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feat(univariate): randomized Cantor-Zassenhaus root search#254

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olympichek wants to merge 9 commits into
Verified-zkEVM:masterfrom
formal-land:gs-univariate-las-vegas
Open

feat(univariate): randomized Cantor-Zassenhaus root search#254
olympichek wants to merge 9 commits into
Verified-zkEVM:masterfrom
formal-land:gs-univariate-las-vegas

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@olympichek olympichek commented Jun 11, 2026

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Overview

This PR adds a Las Vegas randomized Cantor-Zassenhaus univariate root-search backend.

This PR includes:

  • A configurable randomized splitter with probe families and deterministic fallback behavior.
  • Odd-characteristic splitting and characteristic-two trace splitting to support both odd and even (binary) fields.
  • Soundness and completeness proofs for the Las Vegas root-search.
  • Probabilistic proofs for the randomized splitter: each split attempt succeeds with probability at least 1/2 under uniform probes
  • Regression tests for Las Vegas root search.
  • Benchmarks comparing different univariate root search backends.

Technical details

The source of randomness in the executable code is caller-supplied ProbeFamily data. However, once the probe family, config, and input polynomial are fixed, the splitter is pure and deterministic. Tests and concrete field contexts use deterministic probe families; the binary benchmarks precompute fixed-seed probe tables before timing and then pass those tables through the same explicit probe interface.

@olympichek olympichek marked this pull request as ready for review June 12, 2026 19:00
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