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Hash Functions

Cryptographic Hashes

A cryptographic hash function is a function,\(H\) , that when applied on a message,\(M\) , can be used to generate a fixed-length “fingerprint” of the message.

Properties

deterministic

unkeyed

Avalanche effect: a small change in the input causes a significant and unpredictable change in the output hash value.

  • One-way / Preimage resistant: given a hash output \(y\), it's infeasible to find any \(x\) such that \(H(x) = y\)

  • Second preimage resistant: Given an input \(x\), it's infeasible to find another input \(x'\) such that \(H(x) = H(x')\)

  • Collision resistant: It's infeasible to find any pair of messagess \(x,x'\) such that \(H(x) = H(x')\)

infeasible: there is no known way to accomplish it with any realistic amount of computing power

Under certain threat models, hash functions can be used to verify message integrity.