Negligible polynomial mul
negligible_polynomial_mul
Project documentation
If f is negligible, then fun n => ↑(p.eval n) * f n is negligible for any polynomial p. This is the key lemma for handling polynomial-loss security reductions.
Exact Lean statement
theorem negligible_polynomial_mul {f : ℕ → ℝ≥0∞} (hf : negligible f)
(p : Polynomial ℕ) :
negligible (fun n => ↑(p.eval n) * f n)Formal artifact
Lean source
theorem negligible_polynomial_mul {f : ℕ → ℝ≥0∞} (hf : negligible f) (p : Polynomial ℕ) : negligible (fun n => ↑(p.eval n) * f n) := by have heq : ∀ n, (↑(p.eval n) : ℝ≥0∞) * f n = ∑ i ∈ Finset.range (p.natDegree + 1), ↑(p.coeff i) * ((↑n : ℝ≥0∞) ^ i * f n) := by intro n simp [Polynomial.eval_eq_sum_range, Finset.sum_mul, mul_assoc] simp_rw [heq] exact negligible_sum fun i _ => negligible_const_mul (negligible_pow_mul hf i) (ENNReal.natCast_ne_top _)- Project
- VCVio
- License
- Apache-2.0
- Commit
- 2ceb2d825ee3
- Source
- VCVio/CryptoFoundations/Asymptotics/Negligible.lean:79-89
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