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sss: accumulate in i64 and reduce once per coefficient - #19

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noot/fix-profile-harnessfrom
noot/perf-shamir-lazy-reduce

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@noot noot commented Nov 5, 2026

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Shamir share and recover reduced mod q after every multiply-add. Now the powers of the evaluation point are precomputed, products are summed in i64 and reduced once per coefficient. Same results, no new dependencies.

Single thread, 16 servers, 100 clients: share 1.38 → 0.84 ms, recover 194 → 60 µs.

Stacked on #18 (the profile harness fix) only for the benchmark; the library change is independent of it.

share and recover reduced mod q after every scalar product, one 64-bit
division per term per coefficient. the terms are bounded, so they now
accumulate in i64 and reduce once.
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