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feat(univariate): Shoup's trace splitter root search#253

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olympichek wants to merge 5 commits into
Verified-zkEVM:masterfrom
formal-land:gs-univariate-shoup
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feat(univariate): Shoup's trace splitter root search#253
olympichek wants to merge 5 commits into
Verified-zkEVM:masterfrom
formal-land:gs-univariate-shoup

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Overview

This PR adds Shoup's deterministic univariate root-search algorithm in addition to the current smooth-subgroup algorithm.

This PR includes:

  • The Shoup root-search backend and its Frobenius-linear helper layer.
  • Correctness proofs showing that the Shoup backend satisfies the same finite-field root-search contract as the smooth backend.
  • Shared binary-field carrier infrastructure for $\mathrm{GF}(2^{32})$, $\mathrm{GF}(2^{48})$, $\mathrm{GF}(2^{64})$, and $\mathrm{GF}(2^{72})$.
  • Binary-field root contexts and tests that can be reused by later root-search backends.
  • Documentation updates for the new binary-field modules.
  • Univariate root tests and binary-field regression tests for the new concrete field contexts.
  • Benchmarks comparing Shoup and smooth-subgroup algorithms on $\mathrm{GF}(2^{32})$, $\mathrm{GF}(2^{48})$, $\mathrm{GF}(2^{64})$, and $\mathrm{GF}(2^{72})$

@olympichek olympichek force-pushed the gs-univariate-shoup branch from 434d127 to bf85308 Compare June 11, 2026 18:59
@olympichek olympichek force-pushed the gs-univariate-shoup branch from bf85308 to a7bae85 Compare June 13, 2026 19:25
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