The _________ attack is when the attacker is looking for two messages M and M1 that produce the same hash: H(M) = H(M1)

Question

BlackTom AI · Accepted Answer

A birthday attack exploits the birthday paradox to find two distinct messages M and M1 that hash to the same value H(M) = H(M1).

1) Relevant knowledge points and concepts
- Cryptographic hash functions map arbitrary inputs to fixed-size n-bit outputs. Important security properties include collision resistance (hard to find M ≠ M1 with H(M)=H(M1)), preimage resistance, and second-preimage resistance.
- The birthday paradox: in a set of about sqrt(N) randomly chosen items from a space of size N, collisions become likely. For an n-bit hash, N = 2^n possible outputs, so collisions are expected after about 2^{n/2} attempts.
- A "birthday attack" is the practical exploitation of this paradox to find collisions much faster than brute-force preimage search.

2) Step-by-step reasoning
- The attacker generates many distinct messages and computes their hashes.
- Because of the birthday effect, after roughly √(number of possible hash values) samples, two messages will likely share the same hash.
- Therefore the attack specifically seeks two messages M and M1 with H(M)=H(M1), i.e., a collision.

3) Calculations and intermediate steps
- Number of possible outputs N = 2^n for an n-bit hash.
- Expected number of trials k for a substantial collision probability ≈ √N = 2^{n/2}.
- More precisely, using Poisson approximation: P(no collision) ≈ exp(-k(k-1)/(2N)). Setting P≈0.5 gives k ≈ 1.2·√N ≈ 1.2·2^{n/2}.

4) Why the correct answer is correct
- The described attack explicitly looks for two messages that produce the same hash; that is the definition of a collision and of the birthday attack. It leverages the birthday paradox to reduce complexity from about 2^n (preimage) to about 2^{n/2}.

5) Why the other options are incorrect
- MAC: stands for Message Authentication Code, a construction for authenticity/integrity, not the collision-finding attack.
- Hash: is the function itself, not a name for the attack.
- Chaining: refers to modes of building hashes (e.g., Merkle–Damgård chaining), not the collision attack technique.

6) Conclusion
The correct answer is "birthday", which matches the provided answer.

The _________ attack is when the attacker is looking for two messages M and M1 that produce the same hash: H(M) = H(M1)Single choice

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