让我们假设您使用哈希算法:计算rot13，取前10个字符。如果你这样做两次(甚至2000次)，就有可能得到一个更快的函数，但结果是相同的(即只取前10个字符)。

同样，也可以创建一个速度更快的函数，其输出与重复哈希函数相同。因此，您对哈希函数的选择非常重要:与rot13示例一样，并没有给出重复哈希将提高安全性。如果没有研究表明该算法是为递归使用而设计的，那么假设它不会为您提供额外的保护是更安全的。

也就是说:对于除了最简单的哈希函数之外的所有函数，很可能需要密码学专家来计算更快的函数，所以如果你正在防范无法访问密码学专家的攻击者，在实践中使用重复哈希函数可能更安全。

根据我所读到的，实际上可能建议将密码重新哈希数百或数千次。

其思想是，如果您可以花费更多的时间来编码密码，那么攻击者就需要做更多的工作来进行多次猜测以破解密码。这似乎是重哈希的优势——并不是说它在密码学上更安全，而是它只是需要更长的时间来生成字典攻击。

当然，计算机一直在变得更快，所以这种优势会随着时间的推移而减弱(或者需要您增加迭代)。

对于那些说安全的人来说，他们总的来说是正确的。“双重”哈希(或其逻辑扩展，迭代哈希函数)如果处理得当，对于特定的问题是绝对安全的。

对于那些说它不安全的人来说，在这种情况下他们是正确的。在问题中发布的代码是不安全的。让我们来谈谈为什么:

$hashed_password1 = md5( md5( plaintext_password ) );
$hashed_password2 = md5( plaintext_password );

我们关心哈希函数的两个基本性质:

Pre-Image Resistance - Given a hash $h, it should be difficult to find a message $m such that $h === hash($m) Second-Pre-Image Resistance - Given a message $m1, it should be difficult to find a different message $m2 such that hash($m1) === hash($m2) Collision Resistance - It should be difficult to find a pair of messages ($m1, $m2) such that hash($m1) === hash($m2) (note that this is similar to Second-Pre-Image resistance, but different in that here the attacker has control over both messages)...

对于密码的存储，我们真正关心的是Pre-Image Resistance。另外两个没有意义，因为$m1是我们想要保护的用户密码。所以如果攻击者已经拥有了它，哈希就没有什么可以保护的了……

免责声明

接下来的一切都是基于这样一个前提，即我们所关心的是预图像阻力。哈希函数的另外两个基本属性可能不会(通常不会)以同样的方式成立。因此，本文中的结论仅适用于使用哈希函数存储密码的情况。它们一般不适用……

让我们开始

为了便于讨论，让我们创建自己的哈希函数:

function ourHash($input) {
    $result = 0;
    for ($i = 0; $i < strlen($input); $i++) {
        $result += ord($input[$i]);
    }
    return (string) ($result % 256);
}

现在这个哈希函数的作用应该很明显了。它将输入的每个字符的ASCII值相加，然后对该结果取256的模。

让我们来测试一下:

var_dump(
    ourHash('abc'), // string(2) "38"
    ourHash('def'), // string(2) "47"
    ourHash('hij'), // string(2) "59"
    ourHash('klm')  // string(2) "68"
);

现在，让我们看看如果我们围绕一个函数运行几次会发生什么:

$tests = array(
    "abc",
    "def",
    "hij",
    "klm",
);

foreach ($tests as $test) {
    $hash = $test;
    for ($i = 0; $i < 100; $i++) {
        $hash = ourHash($hash);
    }
    echo "Hashing $test => $hash\n";
}

输出:

Hashing abc => 152
Hashing def => 152
Hashing hij => 155
Hashing klm => 155

人力资源管理,哇。我们产生了碰撞!!让我们来看看原因:

下面是对每个可能的哈希输出的字符串进行哈希的输出:

