Hash Function

information security

1. 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

2. 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

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

4. Cryptographic Hash Functions Block diagram

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

6. 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

7. Cryptographic Hash Functions Message Authentication Confidentiality No Confidentiality

8. Cryptographic Hash Functions Message Authentication Confidentiality

9. 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

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

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

12. Cryptographic Hash Functions Digital Signatures

13. 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

14. Cryptographic Hash Functions Digital Signatures

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

16. Cryptographic Hash Functions Password

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

18. 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.

19. Cryptographic Hash Functions Requirements and Security

20. Cryptographic Hash Functions Second Preimage Resistant

21. Cryptographic Hash Functions Second Preimage Resistant

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

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

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

25. Cryptographic Hash Functions Cryptanalysis Merkle – Damgård hash function

26. Cryptographic Hash Functions Cryptanalysis

27. Cryptographic Hash Functions 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

28. Cryptographic Hash Functions Secure Hash Algorithm(SHA)

29. Cryptographic Hash Functions SHA-512 Logic

30. 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

31. Cryptographic Hash Functions SHA-512 Logic

32. Cryptographic Hash Functions SHA-512 Logic Let 32 bit quantity 90AB12CD 16 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

33. Cryptographic Hash Functions SHA-512 Round Function

34. Cryptographic Hash Functions SHA-512 Round Function

35. Cryptographic Hash Functions SHA-512 Round Function

36. Cryptographic Hash Functions SHA-512 Round Function

37. Cryptographic Hash Functions 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)

38. Thank you for your attention