Introduction to Hash Functions

Study Notes

Hash Functions

Hash functions create a fixed-length hash value from a variable-length message.
The hash value is appended to the message at the source.
The receiver recomputes the hash value to authenticate the message.
Hash functions aren't typically considered secret, requiring additional measures for protection.

Hash Function Requirements

A hash function can be applied to any-sized data block.
It produces a fixed-length output for any given input.
Calculating the hash value (H(x)) for a given input (x) is relatively quick.
It's computationally infeasible to determine the original input (x) from the hash value (h), given only h. This is one-way.
It's computationally infeasible to find two different inputs (x and y) that produce the same hash value (H(x) = H(y)). This is known as weak collision resistance.
It's computationally infeasible to find two different inputs (x and y) that produce the same hash value. This is known as strong collision resistance.

Weak and Strong Collision Resistance

Weak Collision Resistance: Given an input (X) and a hashing function (H()), it's very difficult to find another input (X') that produces the same hash value (H(X) = H(X')).
Strong Collision Resistance: Given a hashing function (H()) and two arbitrary inputs (X and Y), it's highly unlikely that they will produce the same hash value (H(X) = H(Y)).

Basic Uses of Hash Function

Method (a): Encrypting the message plus the hash code
- Source A and Destination B share a secret key (K).
- The message is encrypted before it’s transmitted.
- The hash value is also calculated and created.
- The encrypted message and the calculated hash value are transmitted together.
- Destination B recalculates the hash value using the received message. If the hash value matches the one transmitted, the message is authenticated and trusted.
Method (b): Encrypting the hash code using a shared secret key
- The receiver (B) does not decrypt the entire message, only the hash code
- Source and Destination share a secret key
- The hash code is encrypted before it's transmitted
- The message and the encrypted hash code are transmitted together.
- This provides authentication as long as only Source A and Destination B share the key.
Method (c): Encrypting the hash code using a sender's private key
- The hash code is encrypted using the source's private key.
- Provides both authentication and a digital signature
- Only the owner of the private key can generate this encrypted hash code for the message. Hence, only that sender can truly be attributed to the message.
Method (d): Encrypting the result of method(c) with a shared secret key
- Source (A) calculates the hash code and encrypts it using its Private Key (PR).
- This encrypted value is then combined with the original message and encrypted further using a shared secret key between source A and destination B.
- Offers confidentiality on top of authentication.
Method (e): Computing hash code of message plus secret value
- Source and Destination share a secret (S)
- The message and secret are combined, then hashed.
- Only parties sharing the secret can create and verify the hash.
Method (f): Encrypting the result of method (e):
- Uses a shared secret key (K) to encrypt the result (message + hash + shared secret) for confidentiality and integrity. This is a form of encryption to ensure only the intended recipient can read the data.