shamir-secret-sharing/src/index.ts

Simple, independently audited, zero-dependency TypeScript implementation of Shamir's Secret Sharing algorithm

import {getRandomBytes} from 'shamir-secret-sharing/csprng';

// The Polynomial used is: x⁸ + x⁴ + x³ + x + 1
//
// Lookup tables pulled from:
//
//     * https://github.com/hashicorp/vault/blob/9d46671659cbfe7bbd3e78d1073dfb22936a4437/shamir/tables.go
//     * http://www.samiam.org/galois.html
//
// 0xe5 (229) is used as the generator.

// Provides log(X)/log(g) at each index X.
const LOG_TABLE: Readonly<Uint8Array> = new Uint8Array([
  0x00, 0xff, 0xc8, 0x08, 0x91, 0x10, 0xd0, 0x36, 0x5a, 0x3e, 0xd8, 0x43, 0x99, 0x77, 0xfe, 0x18,
  0x23, 0x20, 0x07, 0x70, 0xa1, 0x6c, 0x0c, 0x7f, 0x62, 0x8b, 0x40, 0x46, 0xc7, 0x4b, 0xe0, 0x0e,
  0xeb, 0x16, 0xe8, 0xad, 0xcf, 0xcd, 0x39, 0x53, 0x6a, 0x27, 0x35, 0x93, 0xd4, 0x4e, 0x48, 0xc3,
  0x2b, 0x79, 0x54, 0x28, 0x09, 0x78, 0x0f, 0x21, 0x90, 0x87, 0x14, 0x2a, 0xa9, 0x9c, 0xd6, 0x74,
  0xb4, 0x7c, 0xde, 0xed, 0xb1, 0x86, 0x76, 0xa4, 0x98, 0xe2, 0x96, 0x8f, 0x02, 0x32, 0x1c, 0xc1,
  0x33, 0xee, 0xef, 0x81, 0xfd, 0x30, 0x5c, 0x13, 0x9d, 0x29, 0x17, 0xc4, 0x11, 0x44, 0x8c, 0x80,
  0xf3, 0x73, 0x42, 0x1e, 0x1d, 0xb5, 0xf0, 0x12, 0xd1, 0x5b, 0x41, 0xa2, 0xd7, 0x2c, 0xe9, 0xd5,
  0x59, 0xcb, 0x50, 0xa8, 0xdc, 0xfc, 0xf2, 0x56, 0x72, 0xa6, 0x65, 0x2f, 0x9f, 0x9b, 0x3d, 0xba,
  0x7d, 0xc2, 0x45, 0x82, 0xa7, 0x57, 0xb6, 0xa3, 0x7a, 0x75, 0x4f, 0xae, 0x3f, 0x37, 0x6d, 0x47,
  0x61, 0xbe, 0xab, 0xd3, 0x5f, 0xb0, 0x58, 0xaf, 0xca, 0x5e, 0xfa, 0x85, 0xe4, 0x4d, 0x8a, 0x05,
  0xfb, 0x60, 0xb7, 0x7b, 0xb8, 0x26, 0x4a, 0x67, 0xc6, 0x1a, 0xf8, 0x69, 0x25, 0xb3, 0xdb, 0xbd,
  0x66, 0xdd, 0xf1, 0xd2, 0xdf, 0x03, 0x8d, 0x34, 0xd9, 0x92, 0x0d, 0x63, 0x55, 0xaa, 0x49, 0xec,
  0xbc, 0x95, 0x3c, 0x84, 0x0b, 0xf5, 0xe6, 0xe7, 0xe5, 0xac, 0x7e, 0x6e, 0xb9, 0xf9, 0xda, 0x8e,
  0x9a, 0xc9, 0x24, 0xe1, 0x0a, 0x15, 0x6b, 0x3a, 0xa0, 0x51, 0xf4, 0xea, 0xb2, 0x97, 0x9e, 0x5d,
  0x22, 0x88, 0x94, 0xce, 0x19, 0x01, 0x71, 0x4c, 0xa5, 0xe3, 0xc5, 0x31, 0xbb, 0xcc, 0x1f, 0x2d,
  0x3b, 0x52, 0x6f, 0xf6, 0x2e, 0x89, 0xf7, 0xc0, 0x68, 0x1b, 0x64, 0x04, 0x06, 0xbf, 0x83, 0x38,
]);

