Research proof index

Almost completeness of the Fischlin transform: if the underlying Σ-protocol is perfectly complete, then the signature scheme verifies with probability at least 1 - completenessError ρ b S t where t = FinEnum.card Chal is the challenge space size. Unlike the Fiat-Shamir transform (which is perfectly complete), the Fischlin transform has a non-zero comp...

Simulating the verifier's Fin.mOfFn of random-oracle re-queries on a cache that already stores every re-queried record is deterministic: each query is a cache hit returning the stored value, leaving the cache untouched. The result is the pure product of the per-repetition outputs f i (hash i), where hash i is the value cached at record i.

The allowed subsets of a FluxesFive which has no exotics or zeros. -/ def noExoticsSubsets : (n : ℕ) → Finset (Multiset Fluxes) | 0 => {{}} | 1 => {{⟨0, 1⟩}, {⟨0, 2⟩}, {⟨0, 3⟩}, {⟨1, -1⟩}, {⟨1, 0⟩}, {⟨1, 1⟩}, {⟨1, 2⟩}, {⟨2, -2⟩}, {⟨2, -1⟩}, {⟨2, 0⟩}, {⟨2, 1⟩}, {⟨3, -3⟩}, {⟨3, -2⟩}, {⟨3, -1⟩}, {⟨3, 0⟩}} | 2 => {{⟨0, 1⟩, ⟨0, 1⟩}, {⟨0, 1⟩, ⟨1, -1⟩}, {⟨0, 1...

The allowed subsets of a FluxesTen which has no exotics or zeros. -/ def noExoticsSubsets : (n : ℕ) → Finset (Multiset Fluxes) | 0 => {{}} | 1 => {{⟨1, -1⟩}, {⟨1, 0⟩}, {⟨1, 1⟩}, {⟨2, -1⟩}, {⟨2, 0⟩}, {⟨2, 1⟩}, {⟨3, 0⟩}} | 2 => {{⟨1, -1⟩, ⟨1, 0⟩}, {⟨1, -1⟩, ⟨1, 1⟩}, {⟨1, -1⟩, ⟨2, 1⟩}, {⟨1, 0⟩, ⟨1, 0⟩}, {⟨1, 0⟩, ⟨1, 1⟩}, {⟨1, 0⟩, ⟨2, 0⟩}, {⟨1, 1⟩, ⟨2, -1⟩}...

Completeness of elemsNoExotics, that is, every element of FluxesFive which obeys NoExotics is an element of elemsNoExotics, and every element of elemsNoExotics obeys NoExotics. -/ lemma noExotics_iff_mem_elemsNoExotics (F : FluxesFive) : F.NoExotics ∧ F.HasNoZero ↔ F ∈ elemsNoExotics := by constructor · exact fun ⟨h1, h2⟩ => mem_elemsNoExotics...

Completeness of elemsNoExotics, that is, every element of FluxesFive which obeys NoExotics is an element of elemsNoExotics, and every element of elemsNoExotics obeys NoExotics. -/ lemma noExotics_iff_mem_elemsNoExotics (F : FluxesFive) : F.NoExotics ∧ F.HasNoZero ↔ F ∈ elemsNoExotics := by constructor · exact fun ⟨h1, h2⟩ => mem_elemsNoExotics...