## About SHA512 hash

SHA-512 (Secure Hash Algorithm 512-bit) is a cryptographic hash function belonging to the SHA-2 family, designed by the National Security Agency (NSA) and published by the National Institute of Standards and Technology (NIST) in 2001. It is widely used for secure hashing in various applications, offering a high level of security due to its larger 512-bit hash output.

### Characteristics of SHA-512

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

**Input Padding**:- The input message is padded so that its length is congruent to 896 modulo 1024. Padding involves appending a single '1' bit, followed by '0' bits until the message length is 128 bits short of a multiple of 1024. The length of the original message (before padding) is then appended as a 128-bit integer.

**Processing in Blocks**:- SHA-512 processes the input message in 1024-bit (128-byte) blocks.

**Initialization Vector (IV)**:- SHA-512 starts with a predefined initial state composed of eight 64-bit words:
- H0 = 0x6A09E667F3BCC908
- H1 = 0xBB67AE8584CAA73B
- H2 = 0x3C6EF372FE94F82B
- H3 = 0xA54FF53A5F1D36F1
- H4 = 0x510E527FADE682D1
- H5 = 0x9B05688C2B3E6C1F
- H6 = 0x1F83D9ABFB41BD6B
- H7 = 0x5BE0CD19137E2179

- SHA-512 starts with a predefined initial state composed of eight 64-bit words:
**Compression Function**:- The SHA-512 compression function involves 80 rounds of processing for each 1024-bit block. Each round uses different logical functions, constants, and message schedule operations:
- Logical functions include bitwise operations (AND, OR, XOR, NOT), additions, and shifts/rotations.
- Constants are derived from the first 64 bits of the fractional parts of the cube roots of the first 80 prime numbers.

- The SHA-512 compression function involves 80 rounds of processing for each 1024-bit block. Each round uses different logical functions, constants, and message schedule operations:

### Algorithm Steps

**Initialization**:- Initialize the state variables (H0 to H7) to the predefined values.

**Padding**:- Pad the input message according to the specified padding rules.

**Processing**:- Divide the padded message into 1024-bit blocks.
- For each block, perform the 80 iterations of the compression function, updating the state variables.

**Output**:- After processing all blocks, concatenate the state variables to produce the final 512-bit hash value.

### Security and Usage

**Security**:**Collision Resistance**: SHA-512 provides strong collision resistance due to its large output size, making it extremely difficult for two different inputs to produce the same hash output.**Preimage Resistance**: SHA-512 is resistant to preimage attacks, ensuring that it is computationally infeasible to find an input that hashes to a given output.**Second-Preimage Resistance**: SHA-512 also offers strong resistance to second-preimage attacks, ensuring that it is difficult to find a second input with the same hash as a given input.- SHA-512's large output size provides a significant security margin compared to shorter hash functions.

**Usage**:- SHA-512 is used in various security-critical applications where strong security assurances are required, including digital signatures, SSL/TLS certificates, password hashing, and data integrity verification.
- It is particularly suitable for applications that handle sensitive data and require robust protection against cryptographic attacks.

### Summary

SHA-512 is a cryptographic hash function in the SHA-2 family that produces a 512-bit hash value. It offers strong security properties, including resistance to collisions, preimage attacks, and second-preimage attacks. SHA-512 is widely adopted in both software and hardware implementations for its robustness and effectiveness in ensuring data integrity and authenticity in security-critical applications. Its large output size and strong security guarantees make it a preferred choice for modern cryptographic needs.