Hash Function
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The document discusses hash functions and their properties. It defines a hash function as providing a unique fingerprint of a message in the form of a message digest. The key properties are that it is fast to compute the digest, one-way (cannot find original message from digest), and collision-free (cannot find two messages with the same digest). It then describes an easy hash algorithm that breaks messages into blocks and XORs them before discussing the iterative SHA-1 algorithm in more detail.
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![Easy Hash Algorithm
Break m into n-bit blocks, append zeros to get a multiple
of n.
There are L of them, where L =|m|/n
Fast But not very secure.
=
=
ln21
22221
11211
2
1
...
mmm
mmm
mmm
m
m
m
m
ll
n
n
l
[ ]nccc ...21
⇓⇓⇓⇓
⊕⊕⊕⊕
ymm ii ↵=′](https://image.slidesharecdn.com/hashfunction-190206071357/85/Hash-Function-3-320.jpg)
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Hash Function
- 1. Hash Function Prof. Neeraj Bhargava Kapil Chauhan Department of Computer Science School of Engineering & Systems Sciences MDS University, Ajmer
- 2. Hash Functions Goal: To provide a unique “fingerprint” of the message. properties: 1. Fast to compute y from m. 2. One-way: given y = h(m), can’t find any m’ satisfying h(m’) = y easily. 3. Strongly collision-free: Can’t find any m1 != m2 such that h(m1)=h(m2) Message m (long) Message digest, y (Shorter fixed length)Cryptographic hash Function, h
- 3. Easy Hash Algorithm Break m into n-bit blocks, append zeros to get a multiple of n. There are L of them, where L =|m|/n Fast But not very secure. = = ln21 22221 11211 2 1 ... mmm mmm mmm m m m m ll n n l [ ]nccc ...21 ⇓⇓⇓⇓ ⊕⊕⊕⊕ ymm ii ↵=′
- 4. SHA-1: Notation + ↵ ¬ ⊕ ∨ ∧ Bitwise AND Bitwise OR Bitwise XOR Bitwise NOT Left-shift, with wrap-around
- 5. SHA-1: Iterative compression Iterate over all of the L blocks, output a value that is a function of the last output and the latest block: m1 m2 X0 X1 X2 h’ h’ m3 X3 h’ mL XL h’ 3 (X0 is constant)
- 6. SHA-1: Iterative compression Repeat L times until we have compressed the whole message into a single 160-bit vector. m1 m2 X0 X1 X2 h’ h’ m3 X3 h’ mL XL h’ =h(m)
- 7. SHA-1: Iterative compression Repeat L times until we have compressed the whole message into a single 160-bit vector. m1 m2 X0 X1 X2 h’ h’ m3 X3 h’ mL XL h’ =h(m)