Hash Function

• Applications of Cryptographic Hash Functions
 Message Authentication
 Digital Signatures
 Other Applications
• Two Simple Hash Functions
• Requirements and Security
 Security Requirements for Cryptographic Hash Functions
 Brute-Force Attacks
 Cryptanalysis
• Hash Functions Based on Cipher Block Chaining
• Secure Hash Algorithm (SHA)
 SHA-512 Logic
 SHA-512 Round Function
• 11.6 SHA-3

Cryptographic Hash Functions
Key Points
• Hash function Variable-length message
Fixed-length message digest
h=H(M)
• Cryptographic hash functions iterative use
of a compression function

• Hash function
 One-way property
 Collision-free property
H
“Hash function”
M H(M)
Data Integrity
Computationally infeasible

Block diagram

Applications
1. Message Authentication
2. Digital Signatures
3. Other Applications (Internet protocols)

Message Authentication
• Message authentication
Mechanism or service used to verify the
integrity of a message.
No modification
No insertion
No deletion
No replay

Confidentiality
No
Confidentiality

Confidentiality

• No confidentiality: method (b) has an
advantage over methods (a) and (d)
less computation
• Avoid encryption method (c)
 Encryption software relatively slow
 Encryption hardware high cost
 Time high
 Encryption algorithms patents cost

M: variable-length message
K: secret key K
Output: fixed-size
MAC: message authentication code (keyed hash function)

Digital Signatures
Public key
H
“Hash
function”
M H(M)
Encryption
algorithm
Private
key

Digital Signatures

Digital Signatures
• Digital signature private-key-
encrypted hash code authentication
(only the sender could have produced the
encrypted hash code, essence of the digital
signature technique)
• Confidentiality + Digital signature
message + private-key-encrypted hash code
encrypted using a symmetric secret key

Other Applications
1. One-way password file
2. Intrusion detection
3. Virus detection
4. Pseudorandom function(PRF) or a
Pseudorandom number generator
(PRNG).

Password

Two Simple Hash Functions
1. Bit-by-Bit exclusive-OR (XOR) of every block

Two Simple Hash Functions
2. Rotated exclusive-OR (XOR) of every block
i. Initially set the -bit hash value to zero.
ii. Process each successive -bit block of data as
follows:
a. Rotate the current hash value to the left
by one bit.
b. XOR the block into the hash value.

Requirements and Security

Second Preimage Resistant

Requirements and Security
1. Brute-force attacks bit length
(hash value)
2. Cryptanalysis weaknesses in
cryptographic algorithm

Brute-Force Attacks
• Preimage and second preimage attacks
y H(y)=h
• Collision resistant attacks
y H(y)
Birthday
paradox

Brute-Force Attacks
m: number of hash value bits

Cryptanalysis
Merkle–Damgård hash function

Cryptanalysis

Secure Hash Algorithm(SHA)
• National Institute of Standards and
Technology (NIST)- Federal information
processing standard (FIPS 180)-1993
SHA-0 (1993)
SHA-1 (1995)
SHA-256
SHA-384 (2002)
SHA-512

Secure Hash Algorithm(SHA)

SHA-512 Logic

SHA-512 Logic
1. Append padding bits (length≡896 mod 1024)
2. Append length (128 bits=16 bytes)
3. Initialize hash buffer
4. Process message in 1024-bit blocks
5. Output 80
rounds

SHA-512 Logic
• Let 32 bit quantity 90AB12CD16
• 4 bytes are: 90, AB, 12, CD
• Two ways to store in memory
Address Value
1000 90
1001 AB
1002 12
1003 CD
Address Value
1000 CD
1001 12
1002 AB
1003 90
Big -
endian
Little -
endian

SHA-512 Round Function

SHA-3
• SHA-1& SHA-2 Not broken
• NIST competition (2007) SHA-3
Replace SHA-2 with SHA-3 in any application by
a simple drop-in substitution.
Preserve online nature (SHA-2) small
blocks (no buffer-entire message)

Hash Function

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