About SHA-224

Detailed History of SHA-224 Development

SHA-224 emerged as part of the broader development of the SHA-2 family of cryptographic hash functions, which was initiated in response to growing security concerns about SHA-1. Here's the timeline of its development and standardization:

Origins of the SHA Family

The Secure Hash Algorithm (SHA) family began with SHA-0, which was published by the National Institute of Standards and Technology (NIST) in 1993. After cryptographic weaknesses were discovered in SHA-0, it was quickly replaced by SHA-1 in 1995.

Development of SHA-2

As computational power increased and cryptanalytic techniques advanced in the late 1990s and early 2000s, concerns about the long-term security of SHA-1 grew. In response, the National Security Agency (NSA) designed the SHA-2 family of hash functions, which includes SHA-224, SHA-256, SHA-384, and SHA-512.

Introduction of SHA-224

SHA-224 was first published in 2004 as part of FIPS PUB 180-2 by NIST. It was specifically designed to provide a security level compatible with 112-bit symmetric key cryptography, which was a common requirement for many applications at that time.

Standardization and Adoption

After its publication, SHA-224 was quickly adopted in various cryptographic standards and protocols. It became particularly popular in environments where space efficiency was a concern but robust security was still required. SHA-224's relationship to SHA-256 (it uses the same algorithm with different initialization vectors and truncates the result) made it relatively easy to implement in systems that already supported SHA-256.

Current Status

The most recent version of the standard, FIPS PUB 180-4 (published in 2015), still includes SHA-224 as part of the approved hash algorithms. While newer hash functions like those in the SHA-3 family have been standardized, SHA-224 remains widely used and is considered secure for most applications.

Relationship to SHA-256

SHA-224 is intimately related to SHA-256, sharing most of its design elements but with key differences that give it its unique properties:

Shared Algorithm

SHA-224 uses the same core algorithm as SHA-256, including:

• The same message padding scheme
• The same message schedule expansion procedure
• The same compression function
• The same round constants (K values)
• The same block size (512 bits)

Key Differences

Despite these similarities, SHA-224 differs from SHA-256 in two crucial ways:

1. Different Initial Hash Values (H0): SHA-224 uses a distinct set of initialization vectors compared to SHA-256, which ensures that the hash outputs are completely different even for the same input.
2. Truncated Output: While SHA-256 produces a 256-bit (32-byte) output, SHA-224 truncates its result to 224 bits (28 bytes), discarding the last 32 bits of what would otherwise be a SHA-256 hash.

Implementation Efficiency

The close relationship between SHA-224 and SHA-256 means that implementing SHA-224 in systems that already support SHA-256 is straightforward. Many cryptographic libraries implement SHA-224 as a simple variation of SHA-256, which helps with code reuse and efficiency.

// SHA-224 initial hash values
const H224 = [
  0xc1059ed8, 0x367cd507, 0x3070dd17, 0xf70e5939,
  0xffc00b31, 0x68581511, 0x64f98fa7, 0xbefa4fa4
];

// SHA-256 initial hash values (for comparison)
const H256 = [
  0x6a09e667, 0xbb67ae85, 0x3c6ef372, 0xa54ff53a,
  0x510e527f, 0x9b05688c, 0x1f83d9ab, 0x5be0cd19
];

// SHA-224 output function (truncates the last word)
function formatSHA224Output(H) {
  let result = '';
  // Only use the first 7 words (28 bytes / 224 bits)
  for (let i = 0; i < 7; i++) {
    result += H[i].toString(16).padStart(8, '0');
  }
  return result;
}

// SHA-256 output function (uses all 8 words)
function formatSHA256Output(H) {
  let result = '';
  // Use all 8 words (32 bytes / 256 bits)
  for (let i = 0; i < 8; i++) {
    result += H[i].toString(16).padStart(8, '0');
  }
  return result;
}

Technical Specifications

SHA-224 follows the specifications outlined in FIPS PUB 180-4, with the following key technical characteristics:

Initialization Vectors

SHA-224 uses the following specific initialization vectors (in hexadecimal):

• H₀ = 0xc1059ed8
• H₁ = 0x367cd507
• H₂ = 0x3070dd17
• H₃ = 0xf70e5939
• H₄ = 0xffc00b31
• H₅ = 0x68581511
• H₆ = 0x64f98fa7
• H₇ = 0xbefa4fa4

These values were derived by taking the second 32 bits of the fractional parts of the square roots of the 9th through 16th prime numbers. This method was chosen to provide "nothing up my sleeve" numbers that are unlikely to have been selected to create cryptographic backdoors.

Mathematical Foundations

SHA-224, like all hash functions in the SHA-2 family, is built on sound mathematical principles that ensure its cryptographic properties:

Merkle–Damgård Construction

SHA-224 uses the Merkle–Damgård construction, which takes an input message of arbitrary length and produces a fixed-length output. The construction works by:

1. Padding the input message to a multiple of the block size
2. Dividing the padded message into fixed-size blocks
3. Processing each block with a compression function, using the output of one block as input to the next
4. Taking the final state as the hash output

Davies–Meyer Compression Function

Within the Merkle–Damgård construction, SHA-224 uses a Davies–Meyer compression function, which combines the previous hash state with the current message block using a block cipher (in this case, a custom cipher based on the SHACAL-2 design). This structure helps ensure that changes in the input produce unpredictable changes in the output—a key property for a secure hash function.

