## About SHA3-512 hash

SHA3-512 is a cryptographic hash function that belongs to the SHA-3 (Secure Hash Algorithm 3) family, standardized by the National Institute of Standards and Technology (NIST) in 2015. It is designed to provide a 512-bit hash output, offering a high level of security and resistance to cryptanalytic attacks.

### Characteristics of SHA3-512

**Fixed-Length Output**:- SHA3-512 produces a fixed-length output of 512 bits (64 bytes), regardless of the input data's length.

**Input Padding**:- SHA3-512, like other SHA-3 variants, uses a padding scheme that involves appending a single '1' bit followed by a series of '0' bits to the input message. The padding ensures that the message length is a multiple of the block size required by the permutation function.

**Processing in Blocks**:- SHA3-512 uses a permutation-based sponge construction. The input message is divided into blocks, and each block is processed iteratively through a permutation function.

**Initialization**:- SHA3-512 has an internal state of 1600 bits, organized into a 5x5 matrix of 64-bit lanes. This state is initialized to a fixed value before processing begins.

**Compression Function**:- SHA3-512 employs the Keccak-f permutation function, which operates on the internal state in rounds. During each round, the bits of the internal state are mixed and transformed according to a set of defined rules.

### Algorithm Steps

**Initialization**:- Initialize the internal state and set parameters such as the rate and capacity of the sponge construction.

**Absorbing Phase**:- Absorb the input message by XORing it with portions of the internal state and applying the permutation function iteratively.

**Squeezing Phase**:- Extract the hash value from the final state after all input blocks have been absorbed. This is done by reading out the desired number of bits from the internal state.

**Output**:- The final output is the 512-bit hash value derived from the squeezing phase of the sponge construction.

### Security and Usage

**Security**:- SHA3-512 is designed to provide strong security properties against collision attacks, preimage attacks, and second-preimage attacks. Its sponge construction and use of the Keccak-f permutation function ensure robust resistance against cryptanalytic attacks.

**Usage**:- SHA3-512 is suitable for various cryptographic applications where a 512-bit hash value is needed, such as digital signatures, message authentication codes (MACs), and integrity verification.
- It is particularly recommended in environments where the use of SHA-3 for cryptographic hashing is preferred over SHA-2 due to specific security requirements or considerations, especially when a larger hash output is desired.

### Summary

SHA3-512 is a cryptographic hash function standardized by NIST as part of the SHA-3 family. It produces a fixed-length hash value of 512 bits using a sponge construction with the Keccak-f permutation function. SHA3-512 offers strong security properties and is suitable for applications requiring high security assurances and larger hash outputs. Its adoption continues to grow in security-critical systems due to its design and robustness against cryptographic attacks.