Hashing 0 => 48
Hashing 1 => 49
Hashing 2 => 50
Hashing 3 => 51
Hashing 4 => 52
Hashing 5 => 53
Hashing 6 => 54
Hashing 7 => 55
Hashing 8 => 56
Hashing 9 => 57
Hashing 10 => 97
Hashing 11 => 98
Hashing 12 => 99
Hashing 13 => 100
Hashing 14 => 101
Hashing 15 => 102
Hashing 16 => 103
Hashing 17 => 104
Hashing 18 => 105
Hashing 19 => 106
Hashing 20 => 98
Hashing 21 => 99
Hashing 22 => 100
Hashing 23 => 101
Hashing 24 => 102
Hashing 25 => 103
Hashing 26 => 104
Hashing 27 => 105
Hashing 28 => 106
Hashing 29 => 107
Hashing 30 => 99
Hashing 31 => 100
Hashing 32 => 101
Hashing 33 => 102
Hashing 34 => 103
Hashing 35 => 104
Hashing 36 => 105
Hashing 37 => 106
Hashing 38 => 107
Hashing 39 => 108
Hashing 40 => 100
Hashing 41 => 101
Hashing 42 => 102
Hashing 43 => 103
Hashing 44 => 104
Hashing 45 => 105
Hashing 46 => 106
Hashing 47 => 107
Hashing 48 => 108
Hashing 49 => 109
Hashing 50 => 101
Hashing 51 => 102
Hashing 52 => 103
Hashing 53 => 104
Hashing 54 => 105
Hashing 55 => 106
Hashing 56 => 107
Hashing 57 => 108
Hashing 58 => 109
Hashing 59 => 110
Hashing 60 => 102
Hashing 61 => 103
Hashing 62 => 104
Hashing 63 => 105
Hashing 64 => 106
Hashing 65 => 107
Hashing 66 => 108
Hashing 67 => 109
Hashing 68 => 110
Hashing 69 => 111
Hashing 70 => 103
Hashing 71 => 104
Hashing 72 => 105
Hashing 73 => 106
Hashing 74 => 107
Hashing 75 => 108
Hashing 76 => 109
Hashing 77 => 110
Hashing 78 => 111
Hashing 79 => 112
Hashing 80 => 104
Hashing 81 => 105
Hashing 82 => 106
Hashing 83 => 107
Hashing 84 => 108
Hashing 85 => 109
Hashing 86 => 110
Hashing 87 => 111
Hashing 88 => 112
Hashing 89 => 113
Hashing 90 => 105
Hashing 91 => 106
Hashing 92 => 107
Hashing 93 => 108
Hashing 94 => 109
Hashing 95 => 110
Hashing 96 => 111
Hashing 97 => 112
Hashing 98 => 113
Hashing 99 => 114
Hashing 100 => 145
Hashing 101 => 146
Hashing 102 => 147
Hashing 103 => 148
Hashing 104 => 149
Hashing 105 => 150
Hashing 106 => 151
Hashing 107 => 152
Hashing 108 => 153
Hashing 109 => 154
Hashing 110 => 146
Hashing 111 => 147
Hashing 112 => 148
Hashing 113 => 149
Hashing 114 => 150
Hashing 115 => 151
Hashing 116 => 152
Hashing 117 => 153
Hashing 118 => 154
Hashing 119 => 155
Hashing 120 => 147
Hashing 121 => 148
Hashing 122 => 149
Hashing 123 => 150
Hashing 124 => 151
Hashing 125 => 152
Hashing 126 => 153
Hashing 127 => 154
Hashing 128 => 155
Hashing 129 => 156
Hashing 130 => 148
Hashing 131 => 149
Hashing 132 => 150
Hashing 133 => 151
Hashing 134 => 152
Hashing 135 => 153
Hashing 136 => 154
Hashing 137 => 155
Hashing 138 => 156
Hashing 139 => 157
Hashing 140 => 149
Hashing 141 => 150
Hashing 142 => 151
Hashing 143 => 152
Hashing 144 => 153
Hashing 145 => 154
Hashing 146 => 155
Hashing 147 => 156
Hashing 148 => 157
Hashing 149 => 158
Hashing 150 => 150
Hashing 151 => 151
Hashing 152 => 152
Hashing 153 => 153
Hashing 154 => 154
Hashing 155 => 155
Hashing 156 => 156
Hashing 157 => 157
Hashing 158 => 158
Hashing 159 => 159
Hashing 160 => 151
Hashing 161 => 152
Hashing 162 => 153
Hashing 163 => 154
Hashing 164 => 155
Hashing 165 => 156
Hashing 166 => 157
Hashing 167 => 158
Hashing 168 => 159
Hashing 169 => 160
Hashing 170 => 152
Hashing 171 => 153
Hashing 172 => 154
Hashing 173 => 155
Hashing 174 => 156
Hashing 175 => 157
Hashing 176 => 158
Hashing 177 => 159
Hashing 178 => 160
Hashing 179 => 161
Hashing 180 => 153
Hashing 181 => 154
Hashing 182 => 155
Hashing 183 => 156
Hashing 184 => 157
Hashing 185 => 158
Hashing 186 => 159
Hashing 187 => 160
Hashing 188 => 161
Hashing 189 => 162
Hashing 190 => 154
Hashing 191 => 155
Hashing 192 => 156
Hashing 193 => 157
Hashing 194 => 158
Hashing 195 => 159
Hashing 196 => 160
Hashing 197 => 161
Hashing 198 => 162
Hashing 199 => 163
Hashing 200 => 146
Hashing 201 => 147
Hashing 202 => 148
Hashing 203 => 149
Hashing 204 => 150
Hashing 205 => 151
Hashing 206 => 152
Hashing 207 => 153
Hashing 208 => 154
Hashing 209 => 155
Hashing 210 => 147
Hashing 211 => 148
Hashing 212 => 149
Hashing 213 => 150
Hashing 214 => 151
Hashing 215 => 152
Hashing 216 => 153
Hashing 217 => 154
Hashing 218 => 155
Hashing 219 => 156
Hashing 220 => 148
Hashing 221 => 149
Hashing 222 => 150
Hashing 223 => 151
Hashing 224 => 152
Hashing 225 => 153
Hashing 226 => 154
Hashing 227 => 155
Hashing 228 => 156
Hashing 229 => 157
Hashing 230 => 149
Hashing 231 => 150
Hashing 232 => 151
Hashing 233 => 152
Hashing 234 => 153
Hashing 235 => 154
Hashing 236 => 155
Hashing 237 => 156
Hashing 238 => 157
Hashing 239 => 158
Hashing 240 => 150
Hashing 241 => 151
Hashing 242 => 152
Hashing 243 => 153
Hashing 244 => 154
Hashing 245 => 155
Hashing 246 => 156
Hashing 247 => 157
Hashing 248 => 158
Hashing 249 => 159
Hashing 250 => 151
Hashing 251 => 152
Hashing 252 => 153
Hashing 253 => 154
Hashing 254 => 155
Hashing 255 => 156

