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Adding another answer to my own question with a link to a new paper: "Batch NFS", by Daniel Bernstein and Tanja Lange (http://cr.yp.to/papers.html#batchnfs). This paper shows, assuming standard heuristics regarding the number-field sieve, that a “batch NFS” circuit of area $L^{1.181\dots+o(1)}$ factors $L^{0.5}+o(1)$ separate $B$-bit RSA keys in time ...

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