JavaScript ＜关于逆向RSA非对称加密算法的案例(附原代码)＞--案例(五)

前言:

趁热打铁,标记一下RSA的算法逆向...第二篇会有详解(本篇重在过程)

正文:

废话不说,直接分析步骤图:

到了这里,可以看到在登录的时候,需要验证码(本篇不教反验证码)

下面是正题--->逆他的pwd(密码)

---

总结:

问题:怎么确定一个密文数据是基于什么算法做出来的呢?

答: 1.看他是由什么组成的

• ? ? ? ? --如果光是由 '字母和数字'组成
• ? ? ? ? ? ? ? ? --由字母和数字组成的32位密文数据 ,MD5
• ? ? ? ? ? ? ? ? --由字母和数字组成的64位密文数据 ,SHA-256(生成256位长度的哈希值，这通常以64个十六进制字符呈现)
• ? ? ? ? ? ? ? ? --由字母和数字组成的256位密文数据,RSA?
• ? ? ? ? ---以上是通常的例子

针对rsa,直接抠他代码会比较直接,但是比较繁琐; 当你过了一遍他的代码,没大问题,一样可以引用crypto库进行解密

全篇js代码:

var bitsPerDigit=16
function arrayCopy(src, srcStart, dest, destStart, n)
{
	var m = Math.min(srcStart + n, src.length);
	for (var i = srcStart, j = destStart; i < m; ++i, ++j) {
		dest[j] = src[i];
	}
}
var maxDigitVal = 65535
var biRadixBits =16
function biMultiplyDigit(x, y)
{
	var n, c, uv;


	result = new BigInt();
	n = biHighIndex(x);
	c = 0;
	for (var j = 0; j <= n; ++j) {
		uv = result.digits[j] + x.digits[j] * y + c;
		result.digits[j] = uv & maxDigitVal;
		c = uv >>> biRadixBits;
	}
	result.digits[1 + n] = c;
	return result;
}

