security/framework/redteam/lattice.tex

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\title{Red-team checklist: lattice threshold signatures\\(Pulsar = threshold ML-DSA, Corona = threshold Module-LWE/Raccoon)}
\date{}
\begin{document}\maketitle
\noindent Apply this to Fiat--Shamir-with-aborts lattice threshold schemes. It
encodes the PULSAR-V13 findings. ``FAIL'' = do not ship.

\section{Leakage of long-term key material}
\begin{enumerate}[leftmargin=*]
  \item Does any round broadcast a per-party value that, summed over the
    \emph{public} challenge $c$ across attempts, reconstructs a secret? (The
    V13 leak: unmasked $c\!\cdot\!s_2$, $c\!\cdot\!t_0$ shares $\Rightarrow$
    $c\!\cdot\!s_{2,\mathrm{master}}$ over varying $c$ $\Rightarrow$ master
    key by linear system.) Masking a single share is necessary but NOT
    sufficient if the \emph{aggregate} still reconstructs.
  \item Is the rejection/hint sequence secret-dependent and exposed? The hint
    must be recovered from PUBLIC data ($w' = A z - c t_1 2^d$, $w_1$) via the
    FIPS \texttt{UseHint}, never from $c\!\cdot\!s_2$/$c\!\cdot\!t_0$/$r_0$.
  \item Is full $w$ (or $\mathrm{LowBits}(w)$, boundary distances) ever
    published? $w' - w = c t_0 - c s_2$ leaks the residual.
  \item Does DKG / reshare / keygen reconstruct the master at any party or
    aggregator on a PRODUCTION path? (A trusted-dealer/TEE path must be
    explicitly named and gated.)
\end{enumerate}

\section{Norm bounds and the L2/L$\infty$ trap}
\begin{enumerate}[leftmargin=*]
  \item Every small-norm claim ($\|s_1\|,\|s_2\|\le\eta$, $\|t_0\|$, boundary
    margin) is an L$\infty$ (per-coefficient) bound. A uniform-mask $\Sigma$
    protocol carries ZERO norm information; BDLOP/LNS norm proofs certify L2,
    and $\|x\|_\infty\le\|x\|_2$ is loose by $\sqrt{\dim}$ (often vacuous,
    $>q$). A range gate that cannot imply the L$\infty$ bound must FAIL CLOSED,
    not approximate.
  \item Is the parameter set inside the proven scope? (BCC/CEF: $\|c t_0\|_\infty
    \le \tau 2^{d-1} < \gamma_2$ holds for ML-DSA-65/87, NOT 44.) A threshold
    that underflows/saturates a bound check for an out-of-scope set is a leak.
\end{enumerate}

\section{Nonce / session safety}
\begin{enumerate}[leftmargin=*]
  \item Can a session id collide for a fixed key share? (Corona CRIT-1: same
    $(\mathrm{sid},\mathrm{skShare})\Rightarrow$ same $R\Rightarrow$
    $(z_\Sigma - \sum s_i\lambda_i c)u^{-1}=R$ reopens.) The nonce-PRF key MUST
    derive from $\ge256$ bits of fresh entropy (hedge), not a 64-bit counter,
    and not rest on the consensus layer for uniqueness.
  \item Is the challenge validated as a genuine \texttt{SampleInBall} ($\tau$
    coefficients $\pm1$)? A degenerate $c=0$ strips the $s_1$ binding from a
    partial-$z$ proof.
  \item Is nonce selection canonical / non-grindable (a coordinator cannot pick
    among many valid $w_1$ after seeing the message)?
\end{enumerate}

\section{Accountability and aggregation}
\begin{enumerate}[leftmargin=*]
  \item Is the signer bitmap cryptographically bound to the signature (not a
    free field a forger can rewrite)? Threshold ML-DSA does not encode its
    signer set in the joint key, so accountability needs its own QC.
  \item Does cert verification actually verify the quorum signatures (not a
    fail-open no-op default)? Run \texttt{framework/checks/fail-open.sh}.
  \item Aggregator-host trust: a root-compromised aggregator that sees $c$ and
    all $z_i$ across enough quorum subsets recovers $s_\Sigma$. State this
    limitation in the deployment posture; it is mitigated by TEE/mlock, not
    cryptographically.
\end{enumerate}
\end{document}