Choose s middle card
KZG.CommitmentScheme.choose_s_middle_card
Plain-language statement
chooseSMiddle returns a support set of size n + 1.
Exact Lean statement
lemma choose_s_middle_card (hp : p ≥ n + 2) (α : ZMod p) :
(chooseSMiddle n α).card = n + 1Formal artifact
Lean source
lemma choose_s_middle_card (hp : p ≥ n + 2) (α : ZMod p) : (chooseSMiddle n α).card = n + 1 := by unfold chooseSMiddle set base : Finset (ZMod p) := (Finset.range (n + 2)).image ((↑) : ℕ → ZMod p) with hbase_def by_cases hα : α ∈ base · rw [if_pos hα, Finset.card_erase_of_mem hα] have hbase : base.card = n + 2 := by rw [hbase_def] exact nat_cast_range_card_zmod_of_le (k := n + 2) hp omega · rw [if_neg hα] exact nat_cast_range_card_zmod hp- Project
- ArkLib
- License
- Apache-2.0
- Commit
- fad5cbf80877
- Source
- ArkLib/Commitments/Functional/KZG/FunctionBinding/TauInQueries.lean:137-149
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Project documentation
This lemma proves the final algebraic step in the DG25 Theorem 3.1 proof. It shows that if R > e + 1, then e * (R / (R - 1)) < e + 1. The intuition is that the fraction R / (R - 1) is always greater than 1, but as R gets larger, it gets closer to 1. The hypothesis R > e + 1 provides a strong enough bound to ensure the product e * (fraction) do...
Source project: ArkLib
Person-level attribution pending.
Gadget Decompose coeff
ArkLib.Lattices.Ajtai.gadgetDecompose_coeff
Plain-language statement
The k-th coefficient (k < deg φ) of a gadget-decomposition block is exactly the corresponding digit of the corresponding input coefficient.
Source project: ArkLib
Person-level attribution pending.
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ArkLib.Lattices.Ajtai.gadgetDecompose_lawful
Plain-language statement
The base-b gadget decomposition is a lawful gadget decomposition.
Source project: ArkLib
Person-level attribution pending.