What is the difference between cryptographically secure and insecure hash functions?

A cryptographic hash function possesses properties that make it secure for use in cryptography:

• Pre-image resistance: it is infeasible to recover the original data from the hash (one-wayness).
• Collision resistance: it is extremely difficult to find two different inputs with the same hash.
• Second pre-image resistance: it is infeasible to find a different input that produces the same hash.

Non-cryptographic hash functions, on the other hand, do not guarantee these properties. They can be used for fast indexing or data distribution (e.g., in hash tables), where security is not critical. Such functions are faster but vulnerable to collisions and pre-image attacks.

Example:

• Cryptographic: SHA-256, SHA-3
• Non-cryptographic: simple hash functions for hash tables (e.g., modulus of division)

Thus, the main difference is the level of security and resistance to attacks.