Properties of Hash Functions

In order to be an effective cryptographic tool, the hash function is desired to possess following properties −

• Pre-Image Resistance
  • This property means that it should be computationally hard to reverse a hash function.
  • In other words, if a hash function h produced a hash value z, then it should be a difficult process to find any input value x that hashes to z.
  • This property protects against an attacker who only has a hash value and is trying to find the input.
• Second Pre-Image Resistance
  • This property means given an input and its hash, it should be hard to find a different input with the same hash.
  • In other words, if a hash function h for an input x produces hash value h(x), then it should be difficult to find any other input value y such that h(y) = h(x).
  • This property of hash function protects against an attacker who has an input value and its hash, and wants to substitute different value as legitimate value in place of original input value.
• Collision Resistance
  • This property means it should be hard to find two different inputs of any length that result in the same hash. This property is also referred to as collision free hash function.
  • In other words, for a hash function h, it is hard to find any two different inputs x and y such that h(x) = h(y).
  • Since, hash function is compressing function with fixed hash length, it is impossible for a hash function not to have collisions. This property of collision free only confirms that these collisions should be hard to find.
  • This property makes it very difficult for an attacker to find two input values with the same hash.
  • Also, if a hash function is collision-resistant then it is second pre-image resistant.

Design of Hashing Algorithms

At the heart of a hashing is a mathematical function that operates on two fixed-size blocks of data to create a hash code. This hash function forms the part of the hashing algorithm.

The size of each data block varies depending on the algorithm. Typically the block sizes are from 128 bits to 512 bits. The following illustration demonstrates hash function −

Hashing algorithm involves rounds of above hash function like a block cipher. Each round takes an input of a fixed size, typically a combination of the most recent message block and the output of the last round.

This process is repeated for as many rounds as are required to hash the entire message. Schematic of hashing algorithm is depicted in the following illustration −

Since, the hash value of first message block becomes an input to the second hash operation, output of which alters the result of the third operation, and so on. This effect, known as an avalanche effect of hashing.

Avalanche effect results in substantially different hash values for two messages that differ by even a single bit of data.

Understand the difference between hash function and algorithm correctly. The hash function generates a hash code by operating on two blocks of fixed-length binary data.

Hashing algorithm is a process for using the hash function, specifying how the message will be broken up and how the results from previous message blocks are chained together.