Combining SHA-3 Hash Functions: Is it More Secure?

TL;DR

Generally, simply combining two different hash functions (like those from the SHA-3 competition) doesn’t automatically create a more secure algorithm. It can even reduce security if done incorrectly. While there are ways to combine them securely, it requires careful design and analysis by cryptography experts. A simple concatenation or sequential application is usually not sufficient.

Understanding the Problem

You’re asking whether you can improve a hash function’s security by using two different algorithms from the SHA-3 candidates (like Keccak, BLAKE2b, Grøstl, etc.). The idea seems intuitive: if one algorithm is strong and another is also strong, combining them should be even stronger. However, cryptography isn’t that simple.

Why Combining Isn’t Straightforward

1. Collision Resistance Issues: If you simply concatenate the outputs of two hash functions (e.g., H1(message) || H2(message)), it doesn’t guarantee better collision resistance. An attacker might find collisions in either H1 or H2 that can be exploited to create a collision in the combined output.
2. Length Extension Attacks: Many hash functions are vulnerable to length extension attacks. Combining them naively may not prevent this attack, and could even make it easier.
3. No Proven Security Gains: There’s no mathematical proof that combining two existing hash functions will result in a stronger algorithm without rigorous analysis. It’s possible the combination introduces new weaknesses.

Secure Ways to Combine Hash Functions (Advanced)

If you need to combine hash functions, here are some approaches that cryptography experts use – but these are complex and require deep understanding:

1. Cascade Construction: This involves using one hash function as input to another. For example:
   H2(H1(message)). However, this is only secure if H1 is collision-resistant and the second hash function (H2) has strong properties.
   • Example (Python):

   import hashlib
   
   def cascade_hash(message):
     h1 = hashlib.sha256(message).hexdigest()
     h2 = hashlib.blake2b(h1.encode()).hexdigest()
     return h2
   
   message = b'This is a test message'
   result = cascade_hash(message)
   print(result)

2. Parallel Hash Functions: This involves running multiple hash functions in parallel and combining their outputs. A common approach is to XOR the results.
   • Example (Python):

   import hashlib
   
   def parallel_hash(message):
     h1 = int(hashlib.sha256(message).hexdigest(), 16)
     h2 = int(hashlib.blake2b(message).hexdigest(), 16)
     combined = h1 ^ h2
     return hex(combined)[2:]
   
   message = b'This is a test message'
   result = parallel_hash(message)
   print(result)

3. Multi-Round Constructions: These are more complex designs that involve multiple rounds of hashing and mixing operations. They require careful analysis to ensure security.

Important Considerations

• Cryptographic Expertise: Designing a secure combination requires deep knowledge of cryptography and hash function properties. Don’t attempt this unless you are an expert in the field.
• Formal Analysis: Any combined algorithm must be formally analyzed to prove its security against known attacks (collision resistance, preimage resistance, length extension attacks, etc.).
• Standard Algorithms: It’s almost always better to use well-established and thoroughly vetted hash functions like SHA-3 (Keccak) or BLAKE2b. These have been extensively analyzed by the cryptography community.
  • Example (Python):

  import hashlib
  
  def sha3_hash(message):
    h = hashlib.sha3_256(message).hexdigest()
    return h
  
  message = b'This is a test message'
  result = sha3_hash(message)
  print(result)

Conclusion

Combining SHA-3 candidates isn’t a simple path to a more secure hash function. It’s generally not recommended unless you have significant cryptographic expertise and can perform rigorous security analysis. Stick with established, well-vetted algorithms like SHA-3 or BLAKE2b for most applications.