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Yes, you are looking for the notion of a universal one-way function. Rafael Pass/abhi shelat's notes contain a construction on page 49. The construction is "unnatural" in the sense that it involves parsing the input to the OWF $y$ as a pair $\langle M\rangle || x$, where $\langle M\rangle$ is interpreted as the description of a Turing machine. Then ...


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Miller-Rabin has been known since at least 1980 (according to Wikipedia). Even though it's probabilistic, it's good enough. For example, openssl uses it$^\textrm{1}$. Chapter 4 of the handbook talks about various primality tests, which may gave you a better understanding of the authors' thoughts. $^\textrm{1}$See the source code for bn_prime.c


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