SHA256
為單向加密HASH，不可逆
範例:
var crypto = require('crypto');
let msg = 'test';
var hash = crypto.createHash('sha256').update(msg).digest('base64');
console.log(hash);原理:
#第一步:
把msg轉為二進位的數字msgBit，之後後面先放一個數字1然後pad補k個0 直到msgBit.length + 1 + k % 512 = 448然後最後面再加上64bits的數字，內容為msg的長度(以二進位表示) ex:abc之ASCII二進位長度為24，
所以轉為64bit二進位顯示為0....11000
(以ABC為例子)
#第二步:
寫出八個initial hash value(此為固定值)
原理:
python: hex(int(math.modf(math.sqrt(2))[0]*(1<<32)))
js: 先取math.sqrt(2)的小數，然後乘上2**32，之後轉為16進位，然後取小數前面部分 ex:(0.4142135623730951*(2**32)).toString(16)
H(0)
1 = 6a09e667
H(0)
2 = bb67ae85
先進入到python命令列，然後輸入import math
hex(int(math.modf(math.sqrt(3))[0]*(1<<32)))
H(0)
3 = 3c6ef372
hex(int(math.modf(math.sqrt(5))[0]*(1<<32)))
H(0)
4 = a54ff53a
hex(int(math.modf(math.sqrt(7))[0]*(1<<32)))
H(0)
5 = 510e527f
hex(int(math.modf(math.sqrt(11))[0]*(1<<32)))
H(0)
6 = 9b05688c
hex(int(math.modf(math.sqrt(13))[0]*(1<<32)))
H(0)
7 = 1f83d9ab
hex(int(math.modf(math.sqrt(17))[0]*(1<<32)))
H(0)
8 = 5be0cd19
hex(int(math.modf(math.sqrt(19))[0]*(1<<32)))
之後可以發現上面八個initial number中math.sqrt()都是取首八個質數附註:1<<32在python和js行為會不同，可參考https://stackoverflow.com/questions/45024682/different-behavior-for-1-32-compare-javascript-to-python
#第三步
64個固定k值
原理: 用math cube root的方法找首64個質數
以下用Python為例:
(先定義cube方法，意思即為開三次方根，js可直接用Math.cbrt())
def cube(x):
if 0<=x: return x**(1./3.)
return -(-x)**(1./3.)
-------------------------------------------------------------
hex(int(math.modf(cube(2))[0]*(1<<32))) //0x428a2f98
hex(int(math.modf(cube(3))[0]*(1<<32))) //0x71374491
...#第四步:
使用sha256定義的六個hash function
其中符號定義如下
寫成程式為:
function ch (x, y, z) {
return z ^ (x & (y ^ z))
}
function maj (x, y, z) {
return (x & y) | (z & (x | y))
}
function sigma0 (x) {
return (x >>> 2 | x << 30) ^ (x >>> 13 | x << 19) ^ (x >>> 22 | x << 10)
}
function sigma1 (x) {
return (x >>> 6 | x << 26) ^ (x >>> 11 | x << 21) ^ (x >>> 25 | x << 7)
}
function gamma0 (x) {
return (x >>> 7 | x << 25) ^ (x >>> 18 | x << 14) ^ (x >>> 3)
}
function gamma1 (x) {
return (x >>> 17 | x << 15) ^ (x >>> 19 | x << 13) ^ (x >>> 10)
}#完整範例
const util = require('util');
var bigInt = require("big-integer");
function Hash (blockSize, finalSize) {
this._block = new Buffer(blockSize)
this._finalSize = finalSize
this._blockSize = blockSize
this._len = 0
}
Hash.prototype.digest = function (data, enc) {
data = (data).toString();
//////////////////
let s = ""
let s1 = ""
//將字串轉為二進位ASCII
function ascii (a) {
let dd = "";
for(let i = 0 ; i< a.length; i++) {
let charAscII = a.charAt(i).charCodeAt(0).toString(2)
while(charAscII.length < 8) { //最前面的0都會被省略，所以手動加上
charAscII = 0 + charAscII
}
dd += charAscII;
}
return dd
}
let msgLengthToBinary = ((ascii(data).length).toString(2).length); //計算訊息有幾個字元再轉為二進位數字的長度
let BinarymsgLength = (ascii(data).length); //訊息的二進位的長度
for(i = 0; i < 448 - 1 - BinarymsgLength; i++) {s += 0} //前面補448bit 0
for(i = 0; i < 64 - msgLengthToBinary ; i++) {s1 += 0} //後面補64 bit 0
let msgLength = ascii(data).length;
let frontPad = ascii(data) + 1 + s + s1 + (ascii(data).length).toString(2);
let c0 = bigInt(bin2dec(frontPad)).toString(16); //涉及大數轉進位(MAX_SAFE_INTEGER)
let initPadedValue = c0.substring(0, c0.length - 2) + msgLength.toString(16); //因為太大的數parseInt並轉二進位後面的數字會被省略掉，所以把它加上
let initPadedValueBuffer = Buffer.from(initPadedValue, 'hex');
this._update(initPadedValueBuffer) //傳入一開始pad好之buffer進行main loop hash function
var hash = this._hash() //拼接main loop好的a-h八個區塊
return enc ? hash.toString(enc) : hash //轉為16進位
}
function bin2dec(str){ //大數二進位在用parseInt轉十進位時後面常被省略，所以用此方法
