# SHA-512

May 20, 2023

**SHA-512** (Secure Hash Algorithm 512-bit) is a widely-used cryptographic hash function, which is a part of the SHA-2 (Secure Hash Algorithm 2) family. It was designed by the United States National Security Agency (NSA) and published by the National Institute of Standards and Technology (NIST). SHA-512 is an important tool in computer security, digital signatures, and other applications that require the verification of data integrity. This article provides a comprehensive overview of SHA-512, including its history, algorithm, and applications.

## History

SHA-512, along with the entire SHA-2 family, was first published in 2001 as a Federal Information Processing Standard (FIPS) by NIST. It was introduced as an improvement and successor to the original SHA-1 algorithm, which had shown some weaknesses in the late 1990s. The SHA-2 family consists of six hash functions with digest lengths of 224, 256, 384, and 512 bits, each represented as SHA-224, SHA-256, SHA-384, and SHA-512. The higher the number of bits in the digest, the more secure the hash function is considered to be.

SHA-512 was developed in response to the growing need for stronger cryptographic security and increased resistance to potential attacks. As the computing power of devices continued to improve, the likelihood of successfully launching a brute force or collision attack on the SHA-1 algorithm increased. This led to the development of SHA-512, which offers a higher level of security due to its larger digest size and improved algorithm.

## Algorithm

SHA-512 is based on the Merkle-Damgård construction, a method used to build collision-resistant cryptographic hash functions. It processes input data in chunks of 1024 bits (128 bytes) and produces a fixed-size output, known as the digest or hash, of 512 bits (64 bytes).

At a high level, the SHA-512 algorithm can be summarized in the following steps:

**Preprocessing**: The input data is padded to ensure its length is a multiple of 1024 bits. This involves appending a single ‘1’ bit, followed by a series of ‘0’ bits, and finally a 128-bit block representing the original length of the input data in binary.**Initialization**: The algorithm initializes eight 64-bit state variables, which are derived from the first sixty-four bits of the fractional parts of the square roots of the first eight prime numbers. These state variables are used throughout the hash computation process.**Processing**: The padded input data is divided into 1024-bit blocks, which are then processed in a series of 80 rounds. Each round consists of a series of bitwise operations, modular arithmetic, and logical operations that transform and update the state variables. The operations within each round are designed to ensure non-linearity and to maximize the diffusion of input bits across the entire hash.**Finalization**: After all the input blocks have been processed, the final state variables are concatenated to form the 512-bit hash output.

The security of SHA-512 is primarily based on the high level of complexity and one-way nature of the hash function. It is designed to be computationally expensive to reverse-engineer the input data from the hash, making it highly resistant to preimage attacks. Additionally, the large digest size of SHA-512 significantly reduces the likelihood of collisions, where two different input data produce the same hash.

## Applications

SHA-512 has numerous applications in various fields, including computer security, digital signatures, and data integrity verification. Some common use cases are:

**Password storage**: Storing passwords in plaintext is considered insecure, as attackers could easily access and misuse them. Instead, password hashes are stored using cryptographic hash functions like SHA-512. When a user attempts to log in, their input password is hashed using the same algorithm, and the resulting hash is compared to the stored hash. If the hashes match, the password is considered correct.**Digital signatures**: Digital signatures use public-key cryptography to authenticate the sender and verify the integrity of a message. The message is first hashed using a cryptographic hash function, such as SHA-512, and then encrypted using the sender’s private key. The recipient can then decrypt the signature using the sender’s public key and compare the resulting hash with their own computed hash of the message. If the hashes are identical, it confirms that the message is authentic and has not been tampered with.**Data integrity**: Cryptographic hash functions can be used to ensure the integrity of data transmitted over a network or stored on a device. By computing the hash of the original data and comparing it to the hash of the received or retrieved data, one can determine if the data has been altered, corrupted, or tampered with.**File verification**: Software developers often provide a SHA-512 hash alongside their software downloads. Users can verify the downloaded file’s integrity by computing its hash and comparing it to the provided hash, ensuring that the file has not been corrupted or tampered with during transmission.