How do cryptographic hash function security features work?

Cryptographic hash functions map arbitrary binary strings into fixed-size values using one-directional mathematical operations. Their security relies on properties like preimage resistance, second preimage resistance, and collision resistance. While some functions are provably secure through rigorous mathematical reduction, most widely used functions are based on ad-hoc mixing constructions.

What we know

• Cryptographic hash functions are one-directional mathematical operations that are quick to calculate yet hard to reverse. [3]
• A cryptographic hash function with n bits of hash value is expected to have a preimage resistance strength of n bits. [3]
• Collision resistance strength for a cryptographic hash function is expected to be n/2 bits due to the birthday paradox. [3]
• Cryptographic hash functions can be divided into provably secure functions based on mathematical problems and ad-hoc constructions based on mixing message bits. [4]

Still open

• The source package does not detail which specific ad-hoc hash functions remain unbroken versus those that are no longer in use.

Where to go next

• compared withWhat are non-cryptographic hash functions?
• what followedHow do digital signatures use hash functions?
• how it workedHow does the birthday paradox affect hash collisions?
• a case in pointWhat are provably secure cryptographic hash functions?
• the bigger pictureWhat is a cryptographic hash function?
• an unexpected connectionWhy are some hash functions faster but less secure?Non-cryptographic hash functions omit rigorous security requirements like preimage resistance to achieve faster speeds for CPU-optimized tasks.

Sources

• [1]Comparison of cryptographic hash functions (Wikidata Q5155845) · CC0 1.0
• [2]Comparison of cryptographic hash functions · CC BY-SA 4.0
• [3]Cryptographic hash function · CC BY-SA 4.0
• [4]Security of cryptographic hash functions · CC BY-SA 4.0
• [5]Non-cryptographic hash function · CC BY-SA 4.0