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zeekay
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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.
20 lines
871 B
TeX
20 lines
871 B
TeX
\section{FHE Applications}
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For FHE, the NTT must handle larger polynomial degrees ($n = 1024, 2048, 4096$) and
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larger moduli ($q$ up to 60 bits for RNS representation). The techniques are the same,
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but:
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\begin{itemize}[nosep]
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\item \textbf{Larger degree}: More butterfly layers ($\log_2 n$ layers). AVX2 benefit
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increases because more parallelism is available.
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\item \textbf{Larger modulus}: 16-bit Montgomery does not suffice. We use 32-bit
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Montgomery with 64-bit intermediate products. AVX2 \texttt{VPMULLD} handles 32-bit
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multiplies (8 per instruction instead of 16).
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\item \textbf{RNS}: The Residue Number System represents large integers as tuples of
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residues modulo small primes. Each NTT operates on one residue---enabling parallelism
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across RNS channels.
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\end{itemize}
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%% ============================================================
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