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10 | 10 |
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11 | 11 | <p> |
12 | 12 | A strong cryptographic hash function should be resistant to: |
13 | | - <ul> |
14 | | - <li> |
15 | | - <b>Pre-image attacks</b>. If you know a hash value <code>h(x)</code>, |
16 | | - you should not be able to easily find the input <code>x</code>. |
17 | | - </li> |
18 | | - <li> |
19 | | - <b>Collision attacks</b>. If you know a hash value <code>h(x)</code>, |
20 | | - you should not be able to easily find a different input |
21 | | - <code>y</code> |
22 | | - with the same hash value <code>h(x) = h(y)</code>. |
23 | | - </li> |
24 | | - <li> |
25 | | - <b>Brute force</b>. For passwords and other data with limited |
26 | | - input space, if you know a hash value <code>h(x)</code> |
27 | | - you should not be able to find the input <code>x</code> even using |
28 | | - a brute force attack (without significant computational effort). |
29 | | - </li> |
30 | | - </ul> |
31 | 13 | </p> |
| 14 | + <ul> |
| 15 | + <li> |
| 16 | + <b>Pre-image attacks</b>. If you know a hash value <code>h(x)</code>, |
| 17 | + you should not be able to easily find the input <code>x</code>. |
| 18 | + </li> |
| 19 | + <li> |
| 20 | + <b>Collision attacks</b>. If you know a hash value <code>h(x)</code>, |
| 21 | + you should not be able to easily find a different input |
| 22 | + <code>y</code> |
| 23 | + with the same hash value <code>h(x) = h(y)</code>. |
| 24 | + </li> |
| 25 | + <li> |
| 26 | + <b>Brute force</b>. For passwords and other data with limited |
| 27 | + input space, if you know a hash value <code>h(x)</code> |
| 28 | + you should not be able to find the input <code>x</code> even using |
| 29 | + a brute force attack (without significant computational effort). |
| 30 | + </li> |
| 31 | + </ul> |
32 | 32 |
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33 | 33 | <p> |
34 | 34 | As an example, both MD5 and SHA-1 are known to be vulnerable to collision attacks. |
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51 | 51 |
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52 | 52 | <p> |
53 | 53 | Ensure that you use a strong, modern cryptographic hash function, such as: |
54 | | - <ul> |
55 | | - <li> |
56 | | - Argon2, scrypt, bcrypt, or PBKDF2 for passwords and other data with limited input space where |
57 | | - a dictionary-like attack is feasible. |
58 | | - </li> |
59 | | - <li> |
60 | | - SHA-2, or SHA-3 in other cases. |
61 | | - </li> |
62 | | - </ul> |
63 | 54 | </p> |
64 | 55 |
|
| 56 | + <ul> |
| 57 | + <li> |
| 58 | + Argon2, scrypt, bcrypt, or PBKDF2 for passwords and other data with limited input space where |
| 59 | + a dictionary-like attack is feasible. |
| 60 | + </li> |
| 61 | + <li> |
| 62 | + SHA-2, or SHA-3 in other cases. |
| 63 | + </li> |
| 64 | + </ul> |
| 65 | + |
65 | 66 | <p> |
66 | 67 | Note that special purpose algorithms, which are used to ensure that a message comes from a |
67 | 68 | particular sender, exist for message authentication. These algorithms should be used when |
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