注意数字越来越大的趋势。这就是我们的僵局。对每个元素运行哈希4次($hash = ourHash($hash) ')，结果是:

Hashing 0 => 153
Hashing 1 => 154
Hashing 2 => 155
Hashing 3 => 156
Hashing 4 => 157
Hashing 5 => 158
Hashing 6 => 150
Hashing 7 => 151
Hashing 8 => 152
Hashing 9 => 153
Hashing 10 => 157
Hashing 11 => 158
Hashing 12 => 150
Hashing 13 => 154
Hashing 14 => 155
Hashing 15 => 156
Hashing 16 => 157
Hashing 17 => 158
Hashing 18 => 150
Hashing 19 => 151
Hashing 20 => 158
Hashing 21 => 150
Hashing 22 => 154
Hashing 23 => 155
Hashing 24 => 156
Hashing 25 => 157
Hashing 26 => 158
Hashing 27 => 150
Hashing 28 => 151
Hashing 29 => 152
Hashing 30 => 150
Hashing 31 => 154
Hashing 32 => 155
Hashing 33 => 156
Hashing 34 => 157
Hashing 35 => 158
Hashing 36 => 150
Hashing 37 => 151
Hashing 38 => 152
Hashing 39 => 153
Hashing 40 => 154
Hashing 41 => 155
Hashing 42 => 156
Hashing 43 => 157
Hashing 44 => 158
Hashing 45 => 150
Hashing 46 => 151
Hashing 47 => 152
Hashing 48 => 153
Hashing 49 => 154
Hashing 50 => 155
Hashing 51 => 156
Hashing 52 => 157
Hashing 53 => 158
Hashing 54 => 150
Hashing 55 => 151
Hashing 56 => 152
Hashing 57 => 153
Hashing 58 => 154
Hashing 59 => 155
Hashing 60 => 156
Hashing 61 => 157
Hashing 62 => 158
Hashing 63 => 150
Hashing 64 => 151
Hashing 65 => 152
Hashing 66 => 153
Hashing 67 => 154
Hashing 68 => 155
Hashing 69 => 156
Hashing 70 => 157
Hashing 71 => 158
Hashing 72 => 150
Hashing 73 => 151
Hashing 74 => 152
Hashing 75 => 153
Hashing 76 => 154
Hashing 77 => 155
Hashing 78 => 156
Hashing 79 => 157
Hashing 80 => 158
Hashing 81 => 150
Hashing 82 => 151
Hashing 83 => 152
Hashing 84 => 153
Hashing 85 => 154
Hashing 86 => 155
Hashing 87 => 156
Hashing 88 => 157
Hashing 89 => 158
Hashing 90 => 150
Hashing 91 => 151
Hashing 92 => 152
Hashing 93 => 153
Hashing 94 => 154
Hashing 95 => 155
Hashing 96 => 156
Hashing 97 => 157
Hashing 98 => 158
Hashing 99 => 150
Hashing 100 => 154
Hashing 101 => 155
Hashing 102 => 156
Hashing 103 => 157
Hashing 104 => 158
Hashing 105 => 150
Hashing 106 => 151
Hashing 107 => 152
Hashing 108 => 153
Hashing 109 => 154
Hashing 110 => 155
Hashing 111 => 156
Hashing 112 => 157
Hashing 113 => 158
Hashing 114 => 150
Hashing 115 => 151
Hashing 116 => 152
Hashing 117 => 153
Hashing 118 => 154
Hashing 119 => 155
Hashing 120 => 156
Hashing 121 => 157
Hashing 122 => 158
Hashing 123 => 150
Hashing 124 => 151
Hashing 125 => 152
Hashing 126 => 153
Hashing 127 => 154
Hashing 128 => 155
