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Accelerate odd-degree polynomial square-root recovery - #184
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Replace Tonelli–Shanks in odd-degree polynomial X-norm recovery with a direct norm/Frobenius construction. This avoids searching for a quadratic nonresidue and computing modular powers with exponents that grow with the factor degree.
The implementation adds a reusable Frobenius-product helper using binary doubling and shared composition caches. For BN254 Fp12, seed construction uses one characteristic-sized exponentiation and coefficient Frobenius maps instead of a full coefficient-field exponentiation.
Even-degree recovery retains the existing algorithm. Higher odd degrees also retain the fallback when modular composition is disabled; linear factors use coefficient-field square roots. The new path consumes no coefficient-generator samples. Existing reconstruction and exact norm-identity checks remain in place.
Completed recovery of real degree-153, 259, and 707 factors in approximately 1.59 s, 3.76 s, and 16.44 s.
On the saved cubic fixture, recorded clean-build median recovery time decreased from 2.74 s to 42.9 ms, approximately 64×. This is a fixture-specific measurement, not a general speedup claim.