function biNumBits(x)
{

	var n = biHighIndex(x);
	var d = x.digits[n];
	var m = (n + 1) * bitsPerDigit;
	var result;
	for (result = m; result > m - bitsPerDigit; --result) {
		if ((d & 0x8000) != 0) break;
		d <<= 1;
	}
	return result;
}
var highBitMasks = new Array(0x0000, 0x8000, 0xC000, 0xE000, 0xF000, 0xF800,
                             0xFC00, 0xFE00, 0xFF00, 0xFF80, 0xFFC0, 0xFFE0,
                             0xFFF0, 0xFFF8, 0xFFFC, 0xFFFE, 0xFFFF);
function biShiftLeft(x, n)
{
	var maxDigitVal= 65535
	var digitCount = Math.floor(n / bitsPerDigit);
	var result = new BigInt();
	arrayCopy(x.digits, 0, result.digits, digitCount,
	          result.digits.length - digitCount);
	var bits = n % bitsPerDigit;
	var rightBits = bitsPerDigit - bits;
	for (var i = result.digits.length - 1, i1 = i - 1; i > 0; --i, --i1) {
		result.digits[i] = ((result.digits[i] << bits) & maxDigitVal) |
		                   ((result.digits[i1] & highBitMasks[bits]) >>>
		                    (rightBits));
	}
	result.digits[0] = ((result.digits[i] << bits) & maxDigitVal);
	result.isNeg = x.isNeg;
	return result;
}
function biMultiplyByRadixPower(x, n)
{
	var result = new BigInt();
	arrayCopy(x.digits, 0, result.digits, n, result.digits.length - n);
	return result;
}
function biCompare(x, y)
{
	if (x.isNeg != y.isNeg) {
		return 1 - 2 * Number(x.isNeg);
	}
	for (var i = x.digits.length - 1; i >= 0; --i) {
		if (x.digits[i] != y.digits[i]) {
			if (x.isNeg) {
				return 1 - 2 * Number(x.digits[i] > y.digits[i]);
			} else {
				return 1 - 2 * Number(x.digits[i] < y.digits[i]);
			}
		}
	}
	return 0;
}
function biSubtract(x, y)
{
	var result;
	if (x.isNeg != y.isNeg) {
		y.isNeg = !y.isNeg;
		result = biAdd(x, y);
		y.isNeg = !y.isNeg;
	} else {
		result = new BigInt();
		var n, c;
		c = 0;
		for (var i = 0; i < x.digits.length; ++i) {
			n = x.digits[i] - y.digits[i] + c;
			result.digits[i] = n & 0xffff;
			// Stupid non-conforming modulus operation.
			if (result.digits[i] < 0) result.digits[i] += biRadix;
			c = 0 - Number(n < 0);
		}
		// Fix up the negative sign, if any.
		if (c == -1) {
			c = 0;
			for (var i = 0; i < x.digits.length; ++i) {
				n = 0 - result.digits[i] + c;
				result.digits[i] = n & 0xffff;
				// Stupid non-conforming modulus operation.
				if (result.digits[i] < 0) result.digits[i] += biRadix;
				c = 0 - Number(n < 0);
			}
			// Result is opposite sign of arguments.
			result.isNeg = !x.isNeg;
		} else {
			// Result is same sign.
			result.isNeg = x.isNeg;
		}
	}
	return result;
}
var lowBitMasks = new Array(0x0000, 0x0001, 0x0003, 0x0007, 0x000F, 0x001F,
                            0x003F, 0x007F, 0x00FF, 0x01FF, 0x03FF, 0x07FF,
                            0x0FFF, 0x1FFF, 0x3FFF, 0x7FFF, 0xFFFF);
function biShiftRight(x, n)
{
	var digitCount = Math.floor(n / bitsPerDigit);
	var result = new BigInt();
	arrayCopy(x.digits, digitCount, result.digits, 0,
	          x.digits.length - digitCount);
	var bits = n % bitsPerDigit;
	var leftBits = bitsPerDigit - bits;
	for (var i = 0, i1 = i + 1; i < result.digits.length - 1; ++i, ++i1) {
		result.digits[i] = (result.digits[i] >>> bits) |
		                   ((result.digits[i1] & lowBitMasks[bits]) << leftBits);
	}
	result.digits[result.digits.length - 1] >>>= bits;
	result.isNeg = x.isNeg;
	return result;
}
function biDivideModulo(x, y)
{
	var nb = biNumBits(x);
	var tb = biNumBits(y);
	var origYIsNeg = y.isNeg;
	var q, r;
	if (nb < tb) {
		// |x| < |y|
		if (x.isNeg) {
			q = biCopy(bigOne);
			q.isNeg = !y.isNeg;
			x.isNeg = false;
			y.isNeg = false;
			r = biSubtract(y, x);
			// Restore signs, 'cause they're references.
			x.isNeg = true;
			y.isNeg = origYIsNeg;
		} else {
			q = new BigInt();
			r = biCopy(x);
		}
		return new Array(q, r);
	}

	q = new BigInt();
	r = x;
	var bitsPerDigit =16

	// Normalize Y.
	var t = Math.ceil(tb / bitsPerDigit) - 1;
	var lambda = 0;
	var biHalfRadix= 32768
	while (y.digits[t] < biHalfRadix) {
		y = biShiftLeft(y, 1);
		++lambda;
		++tb;
		t = Math.ceil(tb / bitsPerDigit) - 1;
	}
	// Shift r over to keep the quotient constant. We'll shift the
	// remainder back at the end.
	r = biShiftLeft(r, lambda);
	nb += lambda; // Update the bit count for x.
	var n = Math.ceil(nb / bitsPerDigit) - 1;

