1. Cryptographic Hash Functions Prepared by Dr. Lamiaa Elshenawy
Computer Security
Lecture 6
Ch.11
Cryptographic Hash Functions
Prepared by Dr. Lamiaa Elshenawy

2. 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

3. Cryptographic Hash Functions Key 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)

4. Cryptographic Hash Functions
Hash function Computationally infeasible
One-way property
Collision-free property
Data Integrity H
“Hash function” M
H(M)

5. Cryptographic Hash Functions Block diagram

6. Cryptographic Hash Functions Applications
Message Authentication
Digital Signatures
Other Applications (Internet protocols)

7. Cryptographic Hash Functions Message Authentication
Message authentication Mechanism or service used to verify the integrity of a message.
No modification
No insertion
No deletion
No replay

8. Cryptographic Hash Functions Message Authentication
Confidentiality
No Confidentiality

9. Cryptographic Hash Functions Message Authentication
Confidentiality

10. Cryptographic Hash Functions Message 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

11. Cryptographic Hash Functions Message Authentication
MAC: message authentication code (keyed hash function)
M: variable-length message
K: secret key K
Output: fixed-size

12. Cryptographic Hash Functions Digital Signatures
Private key H
“Hash function” M
H(M)
Encryption algorithm
Public key

13. Cryptographic Hash Functions Digital Signatures

14. Cryptographic Hash Functions 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

15. Cryptographic Hash Functions Digital Signatures

16. Cryptographic Hash Functions Other Applications
One-way password file
Intrusion detection
Virus detection
Pseudorandom function(PRF) or a Pseudorandom number generator (PRNG).

17. Cryptographic Hash Functions Password

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

19. Cryptographic Hash Functions Two Simple Hash Functions
Rotated exclusive-OR (XOR) of every block
Initially set the -bit hash value to zero.
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.

20. Cryptographic Hash Functions Requirements and Security

21. Cryptographic Hash Functions Second Preimage Resistant

22. Cryptographic Hash Functions Second Preimage Resistant

23. Cryptographic Hash Functions Requirements and Security
Brute-force attacks bit length (hash value)
Cryptanalysis weaknesses in cryptographic algorithm

24. Cryptographic Hash Functions Brute-Force Attacks
Preimage and second preimage attacks
y H(y)=h
Collision resistant attacks y
H(y)
Birthday paradox

25. Cryptographic Hash Functions Brute-Force Attacks
m: number of hash value bits

26. Cryptographic Hash Functions Cryptanalysis
Merkle–Damgård hash function

27. Cryptographic Hash Functions Cryptanalysis

28. Cryptographic Hash Functions Secure Hash Algorithm(SHA)
National Institute of Standards and Technology (NIST)- Federal information processing standard (FIPS 180)-1993
SHA (1993)
SHA (1995)
SHA-256
SHA (2002)
SHA-512

29. Cryptographic Hash Functions Secure Hash Algorithm(SHA)

30. Cryptographic Hash Functions SHA-512 Logic

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

33. Cryptographic Hash Functions SHA-512 Logic

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

35. Cryptographic Hash Functions SHA-512 Round Function

36. Cryptographic Hash Functions SHA-512 Round Function

37. Cryptographic Hash Functions SHA-512 Round Function

38. Cryptographic Hash Functions SHA-512 Round Function

39. Cryptographic Hash Functions SHA-3
SHA-1& SHA 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)

40. Length=24 bits=18 hexadecimal
Example
Length=24 bits=18 hexadecimal
ASCII code
M=“abc”
1024-bit massage
Padding bits=896-24=871

41. Cryptographic Hash Functions Example

42. Cryptographic Hash Functions Example
After two rounds

43. Example
After 80 rounds
Hash value

44. Example
512-bit message digest
Finally

45. Thank you for your attention