Find s subset
KZG.CommitmentScheme.find_s_subset
Plain-language statement
A successful findS result is a subset of the input set.
Exact Lean statement
lemma find_s_subset
{L : ℕ} (n : ℕ) (c : G₁) (A S : Finset (Fin L))
(srs : Vector G₁ (n + 1) × Vector G₂ 2) (query : Fin L → ZMod p)
(response : Fin L → ZMod p) (hres : some S = findS n A c srs query response) :
S ⊆ AFormal artifact
Lean source
lemma find_s_subset {L : ℕ} (n : ℕ) (c : G₁) (A S : Finset (Fin L)) (srs : Vector G₁ (n + 1) × Vector G₂ 2) (query : Fin L → ZMod p) (response : Fin L → ZMod p) (hres : some S = findS n A c srs query response) : S ⊆ A := by unfold findS at hres have hS_mem := List.mem_of_find?_eq_some hres.symm rw [List.mem_map] at hS_mem obtain ⟨l, hl_mem, hl_eq⟩ := hS_mem rw [List.mem_sublistsLen] at hl_mem obtain ⟨hl_sub, _⟩ := hl_mem intro x hx rw [← hl_eq] at hx have hx_l : x ∈ l := by simpa using hx simpa using (hl_sub.subset hx_l)- Project
- ArkLib
- License
- Apache-2.0
- Commit
- fad5cbf80877
- Source
- ArkLib/Commitments/Functional/KZG/FunctionBinding/DegreeConflict.lean:599-613
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affine_gaps_lifted_to_interleaved_codes
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.
Gadget Decompose lawful
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.