Hashing 129 => 156
Hashing 130 => 157
Hashing 131 => 158
Hashing 132 => 150
Hashing 133 => 151
Hashing 134 => 152
Hashing 135 => 153
Hashing 136 => 154
Hashing 137 => 155
Hashing 138 => 156
Hashing 139 => 157
Hashing 140 => 158
Hashing 141 => 150
Hashing 142 => 151
Hashing 143 => 152
Hashing 144 => 153
Hashing 145 => 154
Hashing 146 => 155
Hashing 147 => 156
Hashing 148 => 157
Hashing 149 => 158
Hashing 150 => 150
Hashing 151 => 151
Hashing 152 => 152
Hashing 153 => 153
Hashing 154 => 154
Hashing 155 => 155
Hashing 156 => 156
Hashing 157 => 157
Hashing 158 => 158
Hashing 159 => 159
Hashing 160 => 151
Hashing 161 => 152
Hashing 162 => 153
Hashing 163 => 154
Hashing 164 => 155
Hashing 165 => 156
Hashing 166 => 157
Hashing 167 => 158
Hashing 168 => 159
Hashing 169 => 151
Hashing 170 => 152
Hashing 171 => 153
Hashing 172 => 154
Hashing 173 => 155
Hashing 174 => 156
Hashing 175 => 157
Hashing 176 => 158
Hashing 177 => 159
Hashing 178 => 151
Hashing 179 => 152
Hashing 180 => 153
Hashing 181 => 154
Hashing 182 => 155
Hashing 183 => 156
Hashing 184 => 157
Hashing 185 => 158
Hashing 186 => 159
Hashing 187 => 151
Hashing 188 => 152
Hashing 189 => 153
Hashing 190 => 154
Hashing 191 => 155
Hashing 192 => 156
Hashing 193 => 157
Hashing 194 => 158
Hashing 195 => 159
Hashing 196 => 151
Hashing 197 => 152
Hashing 198 => 153
Hashing 199 => 154
Hashing 200 => 155
Hashing 201 => 156
Hashing 202 => 157
Hashing 203 => 158
Hashing 204 => 150
Hashing 205 => 151
Hashing 206 => 152
Hashing 207 => 153
Hashing 208 => 154
Hashing 209 => 155
Hashing 210 => 156
Hashing 211 => 157
Hashing 212 => 158
Hashing 213 => 150
Hashing 214 => 151
Hashing 215 => 152
Hashing 216 => 153
Hashing 217 => 154
Hashing 218 => 155
Hashing 219 => 156
Hashing 220 => 157
Hashing 221 => 158
Hashing 222 => 150
Hashing 223 => 151
Hashing 224 => 152
Hashing 225 => 153
Hashing 226 => 154
Hashing 227 => 155
Hashing 228 => 156
Hashing 229 => 157
Hashing 230 => 158
Hashing 231 => 150
Hashing 232 => 151
Hashing 233 => 152
Hashing 234 => 153
Hashing 235 => 154
Hashing 236 => 155
Hashing 237 => 156
Hashing 238 => 157
Hashing 239 => 158
Hashing 240 => 150
Hashing 241 => 151
Hashing 242 => 152
Hashing 243 => 153
Hashing 244 => 154
Hashing 245 => 155
Hashing 246 => 156
Hashing 247 => 157
Hashing 248 => 158
Hashing 249 => 159
Hashing 250 => 151
Hashing 251 => 152
Hashing 252 => 153
Hashing 253 => 154
Hashing 254 => 155
Hashing 255 => 156

