Compression function

As explained in Real-World Cryptography

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

A compression function takes two inputs and produces one output whose size matches one input. In plain terms, it turns more represented data into less. section 2.5.1

Within SHA-2, the function works as part of a larger sequence:

• A Davies–Meyer construction builds the function from a block cipher. section 2.5.1
• Merkle–Damgård first pads a message and cuts it into fixed-size blocks. section 2.5.1
• It then applies the compression function repeatedly, feeding each previous output into the next call. section 2.5.1

Figure 2.7 A compression function takes two different inputs of size X and Y (here both 16 bytes) and returns an output of size either X or Y.

A size diagram makes the input-to-output reduction concrete before the construction details become more involved. section 2.5.1

How Real-World Cryptography covers it

How deep it goes

Defines the size reduction and outlines Davies–Meyer and Merkle–Damgård, but defers block-cipher details.

Examples

Uses a size diagram, an eight-byte block padding example, and an iterative compression diagram.

What it assumes

Assumes basic hashing context and introduces XOR, while deferring block-cipher understanding.

What you can do after

Evaluate how SHA-2 transforms padded message blocks into a digest through repeated compression.

How it connects

Connects compression functions with SHA-2, block ciphers, Davies–Meyer, Merkle–Damgård, padding, and XOR.

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Also explained in

• 

  liveBookmanning.com
  Hacking CryptographyA 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.

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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 Real-World Cryptography. The section links point to the parts of the book it draws on.