shamir
Version:
A JavaScript implementation of Shamir's Secret Sharing algorithm over GF(256).
243 lines (222 loc) • 8.05 kB
JavaScript
/*
* Copyright © 2019 Simon Massey (massey1905@gmail.com)
*
* Licensed under the Apache License, Version 2.0 (the "License");
* you may not use this file except in compliance with the License.
* You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*/
/* eslint-disable no-bitwise */
function add(a, b) {
return a ^ b;
}
exports.add = add;
/* The Laws of Cryptograhy with Java Code by Neal R. Wagner
http://www.cs.utsa.edu/~wagner/lawsbookcolor/laws.pdf
Page 120 (134) section "20.3 Addition in GP(2^n)" is equal \
to subtraction.
*/
const sub = add;
exports.sub = exports.add;
const LOG = new Uint8Array([
0xff, 0x00, 0x19, 0x01, 0x32, 0x02, 0x1a,
0xc6, 0x4b, 0xc7, 0x1b, 0x68, 0x33, 0xee,
0xdf, 0x03, 0x64, 0x04, 0xe0, 0x0e, 0x34,
0x8d, 0x81, 0xef, 0x4c, 0x71, 0x08, 0xc8,
0xf8, 0x69, 0x1c, 0xc1, 0x7d, 0xc2, 0x1d,
0xb5, 0xf9, 0xb9, 0x27, 0x6a, 0x4d, 0xe4,
0xa6, 0x72, 0x9a, 0xc9, 0x09, 0x78, 0x65,
0x2f, 0x8a, 0x05, 0x21, 0x0f, 0xe1, 0x24,
0x12, 0xf0, 0x82, 0x45, 0x35, 0x93, 0xda,
0x8e, 0x96, 0x8f, 0xdb, 0xbd, 0x36, 0xd0,
0xce, 0x94, 0x13, 0x5c, 0xd2, 0xf1, 0x40,
0x46, 0x83, 0x38, 0x66, 0xdd, 0xfd, 0x30,
0xbf, 0x06, 0x8b, 0x62, 0xb3, 0x25, 0xe2,
0x98, 0x22, 0x88, 0x91, 0x10, 0x7e, 0x6e,
0x48, 0xc3, 0xa3, 0xb6, 0x1e, 0x42, 0x3a,
0x6b, 0x28, 0x54, 0xfa, 0x85, 0x3d, 0xba,
0x2b, 0x79, 0x0a, 0x15, 0x9b, 0x9f, 0x5e,
0xca, 0x4e, 0xd4, 0xac, 0xe5, 0xf3, 0x73,
0xa7, 0x57, 0xaf, 0x58, 0xa8, 0x50, 0xf4,
0xea, 0xd6, 0x74, 0x4f, 0xae, 0xe9, 0xd5,
0xe7, 0xe6, 0xad, 0xe8, 0x2c, 0xd7, 0x75,
0x7a, 0xeb, 0x16, 0x0b, 0xf5, 0x59, 0xcb,
0x5f, 0xb0, 0x9c, 0xa9, 0x51, 0xa0, 0x7f,
0x0c, 0xf6, 0x6f, 0x17, 0xc4, 0x49, 0xec,
0xd8, 0x43, 0x1f, 0x2d, 0xa4, 0x76, 0x7b,
0xb7, 0xcc, 0xbb, 0x3e, 0x5a, 0xfb, 0x60,
0xb1, 0x86, 0x3b, 0x52, 0xa1, 0x6c, 0xaa,
0x55, 0x29, 0x9d, 0x97, 0xb2, 0x87, 0x90,
0x61, 0xbe, 0xdc, 0xfc, 0xbc, 0x95, 0xcf,
0xcd, 0x37, 0x3f, 0x5b, 0xd1, 0x53, 0x39,
0x84, 0x3c, 0x41, 0xa2, 0x6d, 0x47, 0x14,
0x2a, 0x9e, 0x5d, 0x56, 0xf2, 0xd3, 0xab,
0x44, 0x11, 0x92, 0xd9, 0x23, 0x20, 0x2e,
0x89, 0xb4, 0x7c, 0xb8, 0x26, 0x77, 0x99,
0xe3, 0xa5, 0x67, 0x4a, 0xed, 0xde, 0xc5,
0x31, 0xfe, 0x18, 0x0d, 0x63, 0x8c, 0x80,
0xc0, 0xf7, 0x70, 0x07,
]);
/* https://crypto.stackexchange.com/a/21174/13860
*/
const EXP = new Uint8Array([
0x01, 0x03, 0x05, 0x0f, 0x11, 0x33, 0x55,
0xff, 0x1a, 0x2e, 0x72, 0x96, 0xa1, 0xf8,
0x13, 0x35, 0x5f, 0xe1, 0x38, 0x48, 0xd8,
