What characteristics should hash functions have to ensure their efficiency and security?

Hash functions should possess the following characteristics for efficiency and security:

• Determinism: the same input always produces the same output.
• Fast computation: the function should be computed quickly for any input data.
• Collision resistance: it is extremely unlikely that different inputs will produce the same hash.
• Pre-image resistance: it should be infeasible to reconstruct the original data from the hash.
• Uniform distribution: outputs should be evenly distributed across the range of possible values.

For example, in cryptography, collision resistance and pre-image resistance are important, while in data structures (hash tables), speed and uniform distribution are key.