// Provides the exponentiation value at each index X.
const EXP_TABLE: Readonly<Uint8Array> = new Uint8Array([
  0x01, 0xe5, 0x4c, 0xb5, 0xfb, 0x9f, 0xfc, 0x12, 0x03, 0x34, 0xd4, 0xc4, 0x16, 0xba, 0x1f, 0x36,
  0x05, 0x5c, 0x67, 0x57, 0x3a, 0xd5, 0x21, 0x5a, 0x0f, 0xe4, 0xa9, 0xf9, 0x4e, 0x64, 0x63, 0xee,
  0x11, 0x37, 0xe0, 0x10, 0xd2, 0xac, 0xa5, 0x29, 0x33, 0x59, 0x3b, 0x30, 0x6d, 0xef, 0xf4, 0x7b,
  0x55, 0xeb, 0x4d, 0x50, 0xb7, 0x2a, 0x07, 0x8d, 0xff, 0x26, 0xd7, 0xf0, 0xc2, 0x7e, 0x09, 0x8c,
  0x1a, 0x6a, 0x62, 0x0b, 0x5d, 0x82, 0x1b, 0x8f, 0x2e, 0xbe, 0xa6, 0x1d, 0xe7, 0x9d, 0x2d, 0x8a,
  0x72, 0xd9, 0xf1, 0x27, 0x32, 0xbc, 0x77, 0x85, 0x96, 0x70, 0x08, 0x69, 0x56, 0xdf, 0x99, 0x94,
  0xa1, 0x90, 0x18, 0xbb, 0xfa, 0x7a, 0xb0, 0xa7, 0xf8, 0xab, 0x28, 0xd6, 0x15, 0x8e, 0xcb, 0xf2,
  0x13, 0xe6, 0x78, 0x61, 0x3f, 0x89, 0x46, 0x0d, 0x35, 0x31, 0x88, 0xa3, 0x41, 0x80, 0xca, 0x17,
  0x5f, 0x53, 0x83, 0xfe, 0xc3, 0x9b, 0x45, 0x39, 0xe1, 0xf5, 0x9e, 0x19, 0x5e, 0xb6, 0xcf, 0x4b,
  0x38, 0x04, 0xb9, 0x2b, 0xe2, 0xc1, 0x4a, 0xdd, 0x48, 0x0c, 0xd0, 0x7d, 0x3d, 0x58, 0xde, 0x7c,
  0xd8, 0x14, 0x6b, 0x87, 0x47, 0xe8, 0x79, 0x84, 0x73, 0x3c, 0xbd, 0x92, 0xc9, 0x23, 0x8b, 0x97,
  0x95, 0x44, 0xdc, 0xad, 0x40, 0x65, 0x86, 0xa2, 0xa4, 0xcc, 0x7f, 0xec, 0xc0, 0xaf, 0x91, 0xfd,
  0xf7, 0x4f, 0x81, 0x2f, 0x5b, 0xea, 0xa8, 0x1c, 0x02, 0xd1, 0x98, 0x71, 0xed, 0x25, 0xe3, 0x24,
  0x06, 0x68, 0xb3, 0x93, 0x2c, 0x6f, 0x3e, 0x6c, 0x0a, 0xb8, 0xce, 0xae, 0x74, 0xb1, 0x42, 0xb4,
  0x1e, 0xd3, 0x49, 0xe9, 0x9c, 0xc8, 0xc6, 0xc7, 0x22, 0x6e, 0xdb, 0x20, 0xbf, 0x43, 0x51, 0x52,
  0x66, 0xb2, 0x76, 0x60, 0xda, 0xc5, 0xf3, 0xf6, 0xaa, 0xcd, 0x9a, 0xa0, 0x75, 0x54, 0x0e, 0x01,
]);

// Combines two numbers in GF(2^8).
// This can be used for both addition and subtraction.
function add(a: number, b: number): number {
  if (!Number.isInteger(a) || a < 0 || a > 255) {
    throw new RangeError('Number is out of Uint8 range');
  }
  if (!Number.isInteger(b) || b < 0 || b > 255) {
    throw new RangeError('Number is out of Uint8 range');
  }
  return a ^ b;
}

