Capacity

As explained in Real-World Cryptography

The capacity is the portion of a sponge state reserved from direct input absorption and output extraction that contributes to its security.

Capacity is the part of a sponge state kept apart from direct input absorption and output extraction. It is treated like a secret: increasing it strengthens the construction. section 2.5.2

A sponge divides its permutation state into two portions:

• Rate absorbs input through XOR and supplies output during digest extraction. section 2.5.2
• Capacity remains untouched by the input XOR and contributes to security. section 2.5.2
• The boundary is configurable, so SHA-3 variants use different rate and capacity parameters. section 2.5.2

An eight-bit sponge

For an eight-bit permutation with a five-bit rate, the remaining three bits form the capacity. A five-bit input is XORed only into the rate; the permutation then randomizes the complete state. section 2.5.2

Figure 2.13 The permutation f randomizes an input of size 8 bits into an output of the same size. In a sponge construction, this permutation’s input and output are divided into two parts: the rate (of size r and the capacity (of size c).

Shows how a permutation’s state is divided into rate and capacity. section 2.5.2

How Real-World Cryptography covers it

How deep it goes

Explains the rate-capacity split, input XOR behavior, parameter variation, and security tradeoff without descending into implementation detail.

Examples

Uses an eight-bit permutation divided into a five-bit rate and three-bit capacity.

What it assumes

Assumes familiarity with permutations and introduces the rate-capacity division through a small sponge example.

What you can do after

Evaluate/understand how capacity placement and size affect sponge security.

How it connects

Connects capacity to sponge construction, rate, permutation, XOR, and SHA-3.

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Related concepts

• collision-resistant hash functionconfigures · A collision-resistant hash function is a cryptographic hash function for which finding two distinct inputs with the same output is computationally infeasible.

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.