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‎1.2 密碼雜湊.md

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@@ -12,7 +12,7 @@ hash的過程會加入一個隨機的salt，然後salt跟password一起hash。
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以下為在2GHz core上的耗費時間表：
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![](blob:https://legacy.gitbook.com/78af164f-81c6-4ae3-b0f8-48c70df5cb18)
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![](https://easonwang01.gitbooks.io/blockchain-and-cryptography/content/assets/螢幕快照 2018-01-28 下午12.06.21.png)
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再來你可能會想既然每次產生的Hash不同，那要怎麼進行訊息驗證呢？
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‎1.3 SHA原理.md

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# SHA-256實作原理
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### 第一步:
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```
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1.把明文轉為二進位的數字bits
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2.在最後面先放一個數字1
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3.在最後面補 k 個 0 直到明文bits的長度 + 1 + k % 512 = 448
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```
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做完上述三點後，在最後面再加上 64 bits的數字，內容為明文的長度\(以二進位表示\) ，例如：abc之ASCII二進位長度為24 bits
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而 24 之二進位為11000，因為不足 64 bit 於是在前面補0使其成為：`00....11000`，補足64 bits。
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> 以下為 8-bit 之 ASCII 字母：abc 之例子。對照下圖的第一個 8 bits： `01100001` 對應到 `a`，可參照ASCII Table。
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![](https://easonwang01.gitbooks.io/blockchain-and-cryptography/content/assets/螢幕快照 2018-02-01 上午9.01.01.png)
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### 第二步:
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寫出八個 initial hash value（此為被預先定義之固定值）
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#### ![](https://easonwang01.gitbooks.io/blockchain-and-cryptography/content/assets/螢幕快照 2018-02-01 上午9.05.43.png)
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##### 原理：
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```js
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先取Math.sqrt(n)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
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其中math.sqrt(n)，n為從0往上找到的最小八個質數。
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H(0)
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1 = 6a09e667
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(Math.sqrt(2) % 1 * (2**32)).toString(16).substring(0,8)
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H(0)
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2 = bb67ae85
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(Math.sqrt(3) % 1 * (2**32)).toString(16).substring(0,8)
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H(0)
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3 = 3c6ef372
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(Math.sqrt(5) % 1 * (2**32)).toString(16).substring(0,8)
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H(0)
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4 = a54ff53a
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(Math.sqrt(7) % 1 * (2**32)).toString(16).substring(0,8)
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H(0)
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5 = 510e527f
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(Math.sqrt(11) % 1 * (2**32)).toString(16).substring(0,8)
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H(0)
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6 = 9b05688c
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(Math.sqrt(13) % 1 * (2**32)).toString(16).substring(0,8)
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H(0)
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7 = 1f83d9ab
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(Math.sqrt(17) % 1 * (2**32)).toString(16).substring(0,8)
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H(0)
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8 = 5be0cd19
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(Math.sqrt(19) % 1 * (2**32)).toString(16).substring(0,8)
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```
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### 第三步
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寫出 64 個固定 k 值
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![](https://easonwang01.gitbooks.io/blockchain-and-cryptography/content/assets/螢幕快照 2018-02-01 上午9.07.07.png)**原理： **
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```js
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用Math cube root的方法找首64個質數
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(Math.cbrt(2) * (2**32)).toString(16).substring(1,9)
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"428a2f98"
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(Math.cbrt(3) * (2**32)).toString(16).substring(1,9)
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"71374491"
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(Math.cbrt(5) * (2**32)).toString(16).substring(1,9)
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"b5c0fbcf"
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```
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### 第四步:
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使用SHA-256定義的六個邏輯 Function
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![](https://easonwang01.gitbooks.io/blockchain-and-cryptography/content/assets/螢幕快照 2018-02-01 上午9.08.21.png)
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其中符號定義如下
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![](https://easonwang01.gitbooks.io/blockchain-and-cryptography/content/assets/螢幕快照 2018-02-01 上午9.09.22.png)
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寫成程式為:
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```js
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function ch (x, y, z) {
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return z ^ (x & (y ^ z))
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}
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function maj (x, y, z) {
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return (x & y) | (z & (x | y))
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}
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function sigma0 (x) {
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return (x >>> 2 | x << 30) ^ (x >>> 13 | x << 19) ^ (x >>> 22 | x << 10)
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}
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function sigma1 (x) {
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return (x >>> 6 | x << 26) ^ (x >>> 11 | x << 21) ^ (x >>> 25 | x << 7)
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}
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function gamma0 (x) {
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return (x >>> 7 | x << 25) ^ (x >>> 18 | x << 14) ^ (x >>> 3)
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}
