Which concept is most closely associated with the security of hash functions as the number of hashed items grows?

• A. Hash length extension
• B. Birthday attack
• C. Preimage resistance
• D. Pseudorandomness

Answer: (B)

When thinking about hash function security as you hash more inputs, the key issue is collisions—two different inputs producing the same hash. With a fixed output size, the chance of a collision isn’t negligible once you’ve hashed a large enough set of items, and this is governed by the birthday problem. In particular, for an n-bit hash, you start to expect collisions around 2^(n/2) hashed items. This is the essence of a birthday attack: it exploits this collision likelihood to find two inputs that share the same hash. So, the concept that best captures how growing the number of hashed items affects security is the birthday attack, because it directly describes how increasing the input set makes collisions more feasible and tests the hash function’s collision resistance.

Other ideas describe different security aspects not tied to the growth of hashed items: hash length extension is about extending messages in certain hash constructions, preimage resistance is about finding an input that produces a given hash (not about collisions from many inputs), and pseudorandomness concerns whether hash outputs look indistinguishable from random, regardless of how many inputs you hash.