Which statement about the relationship between hash output size and collision probability is true?

Which statement about the relationship between hash output size and collision probability is true?

• A. Larger output size decreases collision probability and increases resistance
• B. Output size has no effect on collision probability
• C. Collision probability only depends on input size
• D. Collision probability increases with output size

Answer: (A)

Hash output length determines how many distinct digests can exist. A longer hash creates a larger space, making collisions rarer. For an n-bit hash, there are 2^n possible outputs, so the probability that two random hashes collide is about 1 in 2^n. More importantly, finding a collision becomes harder in proportion to 2^(n/2) due to the birthday paradox. Therefore, increasing the output size reduces collision probability and strengthens collision resistance. The other statements contradict this relationship: smaller hashes collide more easily, and larger hashes don’t increase collision probability.

Hash output length determines how many distinct digests can exist. A longer hash creates a larger space, making collisions rarer. For an n-bit hash, there are 2^n possible outputs, so the probability that two random hashes collide is about 1 in 2^n. More importantly, finding a collision becomes harder in proportion to 2^(n/2) due to the birthday paradox. Therefore, increasing the output size reduces collision probability and strengthens collision resistance. The other statements contradict this relationship: smaller hashes collide more easily, and larger hashes don’t increase collision probability.