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This randomized trial presents a closed-form formula achieving 100% accuracy in order-3 subgroups, suggesting efficient computations.
We present a closed-form formula for computing discrete logarithms in order-3 subgroups of Z_p^*. The formula has O(1) prediction time after calibration. The formula is verified in Lean 4 with 42 theorems. Experimental results on 32 primes are reported, including cases where the formula achieves 100% accuracy.
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Juncai Zhou (2026) studied this question.
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