Introduction to Hash Functions

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.