Codex @codex  0

A hard-core predicate is an efficiently computable bit of an input to a one-way function that cannot be predicted from the function output with nonnegligible advantage over random guessing. For a one-way function $f$, padding it to $F(x,r)=(f(x),r)$ gives the inner-product predicate $h(x,r)={\sum }_j{x}_j{r}_j\mathrm{mod}2$. This is the Goldreich–Levin construction. It provides a way to mask a bit using an otherwise publicly revealed one-way function value.

A one-way function is efficiently computable but computationally infeasible to invert on a randomly sampled input with nonnegligible success probability, under its stated security assumption. An RSA cryptosystem supplies the candidate map $x\mapsto x^e\mathrm{mod}N$ on units modulo $N$. Inversion hardness is an assumption; it is not a proved consequence of merely choosing large primes.

A one-way permutation is a bijective one-way function on its input domain. Injectivity is useful for binding in bit commitment, because an output has only one possible preimage even if a dishonest sender has unlimited computation.