0x73, 0x95, 0xa4, 0xf7, 0x02, 0x06, 0x0a,
0x1e, 0x22, 0x66, 0xaa, 0xe5, 0x34, 0x5c,
0xe4, 0x37, 0x59, 0xeb, 0x26, 0x6a, 0xbe,
0xd9, 0x70, 0x90, 0xab, 0xe6, 0x31, 0x53,
0xf5, 0x04, 0x0c, 0x14, 0x3c, 0x44, 0xcc,
0x4f, 0xd1, 0x68, 0xb8, 0xd3, 0x6e, 0xb2,
0xcd, 0x4c, 0xd4, 0x67, 0xa9, 0xe0, 0x3b,
0x4d, 0xd7, 0x62, 0xa6, 0xf1, 0x08, 0x18,
0x28, 0x78, 0x88, 0x83, 0x9e, 0xb9, 0xd0,
0x6b, 0xbd, 0xdc, 0x7f, 0x81, 0x98, 0xb3,
0xce, 0x49, 0xdb, 0x76, 0x9a, 0xb5, 0xc4,
0x57, 0xf9, 0x10, 0x30, 0x50, 0xf0, 0x0b,
0x1d, 0x27, 0x69, 0xbb, 0xd6, 0x61, 0xa3,
0xfe, 0x19, 0x2b, 0x7d, 0x87, 0x92, 0xad,
0xec, 0x2f, 0x71, 0x93, 0xae, 0xe9, 0x20,
0x60, 0xa0, 0xfb, 0x16, 0x3a, 0x4e, 0xd2,
0x6d, 0xb7, 0xc2, 0x5d, 0xe7, 0x32, 0x56,
0xfa, 0x15, 0x3f, 0x41, 0xc3, 0x5e, 0xe2,
0x3d, 0x47, 0xc9, 0x40, 0xc0, 0x5b, 0xed,
0x2c, 0x74, 0x9c, 0xbf, 0xda, 0x75, 0x9f,
0xba, 0xd5, 0x64, 0xac, 0xef, 0x2a, 0x7e,
0x82, 0x9d, 0xbc, 0xdf, 0x7a, 0x8e, 0x89,
0x80, 0x9b, 0xb6, 0xc1, 0x58, 0xe8, 0x23,
0x65, 0xaf, 0xea, 0x25, 0x6f, 0xb1, 0xc8,
0x43, 0xc5, 0x54, 0xfc, 0x1f, 0x21, 0x63,
0xa5, 0xf4, 0x07, 0x09, 0x1b, 0x2d, 0x77,
0x99, 0xb0, 0xcb, 0x46, 0xca, 0x45, 0xcf,
0x4a, 0xde, 0x79, 0x8b, 0x86, 0x91, 0xa8,
0xe3, 0x3e, 0x42, 0xc6, 0x51, 0xf3, 0x0e,
0x12, 0x36, 0x5a, 0xee, 0x29, 0x7b, 0x8d,
0x8c, 0x8f, 0x8a, 0x85, 0x94, 0xa7, 0xf2,
0x0d, 0x17, 0x39, 0x4b, 0xdd, 0x7c, 0x84,
0x97, 0xa2, 0xfd, 0x1c, 0x24, 0x6c, 0xb4,
0xc7, 0x52, 0xf6, 0x01, 0x03, 0x05, 0x0f,
0x11, 0x33, 0x55, 0xff, 0x1a, 0x2e, 0x72,
0x96, 0xa1, 0xf8, 0x13, 0x35, 0x5f, 0xe1,
0x38, 0x48, 0xd8, 0x73, 0x95, 0xa4, 0xf7,
0x02, 0x06, 0x0a, 0x1e, 0x22, 0x66, 0xaa,
0xe5, 0x34, 0x5c, 0xe4, 0x37, 0x59, 0xeb,
0x26, 0x6a, 0xbe, 0xd9, 0x70, 0x90, 0xab,
0xe6, 0x31, 0x53, 0xf5, 0x04, 0x0c, 0x14,
0x3c, 0x44, 0xcc, 0x4f, 0xd1, 0x68, 0xb8,
0xd3, 0x6e, 0xb2, 0xcd, 0x4c, 0xd4, 0x67,
0xa9, 0xe0, 0x3b, 0x4d, 0xd7, 0x62, 0xa6,
0xf1, 0x08, 0x18, 0x28, 0x78, 0x88, 0x83,
0x9e, 0xb9, 0xd0, 0x6b, 0xbd, 0xdc, 0x7f,
0x81, 0x98, 0xb3, 0xce, 0x49, 0xdb, 0x76,
0x9a, 0xb5, 0xc4, 0x57, 0xf9, 0x10, 0x30,
0x50, 0xf0, 0x0b, 0x1d, 0x27, 0x69, 0xbb,
0xd6, 0x61, 0xa3, 0xfe, 0x19, 0x2b, 0x7d,
0x87, 0x92, 0xad, 0xec, 0x2f, 0x71, 0x93,
0xae, 0xe9, 0x20, 0x60, 0xa0, 0xfb, 0x16,
0x3a, 0x4e, 0xd2, 0x6d, 0xb7, 0xc2, 0x5d,
0xe7, 0x32, 0x56, 0xfa, 0x15, 0x3f, 0x41,
0xc3, 0x5e, 0xe2, 0x3d, 0x47, 0xc9, 0x40,
0xc0, 0x5b, 0xed, 0x2c, 0x74, 0x9c, 0xbf,
0xda, 0x75, 0x9f, 0xba, 0xd5, 0x64, 0xac,
0xef, 0x2a, 0x7e, 0x82, 0x9d, 0xbc, 0xdf,