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function gamma1 (x) {
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return (x >>> 17 | x << 15) ^ (x >>> 19 | x << 13) ^ (x >>> 10)
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}
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```
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# 完整範例
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> 需要先安裝big-integer模組
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```
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npm install big-integer
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```
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```js
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const util = require('util');
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var bigInt = require("big-integer");
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function Hash (blockSize, finalSize) {
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this._block = new Buffer(blockSize)
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this._finalSize = finalSize
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this._blockSize = blockSize
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this._len = 0
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}
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Hash.prototype.digest = function (data, enc) {
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data = (data).toString();
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//////////////////
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let s = ""
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let s1 = ""
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// 將字串轉為二進位ASCII
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function ascii (a) {
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let dd = "";
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for(let i = 0 ; i< a.length; i++) {
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let charAscII = a.charAt(i).charCodeAt(0).toString(2)
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while(charAscII.length < 8) { // 最前面的0都會被省略，所以手動加上
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charAscII = 0 + charAscII
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}
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dd += charAscII;
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}
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return dd
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}
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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
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let BinarymsgLength = (ascii(data).length); // 訊息的二進位的長度
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for(i = 0; i < 448 - 1 - BinarymsgLength; i++) {s += 0} // 前面補448 bit 的 0
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for(i = 0; i < 64 - msgLengthToBinary ; i++) {s1 += 0} // 後面補64 bit 的 0
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let msgLength = ascii(data).length;
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let frontPad = ascii(data) + 1 + s + s1 + (ascii(data).length).toString(2);
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let c0 = bigInt(bin2dec(frontPad)).toString(16); //涉及大數轉進位(MAX_SAFE_INTEGER)
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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
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let initPadedValueBuffer = Buffer.from(initPadedValue, 'hex');
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this._update(initPadedValueBuffer) //傳入一開始pad好之buffer進行main loop hash function
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var hash = this._hash() //拼接main loop好的a-h八個區塊
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return enc ? hash.toString(enc) : hash //轉為16進位
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}
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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
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var dec = str.toString().split(''), sum = [], hex = [], i, s
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while(dec.length){
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s = 1 * dec.shift()
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for(i = 0; s || i < sum.length; i++){
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s += (sum[i] || 0) * 2
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sum[i] = s % 10
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s = (s - sum[i]) / 10
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}
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}
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while(sum.length){
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hex.push(sum.pop().toString(10))
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}
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return hex.join('')
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}
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var K = [
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0x428A2F98, 0x71374491, 0xB5C0FBCF, 0xE9B5DBA5,
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0x3956C25B, 0x59F111F1, 0x923F82A4, 0xAB1C5ED5,
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0xD807AA98, 0x12835B01, 0x243185BE, 0x550C7DC3,
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0x72BE5D74, 0x80DEB1FE, 0x9BDC06A7, 0xC19BF174,
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0xE49B69C1, 0xEFBE4786, 0x0FC19DC6, 0x240CA1CC,
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0x2DE92C6F, 0x4A7484AA, 0x5CB0A9DC, 0x76F988DA,
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0x983E5152, 0xA831C66D, 0xB00327C8, 0xBF597FC7,
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0xC6E00BF3, 0xD5A79147, 0x06CA6351, 0x14292967,
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0x27B70A85, 0x2E1B2138, 0x4D2C6DFC, 0x53380D13,
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0x650A7354, 0x766A0ABB, 0x81C2C92E, 0x92722C85,
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0xA2BFE8A1, 0xA81A664B, 0xC24B8B70, 0xC76C51A3,
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0xD192E819, 0xD6990624, 0xF40E3585, 0x106AA070,
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0x19A4C116, 0x1E376C08, 0x2748774C, 0x34B0BCB5,
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0x391C0CB3, 0x4ED8AA4A, 0x5B9CCA4F, 0x682E6FF3,
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0x748F82EE, 0x78A5636F, 0x84C87814, 0x8CC70208,
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0x90BEFFFA, 0xA4506CEB, 0xBEF9A3F7, 0xC67178F2
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]
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var W = new Array(64)
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function Sha256 () {
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this.init()
