gen-define-collision-resistance-and-give-one-short-worked-exampl-6153

Define collision resistance and give one short worked example.

# Collision Resistance **Definition:** A hash function H is **collision resistant** if it is computationally infeasible to find two different inputs x and y such that H(x) = H(y). In other words, you cannot practically find two distinct messages that produce the same hash output. ## Short Worked Example **Scenario:** Suppose we have a weak hash function that only outputs 2 bits. ``` H("alice") = 01 H("bob") = 10 H("carol") = 01 ``` **Collision found!** Since H("alice") = H("carol") = 01, we've found a collision. This demonstrates that the hash function is **NOT collision resistant** because we easily found two different inputs ("alice" and "carol") that produce the same output. **Why this matters:** With only 2-bit output, there are only 4 possible hash values (00, 01, 10, 11), so collisions are inevitable and easy to find. Real cryptographic hash functions (like SHA-256) have large output spaces (2^256 possibilities) making collisions computationally infeasible to find, even though they theoretically exist by the pigeonhole principle.