	var b = biMultiplyByRadixPower(y, n - t);
	while (biCompare(r, b) != -1) {
		++q.digits[n - t];
		r = biSubtract(r, b);
	}
	for (var i = n; i > t; --i) {
    var ri = (i >= r.digits.length) ? 0 : r.digits[i];
    var ri1 = (i - 1 >= r.digits.length) ? 0 : r.digits[i - 1];
    var ri2 = (i - 2 >= r.digits.length) ? 0 : r.digits[i - 2];
    var yt = (t >= y.digits.length) ? 0 : y.digits[t];
	var biRadix = 65536
    var yt1 = (t - 1 >= y.digits.length) ? 0 : y.digits[t - 1];
		if (ri == yt) {
			q.digits[i - t - 1] = maxDigitVal;
		} else {
			q.digits[i - t - 1] = Math.floor((ri * biRadix + ri1) / yt);
		}
		var biRadixSquared =4294967296
		var c1 = q.digits[i - t - 1] * ((yt * biRadix) + yt1);
		var c2 = (ri * biRadixSquared) + ((ri1 * biRadix) + ri2);
		while (c1 > c2) {
			--q.digits[i - t - 1];
			c1 = q.digits[i - t - 1] * ((yt * biRadix) | yt1);
			c2 = (ri * biRadix * biRadix) + ((ri1 * biRadix) + ri2);
		}

		b = biMultiplyByRadixPower(y, i - t - 1);
		r = biSubtract(r, biMultiplyDigit(b, q.digits[i - t - 1]));
		if (r.isNeg) {
			r = biAdd(r, b);
			--q.digits[i - t - 1];
		}
	}
	r = biShiftRight(r, lambda);
	// Fiddle with the signs and stuff to make sure that 0 <= r < y.
	q.isNeg = x.isNeg != origYIsNeg;
	if (x.isNeg) {
		if (origYIsNeg) {
			q = biAdd(q, bigOne);
		} else {
			q = biSubtract(q, bigOne);
		}
		y = biShiftRight(y, lambda);
		r = biSubtract(y, r);
	}
	// Check for the unbelievably stupid degenerate case of r == -0.
	if (r.digits[0] == 0 && biHighIndex(r) == 0) r.isNeg = false;

	return new Array(q, r);
}
function biDivide(x, y)
{
	return biDivideModulo(x, y)[0];
}
function biCopy(bi)
{
	var result = new BigInt(true);
	result.digits = bi.digits.slice(0);
	result.isNeg = bi.isNeg;
	return result;
}
function biDivideByRadixPower(x, n)
{
	var result = new BigInt();
	arrayCopy(x.digits, n, result.digits, 0, result.digits.length - n);
	return result;
}
function biModuloByRadixPower(x, n)
{
	var result = new BigInt();
	arrayCopy(x.digits, 0, result.digits, 0, n);
	return result;
}
function BarrettMu_modulo(x)
{
	var q1 = biDivideByRadixPower(x, this.k - 1);
	var q2 = biMultiply(q1, this.mu);
	var q3 = biDivideByRadixPower(q2, this.k + 1);
	var r1 = biModuloByRadixPower(x, this.k + 1);
	var r2term = biMultiply(q3, this.modulus);
	var r2 = biModuloByRadixPower(r2term, this.k + 1);
	var r = biSubtract(r1, r2);
	if (r.isNeg) {
		r = biAdd(r, this.bkplus1);
	}
	var rgtem = biCompare(r, this.modulus) >= 0;
	while (rgtem) {
		r = biSubtract(r, this.modulus);
		rgtem = biCompare(r, this.modulus) >= 0;
	}
	return r;
}
function biMultiply(x, y)
{
	var result = new BigInt();
	var c;
	var n = biHighIndex(x);
	var t = biHighIndex(y);
	var u, uv, k;

	for (var i = 0; i <= t; ++i) {
		c = 0;
		k = i;
		for (j = 0; j <= n; ++j, ++k) {
			uv = result.digits[k] + x.digits[j] * y.digits[i] + c;
			result.digits[k] = uv & maxDigitVal;
			c = uv >>> biRadixBits;
		}
		result.digits[i + n + 1] = c;
	}
	// Someone give me a logical xor, please.
	result.isNeg = x.isNeg != y.isNeg;
	return result;
}
function BarrettMu_multiplyMod(x, y)
{
	/*
	x = this.modulo(x);
	y = this.modulo(y);
	*/
	var xy = biMultiply(x, y);
	return this.modulo(xy);
}

