Compression function

As explained in Hacking Cryptography

A function that combines a fixed-size message block with a fixed-size state to produce a new fixed-size state in an iterative hash construction.

A compression function combines one fixed-size message block with the previous fixed-size state, producing the next state in an iterative hash construction. In a Merkle–Damgård design, padded input is divided into equal-length blocks and processed sequentially until the final state becomes the hash value. section 6.3.1

The processing pattern is:

• Pad the input and divide it into equal-length message blocks. section 6.3.1
• Apply the compression function to the current block and previous state. section 6.3.1
• Repeat for every block, using the resulting state as the next input state. section 6.3.1
• Output the final state as the hash digest in a Merkle–Damgård construction. section 6.5

This role distinguishes compression functions from sponge permutations. A sponge absorbs input by XORing blocks with only its rate portion before applying a permutation; its untouched capacity contributes to collision resistance. section 6.3.2

Figure 6.5 The Merkle–Damgård construction for hash functions

Trace how message blocks and successive internal states flow through the Merkle–Damgård construction. section 6.3.1

How Hacking Cryptography covers it

How deep it goes

Defines sequential state updates and contrasts sponge processing, without detailing the internal round function of a specific hash.

Examples

Uses MD5, SHA-1, SHA-256, and SHA-512 as Merkle–Damgård hash-function examples.

What it assumes

Assumes fixed-size blocks, padding, and hash state; distinguishes these from sponge rate, capacity, and permutation processing.

What you can do after

Evaluate/understand how iterative hash constructions transform message blocks into successive internal states.

How it connects

Connects Merkle–Damgård construction, hash functions, sponge construction, collision resistance, and length-extension attacks.

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Also explained in

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  Real-World CryptographyA compression function maps two inputs to one output whose size is the size of one input, thereby reducing represented data size.

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Related concepts

• Merkle–Damgård constructionused by · The Merkle–Damgård construction builds an arbitrary-length hash function by iteratively applying a fixed-size compression function to padded message blocks.
• compressionimplements · Compression is the transformation of information into a more compact representation to reduce storage or transmission requirements while retaining information needed for recovery or use.

This explainer was generated by Manning's knowledge graph from the text of Hacking Cryptography. The section links point to the parts of the book it draws on.