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Hard-core Predicate




A hard-core predicate captures "in a concentrated sense" the hardness of inverting ''f''. More generally, a hard-core function is a function that has the same property.

While a one-way function is hard to invert, it makes no guarantees about the feasibility of computing partial information about the Preimage . For instance, while RSA is conjectured to be a one-way function, the Jacobi Symbol of the preimage can be easily computed from that of the image.

Therefore a one-way function alone is not sufficient for encryption. This notion is called Semantic Security . Hard-core predicates are used to get around this problem; for instance see Probabilistic Encryption .