function BarrettMu_powMod(x, y)
{
	var result = new BigInt();
	result.digits[0] = 1;
	var a = x;
	var k = y;
	while (true) {
		if ((k.digits[0] & 1) != 0) result = this.multiplyMod(result, a);
		k = biShiftRight(k, 1);
		if (k.digits[0] == 0 && biHighIndex(k) == 0) break;
		a = this.multiplyMod(a, a);
	}
	return result;
}

function BarrettMu(m)
{
	this.modulus = biCopy(m);
	this.k = biHighIndex(this.modulus) + 1;
	var b2k = new BigInt();
	b2k.digits[2 * this.k] = 1; // b2k = b^(2k)
	this.mu = biDivide(b2k, this.modulus);
	this.bkplus1 = new BigInt();
	this.bkplus1.digits[this.k + 1] = 1; // bkplus1 = b^(k+1)
	this.modulo = BarrettMu_modulo;
	this.multiplyMod = BarrettMu_multiplyMod;
	this.powMod = BarrettMu_powMod;
}
function charToHex(c)
{
	var ZERO = 48;
	var NINE = ZERO + 9;
	var littleA = 97;
	var littleZ = littleA + 25;
	var bigA = 65;
	var bigZ = 65 + 25;
	var result;

	if (c >= ZERO && c <= NINE) {
		result = c - ZERO;
	} else if (c >= bigA && c <= bigZ) {
		result = 10 + c - bigA;
	} else if (c >= littleA && c <= littleZ) {
		result = 10 + c - littleA;
	} else {
		result = 0;
	}
	return result;
}
function hexToDigit(s)
{
	var result = 0;
	var sl = Math.min(s.length, 4);
	for (var i = 0; i < sl; ++i) {
		result <<= 4;
		result |= charToHex(s.charCodeAt(i))
	}
	return result;
}
function biHighIndex(x)
{
	var result = x.digits.length - 1;
	while (result > 0 && x.digits[result] == 0) --result;
	return result;
}
function biFromHex(s)
{
	var result = new BigInt();
	var sl = s.length;
	for (var i = sl, j = 0; i > 0; i -= 4, ++j) {
		result.digits[j] = hexToDigit(s.substr(Math.max(i - 4, 0), Math.min(i, 4)));
	}
	return result;
}

function RSAKeyPair(encryptionExponent, decryptionExponent, modulus, keylen)

{

this.e = biFromHex(encryptionExponent);
this.d = biFromHex(decryptionExponent);
this.m = biFromHex(modulus);

if (typeof(keylen) != 'number') { this.chunkSize = 2 * biHighIndex(this.m); }
else { this.chunkSize = keylen / 8; }

this.radix = 16;

this.barrett = new BarrettMu(this.m);
}

function BigInt(flag)
{
	if (typeof flag == "boolean" && flag == true) {
		this.digits = null;
	}
	else {
		this.digits = ZERO_ARRAY.slice(0);
	}
	this.isNeg = false;
}