我们已经把范围缩小到8个值…那就糟糕了……原函数将S(∞)映射到S(256)我们已经创建了一个满射函数将$input映射到$output。

由于我们有一个满射函数，我们不能保证输入的任何子集的映射不会有冲突(事实上，在实践中它们会有冲突)。

这就是这里发生的事!我们的函数很糟糕，但这不是它工作的原因(这就是它工作得如此快速和完全的原因)。

同样的事情也发生在MD5上。它将S(∞)映射到S(2^128)由于不能保证运行MD5(S(output))将是内射的，这意味着它不会有冲突。

TL博士/节

因此，由于直接将输出反馈给md5会产生碰撞，因此每次迭代都会增加碰撞的机会。然而，这是一个线性增长，这意味着虽然2^128的结果集减少了，但它的减少速度还不够快，不足以成为一个关键缺陷。

So,

$output = md5($input); // 2^128 possibilities
$output = md5($output); // < 2^128 possibilities
$output = md5($output); // < 2^128 possibilities
$output = md5($output); // < 2^128 possibilities
$output = md5($output); // < 2^128 possibilities

迭代次数越多，缩减的幅度就越大。

修复

幸运的是，我们有一个简单的方法来解决这个问题:反馈一些东西到进一步的迭代中:

$output = md5($input); // 2^128 possibilities
$output = md5($input . $output); // 2^128 possibilities
$output = md5($input . $output); // 2^128 possibilities
$output = md5($input . $output); // 2^128 possibilities
$output = md5($input . $output); // 2^128 possibilities    

注意，对于$input的每个单独值，进一步的迭代不是2^128。这意味着我们可以生成的$input值仍然会在这条线上发生冲突(因此将在远小于2^128的可能输出上解决或产生共鸣)。但一般情况下，投入美元的理由仍然和单轮融资时一样强烈。

等等，是吗?让我们用ourHash()函数来测试一下。切换到$hash = ourHash($input。$hash);，用于100次迭代:

