From ec9f085615fc952705fd5c4e766e574552452b3e Mon Sep 17 00:00:00 2001 From: mrwulf Date: Fri, 17 Jul 2026 13:31:51 +0200 Subject: [PATCH] =?UTF-8?q?paper=20v0.5:=20B6=20executed=20=E2=80=94=20acc?= =?UTF-8?q?ountability=20games=20+=20explicit=20composition=20theorem=20(I?= =?UTF-8?q?ACR=20track)?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit New \S5.4 'Scheme-level games and a composition theorem' (operator order: third attempt targets an IACR venue): - Game PB (position binding): two accepting openings of different leaves at one (m,n,r) -> explicit B_pb outputs a SHA-256 collision in <= 2(ceil(log2 n)+1) hash evaluations (two-transcript top-down comparison; 32-byte widths make argument pairs recoverable). - Lemma (prefix transport): an accepted ConsRec transcript plus an accepting opening at m collision, by transport induction + PB. Supplies the multi-step closure at paper level. - Game FORK: evidence completeness by construction; frame resistance reduces to EUF-CMA. Win condition deliberately over canonical PAYLOADS, not heads — a second signature on an already-signed payload is not an EUF-CMA forgery (SUF/EUF trap caught in the self-audit pass before integration). - Policy separation as a deterministic lemma (per GPT B6's own suggestion), formal Definition 3, and Theorem 7: the construction is an accountable replay-distribution scheme. - Fixed-function SHA-256 handled per Rogaway's human-ignorance treatment (new citation, arXiv-API/DBLP/Springer-verified: VIETCRYPT, LNCS 4341, pp. 211-228, 2006 — note Rogaway's own page carries a 221- typo): every hash statement is an explicit reduction, the scheme-level continuation of the named-extractor discipline. - Games are non-interactive BECAUSE the operator-adversary holds the signing key (no secrets, no oracles) — stated in the section, mirroring the deployment's non-interactive verification. - Honesty anchored: scope remark + new coverage-table row (two- transcript comparisons and prefix transport are paper-level, not mechanized); Definition 2 re-badged informal with pointer; DGHS two-transcript lineage credited in related work. 19 pages, 0 overfull, suite 115 green. 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\maketitle @@ -71,9 +71,10 @@ are compared. We instantiate the model as the Lean Transparency Log (LTL), using Lean~4 replay attestations and an RFC~9162 Merkle tree. We give explicit -collision-extracting arguments for inclusion and consistency, formalize the -consumer pinning and policy boundaries, and evaluate a live deployment over four -production Ed25519 codebases. The public log contains thirteen leaves; its thirteenth +collision-extracting arguments for inclusion and consistency, lift them to +scheme-level accountability games with an explicit composition theorem, +formalize the consumer pinning and policy boundaries, and evaluate a live +deployment over four production Ed25519 codebases. The public log contains thirteen leaves; its thirteenth leaf attests a Lean mechanization of the accumulator's own security arguments (222 inventoried environment constants, 61 human-reviewed assumption cones, and a single uninterpreted SHA-256 axiom). The mechanization effort also exposed, via differential testing, a nontrivial @@ -153,7 +154,9 @@ what a lightweight consumer learns without executing Lean. Using the RFC~9162 tree unchanged, we define signed views, inclusion receipts, local history pinning, and transferable same-size fork evidence. We give explicit collision-extracting soundness arguments specialized to the consumer -algorithms. +algorithms, and lift them to scheme level: concrete games for position +binding, history binding, and fork evidence, discharged by explicit +reductions (\S\ref{sec:games}). \item \textbf{Boundary-conformance policy.} Each leaf records the exact axiom names reported by Lean. Consumers compare those observations with their own policy; operator labels can veto but cannot @@ -307,6 +310,8 @@ property. It says when conflicting claims become attributable; it does not cryptographically prove that the replay observation was honestly produced. Throughout, ``accountability'' means signed-view and history accountability; observation validity remains external to the mechanism. +Section~\ref{sec:games} states clauses (i)--(iv) as games and explicit +reductions and proves the construction satisfies them. \begin{figure}[t] \centering @@ -374,6 +379,8 @@ enough for a third party to replay. \subsection{Consumer goals} +Each goal below is formalized as a game in Section~\ref{sec:games}. + \begin{description}[leftmargin=1.5em,itemsep=5pt] \item[G1: Position-bound membership.] If a consumer accepts leaf $d$ at index $m$ against signed head $(n,r)$, then $d$ occupies position $m$ in a leaf list @@ -592,6 +599,177 @@ predicate. Consequently the public attestation says exactly this: the model is proved; deployment correspondence is finite-tested and relies on an unmechanized authentic-size/root invariant. +\subsection{Scheme-level games and a composition theorem}\label{sec:games} + +The theorems above bind single artifacts to a reference leaf list. This +subsection lifts them to the scheme: precise experiments for the accountability +clauses of Definition~2, and a theorem that the construction satisfies them. +Two modeling choices deserve emphasis. First, the replay operator \emph{is} the +adversary and legitimately holds the signing key, so the position-binding and +history games contain no secrets and no oracles; any adaptive interaction can +be replayed into a single output, and the games are therefore non-interactive +--- mirroring the deployment, in which receipt verification itself is +non-interactive. Signatures constrain a different party: the frame-resistance +game, in which a third party attempts to fabricate equivocation evidence +against a key holder who never equivocated. Second, SHA-256 is a fixed, +unkeyed function, so ``collision resistance'' cannot be a probability +statement over a key space; following the human-ignorance +treatment~\cite{rogaway}, every hash statement below is an \emph{explicit +reduction} --- a named algorithm transforming a winning transcript into a +concrete collision --- which is the scheme-level continuation of the corpus's +named-extractor discipline. + +\paragraph{Accepted-artifact syntax.} +Fix the algorithms of Section~\ref{sec:construction}. A head $h=(n,r;\sigma)$ +carries the canonical signed payload of \S4.2; $\mathsf{Vf}_{pk}(h)=1$ iff its +signature verifies. An \emph{opening} of leaf $d$ at index $m$ under $(n,r)$ +is a path $P$ with $m (The full walk-through is lecture 11 in the

The paper

Accountable Distribution of Machine-Checked Correctness Evidence: A Transparency Model and the Lean Transparency Log -(PDF, 17 pages, v0.4 — revised after two independent round-12 reviews) — the trust -decomposition (expensive verification produces an observation; transparency makes the -observation accountable; consumer-local policy decides acceptance), collision-extracting -soundness for inclusion and consistency, the policy boundary where operator labels can veto -but never grant acceptance, the live thirteen-leaf deployment whose entry 13 attests the -accumulator's own mechanized model, and the measured model/deployment divergence (3,867 -lied-size cases, every one accepted only by the deployed verifier) reported as a result -rather than hidden. +(PDF, 19 pages, v0.5) — the trust decomposition (expensive verification produces an +observation; transparency makes the observation accountable; consumer-local policy decides +acceptance), collision-extracting soundness for inclusion and consistency, scheme-level +accountability GAMES with an explicit composition theorem (position binding, history +binding, fork evidence — all discharged by named reductions), the policy boundary where +operator labels can veto but never grant acceptance, the live thirteen-leaf deployment +whose entry 13 attests the accumulator's own mechanized model, and the measured +model/deployment divergence (3,867 lied-size cases, every one accepted only by the +deployed verifier) reported as a result rather than hidden. Previous versions: v0.2 (19 pages, the system report) · v0.1 (4 pages).