Which properties of hash functions are critical for message integrity?

Question

BlackTom AI · Accepted Answer

Message integrity depends on two key cryptographic properties: determinism and collision resistance.

Relevant concepts:
- Determinism: a hash function yields the exact same digest for the same input every time. This makes equality checks meaningful.
- Collision resistance: it is computationally infeasible to find two distinct inputs M and M' such that H(M) = H(M'). (Related concepts include preimage and second-preimage resistance, which strengthen the one-way and uniqueness guarantees.)

Step-by-step reasoning (integrity verification process):
1) Sender computes h = H(M) using the hash function and sends M along with h (or sends h via a secure channel).
2) Receiver computes h' = H(M).
3) Receiver compares h' to the received h. If h' = h, the message is accepted as intact; if not, it is rejected.
Why determinism is required: If the hash were non-deterministic, identical messages could produce different digests; the receiver’s computed h' would not reliably match the sender’s h even when the message was not altered. Determinism is therefore essential for any equality check used to assert integrity.
Why collision resistance is required: An active attacker might try to substitute a malicious M' while keeping the same hash value. If collisions are easy to find, the attacker can craft M' such that H(M') = H(M) and the receiver would be fooled into accepting the tampered message. Collision resistance prevents this by making such forgery computationally infeasible.

Why the other options are incorrect:
- Reversibility (ability to recover original message) is not desirable for integrity: hashes are designed to be one-way. If a hash were reversible, it would leak or allow recovery of the original message and undermine confidentiality and other security goals; reversibility is not required for integrity checks.
- “Hashing based on 64 bits is more secure than 128 bit hashing” is false. Security increases with output length: there are 2^64 possible 64-bit hashes vs 2^128 for 128-bit. Under the birthday attack, collision search complexity is about 2^(n/2) (≈2^32 vs 2^64), so 128-bit hashing is far more collision-resistant than 64-bit.

Conclusion: The critical properties for message integrity are Determinism (same input always gives same hash) and Collision resistance (hard to find two inputs with same hash), which matches the provided answer.

Which properties of hash functions are critical for message integrity?多项选择题

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