Hashing 0 => 201
Hashing 1 => 212
Hashing 2 => 199
Hashing 3 => 201
Hashing 4 => 203
Hashing 5 => 205
Hashing 6 => 207
Hashing 7 => 209
Hashing 8 => 211
Hashing 9 => 204
Hashing 10 => 251
Hashing 11 => 147
Hashing 12 => 251
Hashing 13 => 148
Hashing 14 => 253
Hashing 15 => 0
Hashing 16 => 1
Hashing 17 => 2
Hashing 18 => 161
Hashing 19 => 163
Hashing 20 => 147
Hashing 21 => 251
Hashing 22 => 148
Hashing 23 => 253
Hashing 24 => 0
Hashing 25 => 1
Hashing 26 => 2
Hashing 27 => 161
Hashing 28 => 163
Hashing 29 => 8
Hashing 30 => 251
Hashing 31 => 148
Hashing 32 => 253
Hashing 33 => 0
Hashing 34 => 1
Hashing 35 => 2
Hashing 36 => 161
Hashing 37 => 163
Hashing 38 => 8
Hashing 39 => 4
Hashing 40 => 148
Hashing 41 => 253
Hashing 42 => 0
Hashing 43 => 1
Hashing 44 => 2
Hashing 45 => 161
Hashing 46 => 163
Hashing 47 => 8
Hashing 48 => 4
Hashing 49 => 9
Hashing 50 => 253
Hashing 51 => 0
Hashing 52 => 1
Hashing 53 => 2
Hashing 54 => 161
Hashing 55 => 163
Hashing 56 => 8
Hashing 57 => 4
Hashing 58 => 9
Hashing 59 => 11
Hashing 60 => 0
Hashing 61 => 1
Hashing 62 => 2
Hashing 63 => 161
Hashing 64 => 163
Hashing 65 => 8
Hashing 66 => 4
Hashing 67 => 9
Hashing 68 => 11
Hashing 69 => 4
Hashing 70 => 1
Hashing 71 => 2
Hashing 72 => 161
Hashing 73 => 163
Hashing 74 => 8
Hashing 75 => 4
Hashing 76 => 9
Hashing 77 => 11
Hashing 78 => 4
Hashing 79 => 3
Hashing 80 => 2
Hashing 81 => 161
Hashing 82 => 163
Hashing 83 => 8
Hashing 84 => 4
Hashing 85 => 9
Hashing 86 => 11
Hashing 87 => 4
Hashing 88 => 3
Hashing 89 => 17
Hashing 90 => 161
Hashing 91 => 163
Hashing 92 => 8
Hashing 93 => 4
Hashing 94 => 9
Hashing 95 => 11
Hashing 96 => 4
Hashing 97 => 3
Hashing 98 => 17
Hashing 99 => 13
Hashing 100 => 246
Hashing 101 => 248
Hashing 102 => 49
Hashing 103 => 44
Hashing 104 => 255
Hashing 105 => 198
Hashing 106 => 43
Hashing 107 => 51
Hashing 108 => 202
Hashing 109 => 2
Hashing 110 => 248
Hashing 111 => 49
Hashing 112 => 44
Hashing 113 => 255
Hashing 114 => 198
Hashing 115 => 43
Hashing 116 => 51
Hashing 117 => 202
Hashing 118 => 2
Hashing 119 => 51
Hashing 120 => 49
Hashing 121 => 44
Hashing 122 => 255
Hashing 123 => 198
Hashing 124 => 43
Hashing 125 => 51
Hashing 126 => 202
Hashing 127 => 2
Hashing 128 => 51
Hashing 129 => 53
Hashing 130 => 44
Hashing 131 => 255
Hashing 132 => 198
Hashing 133 => 43
Hashing 134 => 51
Hashing 135 => 202
Hashing 136 => 2
Hashing 137 => 51
Hashing 138 => 53
Hashing 139 => 55
Hashing 140 => 255
Hashing 141 => 198
Hashing 142 => 43
Hashing 143 => 51
Hashing 144 => 202
Hashing 145 => 2
Hashing 146 => 51
Hashing 147 => 53
Hashing 148 => 55
Hashing 149 => 58
Hashing 150 => 198
Hashing 151 => 43
Hashing 152 => 51
Hashing 153 => 202
Hashing 154 => 2
Hashing 155 => 51
Hashing 156 => 53
Hashing 157 => 55
Hashing 158 => 58
Hashing 159 => 0
Hashing 160 => 43
Hashing 161 => 51
Hashing 162 => 202
Hashing 163 => 2
Hashing 164 => 51
Hashing 165 => 53
Hashing 166 => 55
Hashing 167 => 58
Hashing 168 => 0
Hashing 169 => 209
Hashing 170 => 51
Hashing 171 => 202
Hashing 172 => 2
Hashing 173 => 51
Hashing 174 => 53
Hashing 175 => 55
Hashing 176 => 58
Hashing 177 => 0
Hashing 178 => 209
Hashing 179 => 216
Hashing 180 => 202
Hashing 181 => 2
Hashing 182 => 51
Hashing 183 => 53
Hashing 184 => 55
Hashing 185 => 58
Hashing 186 => 0
Hashing 187 => 209
Hashing 188 => 216
Hashing 189 => 219
Hashing 190 => 2
Hashing 191 => 51
Hashing 192 => 53
Hashing 193 => 55
Hashing 194 => 58
Hashing 195 => 0
Hashing 196 => 209
Hashing 197 => 216
Hashing 198 => 219
Hashing 199 => 220
Hashing 200 => 248
Hashing 201 => 49
Hashing 202 => 44
Hashing 203 => 255
Hashing 204 => 198
Hashing 205 => 43
Hashing 206 => 51
Hashing 207 => 202
Hashing 208 => 2
Hashing 209 => 51
Hashing 210 => 49
Hashing 211 => 44
Hashing 212 => 255
Hashing 213 => 198
Hashing 214 => 43
Hashing 215 => 51
Hashing 216 => 202
Hashing 217 => 2
Hashing 218 => 51
Hashing 219 => 53
Hashing 220 => 44
Hashing 221 => 255
Hashing 222 => 198
Hashing 223 => 43
Hashing 224 => 51
Hashing 225 => 202
Hashing 226 => 2
Hashing 227 => 51
Hashing 228 => 53
Hashing 229 => 55
Hashing 230 => 255
Hashing 231 => 198
Hashing 232 => 43
Hashing 233 => 51
Hashing 234 => 202
Hashing 235 => 2
Hashing 236 => 51
Hashing 237 => 53
Hashing 238 => 55
Hashing 239 => 58
Hashing 240 => 198
Hashing 241 => 43
Hashing 242 => 51
Hashing 243 => 202
Hashing 244 => 2
Hashing 245 => 51
Hashing 246 => 53
Hashing 247 => 55
Hashing 248 => 58
Hashing 249 => 0
Hashing 250 => 43
Hashing 251 => 51
Hashing 252 => 202
Hashing 253 => 2
Hashing 254 => 51
Hashing 255 => 53