function setMaxDigits(value)
{
	maxDigits = value;
	ZERO_ARRAY = new Array(maxDigits);
	for (var iza = 0; iza < ZERO_ARRAY.length; iza++) ZERO_ARRAY[iza] = 0;
	bigZero = new BigInt();
	bigOne = new BigInt();
	bigOne.digits[0] = 1;
}
var hexToChar = new Array('0', '1', '2', '3', '4', '5', '6', '7', '8', '9',
                          'a', 'b', 'c', 'd', 'e', 'f');
function reverseStr(s)
{
	var result = "";
	for (var i = s.length - 1; i > -1; --i) {
		result += s.charAt(i);
	}
	return result;
}
function digitToHex(n)
{
	var mask = 0xf;
	var result = "";
	for (i = 0; i < 4; ++i) {
		result += hexToChar[n & mask];
		n >>>= 4;
	}
	return reverseStr(result);
}
function biToHex(x)
{
	var result = "";
	var n = biHighIndex(x);
	for (var i = biHighIndex(x); i > -1; --i) {
		result += digitToHex(x.digits[i]);
	}
	return result;
}
function encryptedString(key, s, pad, encoding) {
	var a = new Array();                    // The usual Alice and Bob stuff
	var sl = s.length;                      // Plaintext string length
	var i, j, k;                            // The usual Fortran index stuff
	var padtype;                            // Type of padding to do
	var encodingtype;                       // Type of output encoding
	var rpad;                               // Random pad
	var al;                                 // Array length
	var result = "";                        // Cypthertext result
	var block;                              // Big integer block to encrypt
	var crypt;                              // Big integer result
	var text;                               // Text result
	/*
    * Figure out the padding type.
    */
	if (typeof (pad) == 'string') {
		if (pad == RSAAPP.NoPadding) {
			padtype = 1;
		} else if (pad == RSAAPP.PKCS1Padding) {
			padtype = 2;
		} else {
			padtype = 0;
		}
	} else {
		padtype = 0;
	}
	/*
    * Determine encoding type.
    */
	if (typeof (encoding) == 'string' && encoding == RSAAPP.RawEncoding) {
		encodingtype = 1;
	} else {
		encodingtype = 0;
	}


	if (padtype == 1) {
		if (sl > key.chunkSize) {
			sl = key.chunkSize;
		}
	} else if (padtype == 2) {
		if (sl > (key.chunkSize - 11)) {
			sl = key.chunkSize - 11;
		}
	}

	i = 0;

	if (padtype == 2) {
		j = sl - 1;
	} else {
		j = key.chunkSize - 1;
	}

	while (i < sl) {
		if (padtype) {
			a[j] = s.charCodeAt(i);
		} else {
			a[i] = s.charCodeAt(i);
		}

		i++;
		j--;
	}

	if (padtype == 1) {
		i = 0;
	}

	j = key.chunkSize - (sl % key.chunkSize);

	while (j > 0) {
		if (padtype == 2) {
			rpad = Math.floor(Math.random() * 256);

			while (!rpad) {
				rpad = Math.floor(Math.random() * 256);
			}

			a[i] = rpad;
		} else {
			a[i] = 0;
		}

		i++;
		j--;
	}

	if (padtype == 2) {
		a[sl] = 0;
		a[key.chunkSize - 2] = 2;
		a[key.chunkSize - 1] = 0;
	}
	/*
    * Carve up the plaintext and encrypt each of the resultant blocks.
    */
	al = a.length;

	for (i = 0; i < al; i += key.chunkSize) {
		/*
        * Get a block.
        */
		block = new BigInt();

		j = 0;

		for (k = i; k < (i + key.chunkSize); ++j) {
			block.digits[j] = a[k++];
			block.digits[j] += a[k++] << 8;
		}
		/*
        * Encrypt it, convert it to text, and append it to the result.
        */
		crypt = key.barrett.powMod(block, key.e);
		if (encodingtype == 1) {
			text = biToBytes(crypt);
		} else {
			text = (key.radix == 16) ? biToHex(crypt) : biToString(crypt, key.radix);
		}
		result += text;
	}
	/*
    * Return the result, removing the last space.
    */
//result = (result.substring(0, result.length - 1));
	return result;
}

function rsa(arg) {
      setMaxDigits(130);
      var PublicExponent = "10001";
      var modulus = "be44aec4d73408f6b60e6fe9e3dc55d0e1dc53a1e171e071b547e2e8e0b7da01c56e8c9bcf0521568eb111adccef4e40124b76e33e7ad75607c227af8f8e0b759c30ef283be8ab17a84b19a051df5f94c07e6e7be5f77866376322aac944f45f3ab532bb6efc70c1efa524d821d16cafb580c5a901f0defddea3692a4e68e6cd";
      var key = new RSAKeyPair(PublicExponent, "", modulus);
	  // console.log(key, arg)  验证看一下 -->自己出错了没?
      return encryptedString(key, arg);
  };

console.log(rsa("输入你的密码"))

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(预告---下篇,详解本章的代码)