// Divides two numbers in GF(2^8).
function div(a: number, b: number): number {
  if (!Number.isInteger(a) || a < 0 || a > 255) {
    throw new RangeError('Number is out of Uint8 range');
  }
  if (!Number.isInteger(b) || b < 0 || b > 255) {
    throw new RangeError('Number is out of Uint8 range');
  }
  // This should never happen
  if (b === 0) {
    throw new Error('cannot divide by zero');
  }

  const logA = LOG_TABLE[a]!;
  const logB = LOG_TABLE[b]!;
  const diff = (logA - logB + 255) % 255;
  const result = EXP_TABLE[diff]!;

  return a === 0 ? 0 : result;
}

// Multiplies two numbers in GF(2^8).
function mult(a: number, b: number): number {
  if (!Number.isInteger(a) || a < 0 || a > 255) {
    throw new RangeError('Number is out of Uint8 range');
  }
  if (!Number.isInteger(b) || b < 0 || b > 255) {
    throw new RangeError('Number is out of Uint8 range');
  }
  const logA = LOG_TABLE[a]!;
  const logB = LOG_TABLE[b]!;
  const sum = (logA + logB) % 255;
  const result = EXP_TABLE[sum]!;

  return a === 0 || b === 0 ? 0 : result;
}

// Takes N sample points and returns the value at a given x using a lagrange interpolation.
function interpolatePolynomial(xSamples: Uint8Array, ySamples: Uint8Array, x: number): number {
  if (xSamples.length !== ySamples.length) {
    throw new Error('sample length mistmatch');
  }

  const limit = xSamples.length;

  let basis = 0;
  let result = 0;

  for (let i = 0; i < limit; i++) {
    basis = 1;

    for (let j = 0; j < limit; ++j) {
      if (i === j) {
        continue;
      }
      const num = add(x, xSamples[j]!);
      const denom = add(xSamples[i]!, xSamples[j]!);
      const term = div(num, denom);
      basis = mult(basis, term);
    }

    result = add(result, mult(ySamples[i]!, basis));
  }

  return result;
}

// Evaluates a polynomial with the given x using Horner's method.
function evaluate(coefficients: Uint8Array, x: number, degree: number) {
  if (x === 0) {
    throw new Error('cannot evaluate secret polynomial at zero');
  }

  let result = coefficients[degree]!;

  for (let i = degree - 1; i >= 0; i--) {
    const coefficient = coefficients[i]!;
    result = add(mult(result, x), coefficient);
  }

  return result;
}

// Creates a pseudo-random set of coefficients for a polynomial.
function newCoefficients(intercept: number, degree: number): Readonly<Uint8Array> {
  const coefficients = new Uint8Array(degree + 1);
  coefficients[0] = intercept;
  coefficients.set(getRandomBytes(degree), 1);
  return coefficients;
}

// Creates a set of values from [1, 256).
// Returns a psuedo-random shuffling of the set.
function newCoordinates(): Readonly<Uint8Array> {
  const coordinates = new Uint8Array(255);
  for (let i = 0; i < 255; i++) {
    coordinates[i] = i + 1;
  }

  // Pseudo-randomize the array of coordinates.
  //
  // This impl maps almost perfectly because both of the lists (coordinates and randomIndices)
  // have a length of 255 and byte values are between 0 and 255 inclusive. The only value that
  // does not map neatly here is if the random byte is 255, since that value used as an index
  // would be out of bounds. Thus, for bytes whose value is 255, wrap around to 0.
  //
  // WARNING: This shuffle is biased and should NOT be used if an unbiased shuffle is required.
  //
  // However, Shamir-based secret sharing does not require any particular indexing (shuffled or
  // not) for its security properties to hold; this means including the biased shuffle is not
  // itself problematic here.
  const randomIndices = getRandomBytes(255);
  for (let i = 0; i < 255; i++) {
    const j = randomIndices[i]! % 255; // Make sure to handle the case where the byte is 255.
    const temp = coordinates[i]!;
    coordinates[i] = coordinates[j]!;
    coordinates[j] = temp;
  }

  return coordinates;
}

// Helpers for declarative argument validation.
const AssertArgument = {
  instanceOf(object: any, constructor: Function, message: string) {
    if (object.constructor !== constructor) {
      throw new TypeError(message);
    }
  },

  inRange(n: number, start: number, until: number, message: string) {
    if (!(start < until && n >= start && n < until)) {
      throw new RangeError(message);
    }
  },

  greaterThanOrEqualTo(a: number, b: number, message: string) {
    if (a < b) {
      throw new Error(message);
    }
  },

  equalTo(a: any, b: any, message: string) {
    if (a !== b) {
      throw new Error(message);
    }
  },
};