这里仍然有一个大致的模式，但请注意，它并不比我们的底层函数(已经相当弱了)更有模式。

但是请注意，0和3发生了碰撞，尽管它们不是在一次运行中。这是我之前所说的一个应用(对于所有输入的集合，抗碰撞性保持不变，但由于底层算法的缺陷，特定的碰撞路由可能会打开)。

TL博士/节

通过将输入反馈到每次迭代中，我们有效地打破了之前迭代中可能发生的任何冲突。

因此，md5($input。md5(输入)美元);应该(至少在理论上)与md5($input)一样强。

这重要吗?

是的。这也是RFC 2898中PBKDF2取代PBKDF1的原因之一。考虑两个::的内部循环

PBKDF1：

T_1 = Hash (P || S) ,
T_2 = Hash (T_1) ,
...
T_c = Hash (T_{c-1}) 

其中c是迭代计数，P是密码，S是盐

PBKDF2：

U_1 = PRF (P, S || INT (i)) ,
U_2 = PRF (P, U_1) ,
...
U_c = PRF (P, U_{c-1})

PRF实际上只是一个HMAC。但是为了我们的目的，我们假设PRF(P, S) = Hash(P || S)(也就是说，两个输入的PRF是相同的，粗略地说，就是两个输入连接在一起的哈希)。其实不是，但就我们的目的而言是。

因此PBKDF2维护底层哈希函数的抗碰撞性，而PBKDF1则没有。

将所有这些联系在一起:

我们知道迭代哈希的安全方法。事实上:

$hash = $input;
$i = 10000;
do {
   $hash = hash($input . $hash);
} while ($i-- > 0);

通常是安全的。

现在，为了了解我们为什么要哈希它，我们来分析熵的运动。

哈希接受无限集:S(∞)，并产生一个较小的、一致大小的集合S(n)。下一次迭代(假设输入被传递回)将S(∞)再次映射到S(n):

S(∞) -> S(n)
S(∞) -> S(n)
S(∞) -> S(n)
S(∞) -> S(n)
S(∞) -> S(n)
S(∞) -> S(n)

请注意，最终输出的熵值与第一个输出的熵值完全相同。迭代不会“使它更加模糊”。熵是相等的。不存在不可预测性的神奇来源(这是一个伪随机函数，而不是随机函数)。

然而，迭代是有好处的。它人为地使哈希过程变慢。这就是为什么迭代是个好主意。事实上，这是大多数现代密码哈希算法的基本原理(事实上，一遍又一遍地做某事会使它变慢)。

缓慢是好的，因为它正在对抗主要的安全威胁:暴力强制。我们的哈希算法越慢，攻击者就越难攻击从我们这里窃取的密码哈希。这是一件好事!!

