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

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

Cryptographic Hash Functions Block diagram

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

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

Cryptographic Hash Functions Message Authentication Confidentiality No Confidentiality

Cryptographic Hash Functions Message Authentication Confidentiality

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

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

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

Cryptographic Hash Functions Digital Signatures

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

Cryptographic Hash Functions Digital Signatures

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

Cryptographic Hash Functions Password

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

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.

Cryptographic Hash Functions Requirements and Security

Cryptographic Hash Functions Second Preimage Resistant

Cryptographic Hash Functions Second Preimage Resistant

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

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

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

Cryptographic Hash Functions Cryptanalysis Merkle–Damgård hash function

Cryptographic Hash Functions Cryptanalysis

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

Cryptographic Hash Functions Secure Hash Algorithm(SHA)

Cryptographic Hash Functions SHA-512 Logic

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

Cryptographic Hash Functions SHA-512 Logic

Cryptographic Hash Functions SHA-512 Logic Let 32 bit quantity 90AB12CD16 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

Cryptographic Hash Functions SHA-512 Round Function

Cryptographic Hash Functions SHA-512 Round Function

Cryptographic Hash Functions SHA-512 Round Function

Cryptographic Hash Functions SHA-512 Round Function

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)

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

Cryptographic Hash Functions Example

Cryptographic Hash Functions Example After two rounds

Example After 80 rounds Hash value

Example 512-bit message digest Finally

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