53.000Z (over 1 year ago)
• Last Synced: 2023-10-15T20:50:37.596Z (over 1 year ago)
• Language: TypeScript
• Size: 3.8 MB
• Stars: 0
• Watchers: 1
• Forks: 0
• Open Issues: 0
• Metadata Files:
  • Readme: README.md

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README

        
## istar

--

Istar is a collection of mathematical primitives such as finite fields or elliptic curves and cryptographic protocols.

### Finite Fields

```ts

// Create a new finite field class with modulus p = 251

class F_251 extends createField(251n) {}

// initiate a finite field element

let a = F_251.from(5n);

a.add(5n).toBigint() === 10n; // true

a.add(251n).toBigint() === 5n; // true

```

### Polynomials over Finite Fields

```ts

// Create a new finite field class with modulus p = 251

class F_251 extends createField(251n) {}

// Create a new polynomial class based on F_251

class P_251 extends createPolynomial(F_251) {}

// initiate a polynomial

let p = P_251.from([F_251.from(12n), F_251.from(2n), F_251.from(1n)]);

```

### Elliptic Curves over Finite Fields

```ts

// Create a new finite field class with modulus p = 251

class F_251 extends createField(251n) {}

// Create a new elliptic curve class over a finite field

class G extends createEllipticCurveGroup(F_251, {

  a: 0n,

  b: 3n,

  g: { x: 1n, y: 2n },

}) {}

```

### Extension fields

```ts

// Create a new finite field class with modulus p = 251

class F_251 extends createField(251n) {}

// Extend the field

let ir = P.from([F.from(2n), F.from(0n), F.from(1n)]);

class Fk extends extend(F, ir.coefficients, 2n) {}

```