Ch.08. A strong cryptographic hash function guarantees mathematically that no two distinct messages will ever produce the same hash value.Single choice
A
True
B
False

Question

Ch.08. A strong cryptographic hash function guarantees mathematically that no two distinct messages will ever produce the same hash value.

BlackTom AI · Accepted Answer

A cryptographic hash function maps inputs of arbitrary length to fixed-length outputs, so by the pigeonhole principle collisions must exist; therefore the statement is false.

1) Relevant knowledge points and concepts
- Hash function: deterministic mapping from messages of arbitrary length to fixed-size digests.
- Pigeonhole principle: if more possible inputs than outputs exist, at least two distinct inputs map to the same output.
- Cryptographic properties: preimage resistance, second-preimage resistance, and collision resistance. Collision resistance means it is computationally infeasible to find two distinct messages with the same digest, not that collisions do not exist.

2) Step-by-step reasoning
- Most cryptographic hashes (e.g., SHA-256) produce an n-bit output; that gives 2^n possible hash values.
- Message space is effectively infinite (all possible bit strings of any length), so there are more possible messages than hash values.
- By the pigeonhole principle, some distinct messages must map to the same n-bit value. Hence collisions exist mathematically.

3) Intermediate numerical illustration
- For SHA-256, n = 256, so there are 2^256 distinct hash values. But there are infinitely many possible messages (or at least more than 2^256 practical inputs), so collisions are guaranteed to exist. Practically, due to the birthday paradox, a collision is expected after ~2^(n/2) random hashes (≈2^128 for SHA-256), which is astronomically large but finite.

4) Why the correct answer is correct
- The statement claims a mathematical guarantee that no two distinct messages will ever produce the same hash. That contradicts the pigeonhole principle because fixed-length outputs cannot uniquely represent every distinct input. Cryptographic strength only provides computational infeasibility of finding collisions, not their impossibility.

5) Why the other option is incorrect
- “True” would assert absolute impossibility of collisions for a strong hash—this is incorrect. Even “strong” (collision-resistant) hashes can never avoid collisions by definition; they only make finding them hard. Historical collisions (e.g., MD5, SHA-1 weaknesses) show collisions can be found for weaker algorithms.

6) Conclusion
Therefore, the correct answer is False, which matches the provided answer.

Ch.08. A strong cryptographic hash function guarantees mathematically that no two distinct messages will ever produce the same hash value.Single choice

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