SHA-3

As explained in Hacking Cryptography

SHA-3 is a standardized family of cryptographic hash algorithms based on a sponge construction.

SHA-3 is a standardized family of cryptographic hash algorithms built from Keccak’s sponge construction. It was selected after NIST’s competition, initiated in response to concerns about SHA-1 and SHA-2. section 6.3.2 section 6.3

A sponge processes input in two phases. During absorption, message blocks are XORed into only the rate portion of an internal state before permutation. During squeezing, output is read from that portion while the state is repeatedly permuted, allowing arbitrary-length output. section 6.3.2

The rate–capacity split determines how the construction handles data and resists collisions:

• Rate (r) identifies the state portion written during absorption and read during squeezing. section 6.3.2
• Capacity (c) remains untouched by external input and output while still being mixed by the permutation; it determines collision resistance. section 6.3.2
• For fixed-length SHA-3 variants, collision resistance is the smaller of half the output size and half the capacity. section 6.3.2

Figure 6.6 Sponge construction has an absorption phase and a squeezing phase.

Use the sponge diagram to trace absorption, permutation, squeezing, and the separation between rate and capacity. section 6.3.2

Table 6.2 SHA-3 family of sponge-based hash functions

Hash function	Output size \(d\) (bits)	Rate \(r\) (bits)	Capacity \(c\) (bits)	Collision resistance (bits)
SHA3-224	224	1152	448	\(\frac{d}{2} = 112\)
SHA3-256	256	1088	512	\(\frac{d}{2} = 128\)
SHA3-384	384	832	768	\(\frac{d}{2} = 192\)
SHA3-512	512	576	1,024	\(\frac{d}{2} = 256\)
SHAKE128	\(d\)	1,344	256	\(min(\frac{d}{2}, \frac{c}{2}) = min(\frac{d}{2}, 128)\)
SHAKE256	\(d\)	1,088	512	\(min(\frac{d}{2}, \frac{c}{2}) = min(\frac{d}{2}, 256)\)

Compare SHA3-224, SHA3-256, SHA3-384, SHA3-512, SHAKE128, and SHAKE256 by output size, rate, capacity, and collision resistance. section 6.3.2

The sponge design contrasts with Merkle–Damgård hashing. SHA-1 and SHA-2 use the older construction and are susceptible to length-extension attacks; sponge-based SHA-3 avoids that weakness. section 7.3 section 6.3

How Hacking Cryptography covers it

How deep it goes

Explains absorption, squeezing, rate, capacity, and collision-resistance calculations, but does not provide implementation code.

Examples

Compares SHA3-224 through SHA3-512 and SHAKE128/256 using output, rate, capacity, and collision-resistance parameters.

What it assumes

Assumes familiarity with cryptographic hashes and introduces sponge terminology while contrasting it with Merkle–Damgård processing.

What you can do after

Evaluate hash constructions by tracing sponge phases, rate-capacity parameters, and exposure to length-extension attacks.

How it connects

Connects SHA-3 to cryptographic hash functions, Keccak, sponge construction, Merkle–Damgård construction, collision resistance, and length-extension attacks.

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Also explained in

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  Software Security for DevelopersSHA-3 is a family of cryptographic hash algorithms standardized with multiple output sizes including 224, 256, 384, and 512 bits.
• 

  liveBookmanning.com
  Real-World CryptographySHA-3 is a standardized family of cryptographic hash functions based on the Keccak sponge construction.

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Related concepts

• sponge constructionimplements · A sponge construction absorbs input into a state through repeated permutation applications and squeezes output from that state, supporting outputs of arbitrary length.
• hash functionkind of · A hash function deterministically maps input data to a value in a bounded output range, commonly for indexing, lookup, comparison, or integrity checking.
• cryptographic hashkind of · A cryptographic hash is a fixed-length digest computed from input data by a deterministic function designed to resist preimage, second-preimage, and collision attacks.
• cryptographic algorithmkind of · A cryptographic algorithm is a mathematical procedure that transforms data or generates cryptographic values to provide security properties such as confidentiality, integrity, or authentication.

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