import { Curve } from './curve';
/**
 * Get the modular result of an operation.
 *
 * @param {Curve} curve
 * @param {bigint} n
 * @return {bigint}
 */
export declare const mod: (curve: Curve | bigint, n: bigint) => bigint;
/**
 * Returns the greatest common divisor of a and b.
 *
 * @param {bigint} a
 * @param {bigint} b
 * @return {{ g: bigint, x: bigint, y: bigint }}
 */
export declare const eGcd: (a: bigint, b: bigint) => {
    g: bigint;
    x: bigint;
    y: bigint;
};
/**
 * Get the ring of integers modulo n.
 *
 * @param {bigint} a
 * @param {bigint} n
 * @return {bigint}
 */
export declare const toZn: (a: bigint, n: bigint) => bigint;
/**
 * Returns the modular inverse.
 *
 * @param {bigint} a
 * @param {bigint} modulo
 */
export declare const modInverse: (a: bigint, modulo: bigint) => bigint;
/**
 * a + b
 *
 * @param {Curve} curve
 * @param {bigint} a
 * @param {bigint} b
 * @return {bigint}
 */
export declare const add: (curve: Curve, a: bigint, b: bigint) => bigint;
/**
 * a - b
 *
 * @param {Curve} curve
 * @param {bigint} a
 * @param {bigint} b
 * @return {bigint}
 */
export declare const subtract: (curve: Curve, a: bigint, b: bigint) => bigint;
/**
 * a * b
 *
 * @param {Curve} curve
 * @param {bigint} a
 * @param {bigint} b
 * @return {bigint}
 */
export declare const multiply: (curve: Curve, a: bigint, b: bigint) => bigint;
/**
 * a / b
 *
 * @param {Curve} curve
 * @param {bigint} a
 * @param {bigint} b
 * @return {bigint}
 */
export declare const divide: (curve: Curve, a: bigint, b: bigint) => bigint;
/**
 * a ^ b
 *
 * @param {Curve} curve
 * @param {bigint} a
 * @param {bigint} b
 * @return {bigint}
 */
export declare const power: (curve: Curve, a: bigint, b: bigint) => bigint;
/**
 * Get the square roots from a y² value on the curve.
 *
 * @param {Curve} curve
 * @param {bigint} value
 * @return {[bigint, bigint]}
 */
export declare const squareRoots: (curve: Curve, value: bigint) => [bigint, bigint];
export declare const random: (curve: Curve) => bigint;