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A hard-core predicate of a one-way function $f$ is a predicate b (i.e., a function whose output is a single bit) which is easy to compute (as a function of x) but is hard to compute given $f(x)$.
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Hard-core bits from RSA assumption
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Assume that we have a way, given $x^e \bmod N$, to derive the parity of $x_S$. We further assume that $2 > N / 2^k > 1.5$ for some integer $k$, that is, the two msbits of $ …