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this._w = W // new Array(64)
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Hash.call(this, 64, 56)
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}
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util.inherits(Sha256, Hash)
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Sha256.prototype.init = function () {
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this._a = 0x6a09e667
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this._b = 0xbb67ae85
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this._c = 0x3c6ef372
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this._d = 0xa54ff53a
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this._e = 0x510e527f
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this._f = 0x9b05688c
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this._g = 0x1f83d9ab
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this._h = 0x5be0cd19
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return this
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}
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function ch (x, y, z) {
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return z ^ (x & (y ^ z))
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}
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function maj (x, y, z) {
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return (x & y) | (z & (x | y))
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}
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function sigma0 (x) {
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return (x >>> 2 | x << 30) ^ (x >>> 13 | x << 19) ^ (x >>> 22 | x << 10)
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}
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function sigma1 (x) {
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return (x >>> 6 | x << 26) ^ (x >>> 11 | x << 21) ^ (x >>> 25 | x << 7)
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}
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function gamma0 (x) {
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return (x >>> 7 | x << 25) ^ (x >>> 18 | x << 14) ^ (x >>> 3)
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}
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function gamma1 (x) {
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return (x >>> 17 | x << 15) ^ (x >>> 19 | x << 13) ^ (x >>> 10)
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}
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Sha256.prototype._update = function (M) {
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var W = this._w
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var a = this._a | 0
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var b = this._b | 0
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var c = this._c | 0
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var d = this._d | 0
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var e = this._e | 0
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var f = this._f | 0
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var g = this._g | 0
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var h = this._h | 0
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for (var i = 0; i < 16; ++i) W[i] = M.readInt32BE(i * 4)
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for (; i < 64; ++i) W[i] = (gamma1(W[i - 2]) + W[i - 7] + gamma0(W[i - 15]) + W[i - 16]) | 0
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for (var j = 0; j < 64; ++j) {
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var T1 = (h + sigma1(e) + ch(e, f, g) + K[j] + W[j]) | 0
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var T2 = (sigma0(a) + maj(a, b, c)) | 0
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h = g
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g = f
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f = e
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e = (d + T1) | 0
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d = c
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c = b
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b = a
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a = (T1 + T2) | 0
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}
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this._a = (a + this._a) | 0
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this._b = (b + this._b) | 0
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this._c = (c + this._c) | 0
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this._d = (d + this._d) | 0
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this._e = (e + this._e) | 0
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this._f = (f + this._f) | 0
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this._g = (g + this._g) | 0
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this._h = (h + this._h) | 0
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}
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Sha256.prototype._hash = function () {
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var H = new Buffer(32)
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H.writeInt32BE(this._a, 0)
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H.writeInt32BE(this._b, 4)
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H.writeInt32BE(this._c, 8)
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H.writeInt32BE(this._d, 12)
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H.writeInt32BE(this._e, 16)
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H.writeInt32BE(this._f, 20)
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H.writeInt32BE(this._g, 24)
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H.writeInt32BE(this._h, 28)
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return H
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}
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// 執行:
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let hashString = new Sha256().digest('test','hex');
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console.log(hashString)
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```
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使用 Node.js 的 crypto 模組進行驗證，可以得到相同的雜湊值。
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```js
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const crypto = require('crypto');
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let result = crypto.createHash('sha256').update('test').digest('hex')
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console.log(result)
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```
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參考資料：
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> [http://www.iwar.org.uk/comsec/resources/cipher/sha256-384-512.pdf](http://www.iwar.org.uk/comsec/resources/cipher/sha256-384-512.pdf)
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#
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