/**
 * Splits a `secret` into `shares` number of shares, requiring `threshold` of them to reconstruct `secret`.
 *
 * @param secret The secret value to split into shares.
 * @param shares The total number of shares to split `secret` into. Must be at least 2 and at most 255.
 * @param threshold The minimum number of shares required to reconstruct `secret`. Must be at least 2 and at most 255.
 * @returns A list of `shares` shares.
 */
export async function split(
  secret: Uint8Array,
  shares: number,
  threshold: number,
): Promise<Uint8Array[]> {
  // secret must be a non-empty Uint8Array
  AssertArgument.instanceOf(secret, Uint8Array, 'secret must be a Uint8Array');
  AssertArgument.greaterThanOrEqualTo(secret.byteLength, 1, 'secret cannot be empty');

  // shares must be a number in the range [2, 256)
  AssertArgument.instanceOf(shares, Number, 'shares must be a number');
  AssertArgument.inRange(shares, 2, 256, 'shares must be at least 2 and at most 255');

  // threshold must be a number in the range [2, 256)
  AssertArgument.instanceOf(threshold, Number, 'threshold must be a number');
  AssertArgument.inRange(threshold, 2, 256, 'threshold must be at least 2 and at most 255');

  // total number of shares must be greater than or equal to the required threshold
  AssertArgument.greaterThanOrEqualTo(shares, threshold, 'shares cannot be less than threshold');

  const result: Uint8Array[] = [];
  const secretLength = secret.byteLength;
  const xCoordinates = newCoordinates();

  for (let i = 0; i < shares; i++) {
    const share = new Uint8Array(secretLength + 1);
    share[secretLength] = xCoordinates[i]!;
    result.push(share);
  }

  const degree = threshold - 1;

  for (let i = 0; i < secretLength; i++) {
    const byte = secret[i]!;
    const coefficients = newCoefficients(byte, degree);

    for (let j = 0; j < shares; ++j) {
      const x = xCoordinates[j]!;
      const y = evaluate(coefficients, x, degree);
      result[j]![i] = y;
    }
  }

  return result;
}

/**
 * Combines `shares` to reconstruct the secret.
 *
 * @param shares A list of shares to reconstruct the secret from. Must be at least 2 and at most 255.
 * @returns The reconstructed secret.
 */
export async function combine(shares: Uint8Array[]): Promise<Uint8Array> {
  // Shares must be an array with length in the range [2, 256)
  AssertArgument.instanceOf(shares, Array, 'shares must be an Array');
  AssertArgument.inRange(
    shares.length,
    2,
    256,
    'shares must have at least 2 and at most 255 elements',
  );

  // Shares must be a Uint8Array with at least 2 bytes and all shares must have the same byte length.
  const share1 = shares[0]!;
  AssertArgument.instanceOf(share1, Uint8Array, 'each share must be a Uint8Array');
  for (const share of shares) {
    AssertArgument.instanceOf(share, Uint8Array, 'each share must be a Uint8Array');
    AssertArgument.greaterThanOrEqualTo(share.byteLength, 2, 'each share must be at least 2 bytes');
    AssertArgument.equalTo(
      share.byteLength,
      share1.byteLength,
      'all shares must have the same byte length',
    );
  }

  const sharesLength = shares.length;
  const shareLength = share1.byteLength;

  // This will be our reconstructed secret
  const secretLength = shareLength - 1;
  const secret = new Uint8Array(secretLength);

  const xSamples = new Uint8Array(sharesLength);
  const ySamples = new Uint8Array(sharesLength);

  const samples: Set<number> = new Set();
  for (let i = 0; i < sharesLength; i++) {
    const share = shares[i]!;
    const sample = share[shareLength - 1]!;

    // The last byte of each share should be a unique value between 1-255 inclusive.
    if (samples.has(sample)) {
      throw new Error('shares must contain unique values but a duplicate was found');
    }

    samples.add(sample);
    xSamples[i] = sample;
  }

  // Reconstruct each byte
  for (let i = 0; i < secretLength; i++) {
    // Set the y value for each sample
    for (let j = 0; j < sharesLength; ++j) {
      ySamples[j] = shares[j]![i]!;
    }

    // Interpolate the polynomial and compute the value at 0
    secret[i] = interpolatePolynomial(xSamples, ySamples, 0);
  }

  return secret;
}