我要大胆地说，在某些情况下，它更安全……不过先别给我投反对票!

从数学/密码学的角度来看，它不太安全，我相信其他人会给你一个比我更清楚的解释。

然而，存在大量的MD5哈希数据库，其中更可能包含“密码”文本而不是它的MD5。所以通过双重哈希，你会降低这些数据库的有效性。

当然，如果你使用盐，那么这个优点(缺点?)就消失了。

正如本文中的一些回应所建议的，在某些情况下，它可能会提高安全性，而在其他情况下，它肯定会损害安全性。有一种更好的解决方案肯定会提高安全性。不是将计算哈希的次数翻倍，而是将盐的大小翻倍，或者将哈希中使用的比特数翻倍，或者两者都做!从SHA-245跳到SHA-512。

一次哈希密码是不安全的

不，多重哈希并不是更不安全;它们是安全使用密码的重要组成部分。

迭代散列会增加攻击者尝试候选密码列表中的每个密码所需的时间。您可以轻松地将攻击密码所需的时间从数小时增加到数年。

简单的迭代是不够的

仅仅将哈希输出链接到输入不足以保证安全性。迭代应该在保留密码熵的算法上下文中进行。幸运的是，有几个已经发表的算法已经经过了足够的审查，使他们对自己的设计充满信心。

像PBKDF2这样的良好的密钥派生算法将密码注入到每一轮哈希中，从而减轻了对哈希输出中冲突的担忧。PBKDF2可以按原样用于密码身份验证。Bcrypt使用加密步骤进行密钥推导;这样，如果发现了反向密钥推导的快速方法，攻击者仍然必须完成已知的明文攻击。

如何破解密码

存储的密码需要防止离线攻击。如果密码没有加盐，它们可以被预先计算的字典攻击破坏(例如，使用彩虹表)。否则，攻击者必须花时间为每个密码计算哈希，并查看它是否与存储的哈希匹配。

并非所有密码的可能性都是一样的。攻击者可能会穷尽搜索所有短密码，但他们知道，每增加一个字符，暴力破解成功的几率就会急剧下降。相反，他们使用最可能的密码的有序列表。他们从“password123”开始，逐步使用不太常用的密码。

假设攻击者名单很长，有100亿候选人;再假设一个桌面系统每秒可以计算100万次哈希。如果只使用一次迭代，攻击者可以在不到3小时的时间内测试她的整个列表。但如果只使用2000次迭代，时间就会延长到近8个月。要打败一个更复杂的攻击者——例如，能够下载一个可以利用他们GPU能力的程序的攻击者——你需要更多的迭代。

多少才够?

使用的迭代次数是安全性和用户体验之间的权衡。攻击者可以使用的专用硬件很便宜，但它仍然可以每秒执行数亿次迭代。攻击者系统的性能决定了在给定的迭代次数下需要多长时间才能破解密码。但是您的应用程序不太可能使用这种专用硬件。在不惹恼用户的情况下，您可以执行多少迭代取决于您的系统。

您可能可以在身份验证期间让用户多等待3 / 4秒左右。分析您的目标平台，并使用尽可能多的迭代。我测试过的平台(移动设备上的一个用户，或者服务器平台上的许多用户)可以轻松地支持6万到12万次迭代的PBKDF2，或者成本因子为12或13的bcrypt。

更多的背景

Read PKCS #5 for authoritative information on the role of salt and iterations in hashing. Even though PBKDF2 was meant for generating encryption keys from passwords, it works well as a one-way-hash for password authentication. Each iteration of bcrypt is more expensive than a SHA-2 hash, so you can use fewer iterations, but the idea is the same. Bcrypt also goes a step beyond most PBKDF2-based solutions by using the derived key to encrypt a well-known plain text. The resulting cipher text is stored as the "hash," along with some meta-data. However, nothing stops you from doing the same thing with PBKDF2.

以下是我写的关于这个话题的其他答案:

哈希密码 哈希密码 盐 隐藏的盐 PBKDF2和bcrypt Bcrypt