0x7a, 0x8e, 0x89, 0x80, 0x9b, 0xb6, 0xc1,
0x58, 0xe8, 0x23, 0x65, 0xaf, 0xea, 0x25,
0x6f, 0xb1, 0xc8, 0x43, 0xc5, 0x54, 0xfc,
0x1f, 0x21, 0x63, 0xa5, 0xf4, 0x07, 0x09,
0x1b, 0x2d, 0x77, 0x99, 0xb0, 0xcb, 0x46,
0xca, 0x45, 0xcf, 0x4a, 0xde, 0x79, 0x8b,
0x86, 0x91, 0xa8, 0xe3, 0x3e, 0x42, 0xc6,
0x51, 0xf3, 0x0e, 0x12, 0x36, 0x5a, 0xee,
0x29, 0x7b, 0x8d, 0x8c, 0x8f, 0x8a, 0x85,
0x94, 0xa7, 0xf2, 0x0d, 0x17, 0x39, 0x4b,
0xdd, 0x7c, 0x84, 0x97, 0xa2, 0xfd, 0x1c,
0x24, 0x6c, 0xb4, 0xc7, 0x52, 0xf6,
]);
function mul(a, b) {
if (a === 0 || b === 0) {
return 0;
}
return EXP[LOG[a] + LOG[b]];
}
exports.mul = mul;
function div(a, b) {
// multiply by the inverse of b
return mul(a, EXP[255 - LOG[b]]);
}
exports.div = div;
function degree(p) {
// eslint-disable-next-line no-plusplus
for (let i = p.length - 1; i >= 1; i--) {
if (p[i] !== 0) {
return i;
}
}
return 0;
}
exports.degree = degree;
/**
* Calculates f(0) of the given points using Lagrangian interpolation.
* @param {array[Uint8Array]} points The supplied point.
*/
function interpolate(points) {
const x = 0;
let y = 0;
// eslint-disable-next-line no-plusplus
for (let i = 0; i < points.length; i++) {
const aX = points[i][0];
const aY = points[i][1];
let li = 1;
// eslint-disable-next-line no-plusplus
for (let j = 0; j < points.length; j++) {
const bX = points[j][0];
if (i !== j) {
li = mul(li, div(sub(x, bX), sub(aX, bX)));
}
}
y = add(y, mul(li, aY));
}
return y;
}
exports.interpolate = interpolate;
/**
* Generates a random polynomal of the correct degree and sets x as the first coefficient.
* @param {function int -> array[Uint8Array]} randomBytes Takes a length and returns a
* Uint8Array of that length.
* @param {Number} d The degree of the polynomial driven by the number shares and join threshold.
* @param {Number} x The point to hide.
* @return {Uint8Array} The random polynomial with x as the fist coefficient.
*/
function generate(randomBytes, d, x) {
let p = null;
// generate random polynomials until we find one of the given degree
do {
p = randomBytes(d + 1);
} while (degree(p) !== d);
// set y intercept
p[0] = x;
return p;
}
exports.generate = generate;
/**
* Evaluates a polynomal at point x using Horner's method.
* @param {Uint8Array} p The polynomial
* @return {Number} x The point to evaluate.
*/
function evaluate(p, x) {
let result = 0;
// eslint-disable-next-line no-plusplus
for (let i = p.length - 1; i >= 0; i--) {
result = add(mul(result, x), p[i]);
}
return result;
}
exports.eval = evaluate;