var dec = str.toString().split(''), sum = [], hex = [], i, s
while(dec.length){
s = 1 * dec.shift()
for(i = 0; s || i < sum.length; i++){
s += (sum[i] || 0) * 2
sum[i] = s % 10
s = (s - sum[i]) / 10
}
}
while(sum.length){
hex.push(sum.pop().toString(10))
}
return hex.join('')
}
var K = [
0x428A2F98, 0x71374491, 0xB5C0FBCF, 0xE9B5DBA5,
0x3956C25B, 0x59F111F1, 0x923F82A4, 0xAB1C5ED5,
0xD807AA98, 0x12835B01, 0x243185BE, 0x550C7DC3,
0x72BE5D74, 0x80DEB1FE, 0x9BDC06A7, 0xC19BF174,
0xE49B69C1, 0xEFBE4786, 0x0FC19DC6, 0x240CA1CC,
0x2DE92C6F, 0x4A7484AA, 0x5CB0A9DC, 0x76F988DA,
0x983E5152, 0xA831C66D, 0xB00327C8, 0xBF597FC7,
0xC6E00BF3, 0xD5A79147, 0x06CA6351, 0x14292967,
0x27B70A85, 0x2E1B2138, 0x4D2C6DFC, 0x53380D13,
0x650A7354, 0x766A0ABB, 0x81C2C92E, 0x92722C85,
0xA2BFE8A1, 0xA81A664B, 0xC24B8B70, 0xC76C51A3,
0xD192E819, 0xD6990624, 0xF40E3585, 0x106AA070,
0x19A4C116, 0x1E376C08, 0x2748774C, 0x34B0BCB5,
0x391C0CB3, 0x4ED8AA4A, 0x5B9CCA4F, 0x682E6FF3,
0x748F82EE, 0x78A5636F, 0x84C87814, 0x8CC70208,
0x90BEFFFA, 0xA4506CEB, 0xBEF9A3F7, 0xC67178F2
]
var W = new Array(64)
function Sha256 () {
this.init()
this._w = W // new Array(64)
Hash.call(this, 64, 56)
}
util.inherits(Sha256, Hash)
Sha256.prototype.init = function () {
this._a = 0x6a09e667
this._b = 0xbb67ae85
this._c = 0x3c6ef372
this._d = 0xa54ff53a
this._e = 0x510e527f
this._f = 0x9b05688c
this._g = 0x1f83d9ab
this._h = 0x5be0cd19
return this
}
function ch (x, y, z) {
return z ^ (x & (y ^ z))
}
function maj (x, y, z) {
return (x & y) | (z & (x | y))
}
function sigma0 (x) {
return (x >>> 2 | x << 30) ^ (x >>> 13 | x << 19) ^ (x >>> 22 | x << 10)
}
function sigma1 (x) {
return (x >>> 6 | x << 26) ^ (x >>> 11 | x << 21) ^ (x >>> 25 | x << 7)
}
function gamma0 (x) {
return (x >>> 7 | x << 25) ^ (x >>> 18 | x << 14) ^ (x >>> 3)
}
function gamma1 (x) {
return (x >>> 17 | x << 15) ^ (x >>> 19 | x << 13) ^ (x >>> 10)
}
Sha256.prototype._update = function (M) {
var W = this._w
var a = this._a | 0
var b = this._b | 0
var c = this._c | 0
var d = this._d | 0
var e = this._e | 0
var f = this._f | 0
var g = this._g | 0
var h = this._h | 0
for (var i = 0; i < 16; ++i) W[i] = M.readInt32BE(i * 4)
for (; i < 64; ++i) W[i] = (gamma1(W[i - 2]) + W[i - 7] + gamma0(W[i - 15]) + W[i - 16]) | 0
for (var j = 0; j < 64; ++j) {
var T1 = (h + sigma1(e) + ch(e, f, g) + K[j] + W[j]) | 0
var T2 = (sigma0(a) + maj(a, b, c)) | 0
h = g
g = f
f = e
e = (d + T1) | 0
d = c
c = b
b = a
a = (T1 + T2) | 0
}
this._a = (a + this._a) | 0
this._b = (b + this._b) | 0
this._c = (c + this._c) | 0
this._d = (d + this._d) | 0
this._e = (e + this._e) | 0
this._f = (f + this._f) | 0
this._g = (g + this._g) | 0
this._h = (h + this._h) | 0
}
Sha256.prototype._hash = function () {
var H = new Buffer(32)
H.writeInt32BE(this._a, 0)
H.writeInt32BE(this._b, 4)
H.writeInt32BE(this._c, 8)
H.writeInt32BE(this._d, 12)
H.writeInt32BE(this._e, 16)
H.writeInt32BE(this._f, 20)
H.writeInt32BE(this._g, 24)
H.writeInt32BE(this._h, 28)
return H
}
//範例:
let hashString = new Sha256().digest('1234567','hex');
console.log(hashString)也可用Node.js的crypto模組
var crypto = require('crypto');
let a = crypto.createHash('sha256').update('1234567').digest()
console.log(a.toString('hex'))Reference:
https://github.com/peterolson/BigInteger.js(大數轉換無法用在parseInt，toString())
http://www.danvk.org/hex2dec.html
https://stackoverflow.com/questions/18626844/convert-a-large-integer-to-a-hex-string-in-javascript (其解答dec2hex在數字更大時還是無法解決問題，但可做為參考)
Python內建BigInteger所以如用Python則不會有問題
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