papers/lux-sovereign-keys/sections/03-fhe-for-private-computation.tex

\section{FHE for Private Computation}

\label{sec:fhe}

\subsection{Motivation}

Some computations require operating on data from multiple parties without
revealing individual values.  Examples in the securities domain:
\begin{itemize}[nosep]
  \item Accreditation verification: does an investor's income exceed
        a threshold without revealing the exact amount?
  \item Private voting: aggregate votes without revealing individual choices.
  \item Compliance checks: verify aggregate investment limits across
        multiple accounts.
\end{itemize}

\subsection{Implementation}

The FHE module in \texttt{lux/transfer/pkg/crypto/fhe.go} uses lattice-based
fully homomorphic encryption from the \texttt{luxfi/fhe} library:

\begin{lstlisting}[language=Go,caption={fhe.go: parameter initialization}]
func NewFHEKey() (*FHEKey, error) {
    params, err := fhe.NewParametersFromLiteral(fhe.PN10QP27)
    intParams, err := fhe.NewIntegerParams(params, 2)
    kg := fhe.NewKeyGenerator(params)
    sk, pk := kg.GenKeyPair()
    return &FHEKey{
        params: params, intParams: intParams,
        sk: sk, pk: pk,
    }, nil
}
\end{lstlisting}

The parameter set \texttt{PN10QP27} provides approximately 128-bit security.
Integer operations support 64-bit unsigned values, sufficient for monetary
amounts and share counts.

\subsection{Encrypted Comparison}

The core operation is homomorphic comparison, enabling threshold checks
on encrypted data:

\begin{lstlisting}[language=Go,caption={fhe.go: encrypted comparison}]
func CompareEncrypted(a, b *FHECiphertext,
                      key *FHEEvalKey) (int, error) {
    // Computed homomorphically, then single-bit
    // results are decrypted.
    // In production the final decryption would
    // be done via MPC.
}
\end{lstlisting}

The comparison result is a single encrypted bit.  In the sovereign model,
the final decryption is distributed via MPC among user-controlled signers,
so no single party learns the underlying values.

\subsection{Integration with Sovereign Keys}

FHE ciphertexts are encrypted under the vault's FHE public key (generated
alongside the ML-KEM key pair).  The FHE secret key is held by the user
or split via MPC among user-designated parties.  The provider stores
ciphertexts and can perform homomorphic operations, but cannot decrypt
the results.

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