Core Mathematical Operations

SHA-224 relies on several mathematical operations that work together to create its cryptographic properties:

• Modular Addition (⊞): Addition modulo 2^32, which helps create diffusion in the algorithm
• Bitwise Operations (AND, OR, XOR, NOT): Create nonlinearity and prevent differential cryptanalysis
• Bitwise Rotation (ROTRⁿ): Circular right shift by n positions, contributing to the avalanche effect
• Logical Functions: Custom functions that combine basic operations to create complex relationships

Key Mathematical Functions

SHA-224 defines several specific functions that are applied during message processing:

These functions are carefully designed to ensure that SHA-224 exhibits strong resistance to various cryptographic attacks, including collision attacks, preimage attacks, and related-key attacks.

Security Characteristics

SHA-224 provides a balance of security and efficiency that makes it suitable for many cryptographic applications:

Security Level

SHA-224 provides 112 bits of security against collision attacks and 224 bits against preimage attacks. This means:

• Finding two different inputs that hash to the same output requires approximately 2^112 operations (collision resistance)
• Finding an input that hashes to a specific output requires approximately 2^224 operations (preimage resistance)
• Finding an input that hashes to an output with the same value as a given hash requires approximately 2^224 operations (second preimage resistance)

Length Extension Resistance

Like other SHA-2 family members, SHA-224 is vulnerable to length extension attacks where, given H(M), an attacker can find H(M || X) without knowing M. This is a property of the Merkle–Damgård construction and is important to consider when using SHA-224 in certain cryptographic protocols. When protection against length extension attacks is required, SHA-224 should be used with constructions like HMAC or in a hash-twice pattern.

Side-Channel Resistance

Implementations of SHA-224 can be vulnerable to side-channel attacks, where an attacker gains information through the physical implementation rather than weaknesses in the algorithm itself. Properly implemented, constant-time versions of SHA-224 can mitigate this risk.

Quantum Resistance

Against quantum computers, SHA-224 offers better resistance than symmetric ciphers of the same size due to the limited speedup that Grover's algorithm provides for preimage attacks. However, the collision resistance is reduced to approximately 2^56 operations with quantum algorithms, which may become a concern as quantum computing advances.

Design Principles

The design of SHA-224 follows several key principles that ensure its cryptographic strength:

Creators and Contributors

SHA-224, as part of the SHA-2 family, was developed by the National Security Agency (NSA) and published by the National Institute of Standards and Technology (NIST). While the specific individuals involved in its design are not publicly credited—as is common with cryptographic algorithms developed by government agencies—several key organizations and their contributions can be identified:

Standardization Process

The standardization of SHA-224 followed NIST's established process for cryptographic algorithms:

Initial Publication

SHA-224 was first standardized in FIPS PUB 180-2, published in August 2002 and amended in February 2004. This publication introduced SHA-224 alongside the other members of the SHA-2 family (SHA-256, SHA-384, and SHA-512).

Public Review

Before finalization, NIST solicited comments from the public, including cryptographers, industry experts, and potential users of the algorithm. This review process helped ensure that the algorithm met the needs of its intended users and withstood scrutiny from the cryptographic community.

Updates and Revisions

The standard has been updated several times since its initial publication:

• FIPS PUB 180-3 (October 2008): Refined the standard with additional implementation guidance.
• FIPS PUB 180-4 (March 2012, updated August 2015): The current version of the standard, which added two additional hash algorithms (SHA-512/224 and SHA-512/256) and provided further clarifications.

Implementation and Validation Program

To ensure correct implementation, NIST established the Cryptographic Algorithm Validation Program (CAVP), which provides validation testing for all approved cryptographic algorithms, including SHA-224. Software and hardware implementations can be tested against known test vectors to verify their correctness.

NIST Publications and References

Several key NIST publications provide authoritative information about SHA-224:

Primary Standards

• FIPS PUB 180-4: Secure Hash Standard - The definitive specification of SHA-224 and other SHA-2 algorithms.
• NIST SP 800-107: Recommendation for Applications Using Approved Hash Algorithms - Guidance on using SHA-224 and other hash functions in various applications.

Implementation Guidance

• Cryptographic Algorithm Validation Program (CAVP) - Secure Hashing - Information about the validation process for SHA-224 implementations.
• Cryptographic Module Validation Program (CMVP) - Validation for cryptographic modules that include SHA-224 implementations.

Security Analyses

• NIST SP 800-131A: Transitioning the Use of Cryptographic Algorithms and Key Lengths - Assessment of the security strength of SHA-224 relative to other algorithms.
• NIST SP 800-57: Recommendation for Key Management - Guidance on appropriate use cases for SHA-224 based on security requirements.

Timeline of Developments

External Links to Cryptography Resources