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Restructured from flat .tex/.pdf files into per-paper subdirectories. Added Antje Worring as co-author on all papers. Synced PDFs to pdfs/ for download site.
49 lines
1.7 KiB
TeX
49 lines
1.7 KiB
TeX
\section{Security Analysis}
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\label{sec:security}
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\subsection{Cryptographic Security}
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Both TFHE and BFV derive their security from Ring-LWE~\cite{lyubashevsky2010ideal}.
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Our parameter selection:
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\begin{table}[ht]
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\centering
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\caption{Security parameters.}
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\label{tab:security-params}
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\begin{tabular}{lrrr}
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\toprule
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\textbf{Scheme} & \textbf{$N$} & \textbf{$\log_2 q$} & \textbf{Classical Security} \\
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\midrule
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TFHE & 1{,}024 & 27 & 128 bits \\
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BFV-128 & 4{,}096 & 218 & 128 bits \\
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BFV-192 & 8{,}192 & 438 & 192 bits \\
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BFV-256 & 16{,}384 & 881 & 256 bits \\
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\bottomrule
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\end{tabular}
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\end{table}
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Security levels are estimated using the lattice-estimator~\cite{albrecht2015lattice}
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with BKZ-$\beta$ cost model and core-SVP hardness assumption.
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\subsection{Semantic Security}
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FHE provides IND-CPA (indistinguishable under chosen plaintext attack) security:
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an adversary cannot distinguish encryptions of different plaintexts. This means:
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\begin{itemize}[leftmargin=2em]
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\item Encrypted balances reveal nothing about the plaintext balance.
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\item Encrypted order prices reveal nothing about the plaintext price.
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\item Encrypted votes reveal nothing about the plaintext vote.
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\end{itemize}
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FHE does \emph{not} provide IND-CCA2 security (indistinguishable under adaptive
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chosen ciphertext attack). Ciphertexts are malleable by design---this is what
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enables homomorphic computation. Access control for decryption (Section~\ref{sec:fhe-vm})
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is therefore critical: only authorized parties can decrypt, preventing an adversary
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from using the decryption oracle to break semantic security.
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%% ========================================================================
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%% 9. RELATED WORK
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%% ========================================================================
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