Formalizing Human Ignorance: Collision-Resistant Hashing Without the Keys

摘要

There is a rarely mentioned foundational problem involving collision-resistant hash-functions: common constructions are keyless, but formal definitions are keyed. The discrepancy stems from the fact that a function H: {0, 1}~* → {0, 1}~n always admits an efficient collision-finding algorithm, it's just that us human beings might be unable to write the program down. We explain a simple way to sidestep this difficulty that avoids having to key our hash functions. The idea is to state theorems in a way that prescribes an explicitly-given reduction, normally a black-box one. We illustrate this approach using well-known examples involving digital signatures, pseudorandom functions, and the Merkle-Damgard construction.