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Computer Security
Lecture 6Ch.11
Cryptographic Hash FunctionsPrepared by Dr. Lamiaa Elshenawy
Cryptographic Hash Functions
• 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 FunctionsKey Points
• Hash function Variable-length message Fixed-length message digest
• Cryptographic hash functions iterative use of a compression function
• Compression function
Specific function (SHA)
Symmetric block cipher (Whirlpool)
Cryptographic Hash Functions
• Hash function Computationally infeasible
One-way property Collision-free property
H“Hash function”M H(M)
Data Integrity
Cryptographic Hash FunctionsBlock diagram
Cryptographic Hash FunctionsApplications
1. Message Authentication2. Digital Signatures3. Other Applications (Internet protocols)
Cryptographic Hash FunctionsMessage Authentication
• Message authentication Mechanism or service used to verify the integrity of a message.
No modificationNo insertionNo deletionNo replay
Cryptographic Hash FunctionsMessage Authentication
Confidentiality
No Confidentiality
Cryptographic Hash FunctionsMessage Authentication
Confidentiality
Cryptographic Hash FunctionsMessage Authentication
• 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
Cryptographic Hash FunctionsMessage Authentication
M: variable-length message K: secret key KOutput: fixed-size
MAC: message authentication code (keyed hash function)
Cryptographic Hash FunctionsDigital Signatures
Public key
H“Hash
function”M H(M)
Encryption algorithm
Private key
Cryptographic Hash FunctionsDigital Signatures
Cryptographic Hash FunctionsDigital 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 codeencrypted using a symmetric secret key
Cryptographic Hash FunctionsDigital Signatures
Cryptographic Hash FunctionsOther Applications
1. One-way password file2. Intrusion detection3. Virus detection4. Pseudorandom function(PRF) or a
Pseudorandom number generator (PRNG).
Cryptographic Hash FunctionsPassword
Cryptographic Hash FunctionsTwo Simple Hash Functions
1. Bit-by-Bit exclusive-OR (XOR) of every block
Cryptographic Hash FunctionsTwo Simple Hash Functions
2. Rotated exclusive-OR (XOR) of every blocki. 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.
Cryptographic Hash FunctionsRequirements and Security
Cryptographic Hash FunctionsSecond Preimage Resistant
Cryptographic Hash FunctionsSecond Preimage Resistant
Cryptographic Hash FunctionsRequirements and Security
1. Brute-force attacks bit length (hash value)
2. Cryptanalysis weaknesses in cryptographic algorithm
Cryptographic Hash FunctionsBrute-Force Attacks
• Preimage and second preimage attacks
y H(y)=h
• Collision resistant attacks
y H(y)
Birthday paradox
Cryptographic Hash FunctionsBrute-Force Attacks
m: number of hash value bits
Cryptographic Hash FunctionsCryptanalysis
Merkle–Damgård hash function
Cryptographic Hash FunctionsCryptanalysis
Cryptographic Hash FunctionsSecure Hash Algorithm(SHA)
• National Institute of Standards and Technology (NIST)- Federal information processing standard (FIPS 180)-1993
SHA-0 (1993)SHA-1 (1995)SHA-256SHA-384 (2002)SHA-512
Cryptographic Hash FunctionsSecure Hash Algorithm(SHA)
Cryptographic Hash FunctionsSHA-512 Logic
Cryptographic Hash FunctionsSHA-512 Logic
1. Append padding bits (length896 mod 1024)2. Append length (128 bits=16 bytes)3. Initialize hash buffer
4. Process message in 1024-bit blocks5. Output 80
rounds
Cryptographic Hash FunctionsSHA-512 Logic
Cryptographic Hash FunctionsSHA-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
Cryptographic Hash FunctionsSHA-512 Round Function
Cryptographic Hash FunctionsSHA-512 Round Function
Cryptographic Hash FunctionsSHA-512 Round Function
Cryptographic Hash FunctionsSHA-512 Round Function
Cryptographic Hash FunctionsSHA-3
• SHA-1& SHA-2 Not broken • NIST competition (2007) SHA-3Replace 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)
Example
M=“abc”
ASCII code
Padding bits=896-24=871
Length=24 bits=18 hexadecimal
1024-bit massage
Cryptographic Hash FunctionsExample
Cryptographic Hash FunctionsExample
After two rounds
Example
After 80 rounds
Hash value
Example
512-bit message digest Finally
Thank you for your attention
