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Fix bit length proof

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jude
2023-04-28 10:32:05 +01:00
parent 574287d07b
commit 6005cd6aff
6 changed files with 77 additions and 37 deletions
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whitepaper/Dissertation.tex
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@ -1030,6 +1030,8 @@ The other proofs do not translate so trivially to this structure however. In fac
\textbf{Optimising language.} An optimising language may be able to reduce the time taken to encrypt. On the browser, this could involve using WASM as a way to execute compiled code within the browser, although WASM does not always outperform JavaScript \cite{wasm}.
Another approach is to use a web extension to communicate with a system daemon providing the relevant functionality. This is language-agnostic (except that the extension itself must be JavaScript), and the daemon could take advantage of other system features such as multiple cores. The multi-round proofs in particular are embarrassingly parallel, as each round is independent of the other rounds.
\subsection{Complexity results}
All measurements were taken on Brave 1.50.114 (Chromium 112.0.5615.49) 64-bit, using a Ryzen 5 3600 CPU: a consumer CPU from 2019. Absolute timings are extremely dependent on the browser engine: for example Firefox 111.0.1 was typically 4 times slower than the results shown.
@ -1042,9 +1044,9 @@ All measurements were taken on Brave 1.50.114 (Chromium 112.0.5615.49) 64-bit, u
\label{table1}
\begin{tabularx}{\hsize}{c *4{>{\Centering}X}}
\toprule
Modulus size & Na\"ive encrypt & Jacobi encrypt & Jacobi encrypt with pre-computation & RSA encrypt \\
Modulus size & Paillier encrypt & Jurik encrypt & Jurik encrypt with pre-computation & RSA encrypt \\
\midrule
$|n| = 1024$ & 6.0ms & 4ms & 1.4ms & 0.015ms \\
$|n| = 1024$ & 6.0ms & 4.0ms & 1.4ms & 0.015ms \\
$|n| = 2048$ & 34ms & 22ms & 7.6ms & 0.040ms \\
$|n| = 4096$ & 189ms & 128ms & -- & 0.093ms \\
\bottomrule
@ -1053,20 +1055,21 @@ All measurements were taken on Brave 1.50.114 (Chromium 112.0.5615.49) 64-bit, u
\begin{table}
\fontsize{10pt}{10pt}\selectfont
\caption{Time\parnote{$|n| = 4096$ uses a less-optimised encryption method, as the browser frequently timed out attempting to pre-compute for the more-optimised version.} to process proofs}
\begin{tabularx}{\hsize}{c *6{>{\Centering}X}}
\caption{Time\parnote{$|n| = 4096$ uses a less-optimised encryption method, as the browser frequently timed out attempting to pre-compute for the more-optimised version.} to process non-interactive proofs}
\begin{tabularx}{\hsize}{c *8{>{\Centering}X}}
\toprule
\multirow{2}{*}{Modulus size} &
\multicolumn{2}{c}{Proof-of-zero non-interactive} &
\multicolumn{2}{c}{Proof-of-zero} &
\multicolumn{2}{c}{\hyperref[protocol1]{Protocol~\ref*{protocol1}} with $t = 24$} &
\multicolumn{2}{c}{BCDG Range with $t = 24$}
\multicolumn{2}{c}{BCDG Range with $t = 24$} &
\multicolumn{2}{c}{\hyperref[protocol1]{Protocol~\ref*{protocol4}} with $t = 24$}
\tabularnewline
\cmidrule(l){2-3}\cmidrule(l){4-5}\cmidrule(l){6-7}
& Prover & Verifier & Prover & Verifier & Prover & Verifier \\
\cmidrule(l){2-3}\cmidrule(l){4-5}\cmidrule(l){6-7}\cmidrule(l){8-9}
& Prover & Verifier & Prover & Verifier & Prover & Verifier & Prover & Verifier \\
\midrule
$|n| = 1024$ & 10ms & 18ms & 1,420ms & 2,140ms & 443ms & 655ms \\
$|n| = 2048$ & 44ms & 68ms & 6,390ms & 8,140ms & 1,980ms & 2,400ms \\
$|n| = 4096$ & 225ms & 292ms & 41,500ms & 34,400ms & 14,300ms & 11,400ms \\
$|n| = 1024$ & 10ms & 18ms & 1,420ms & 2,140ms & 443ms & 655ms & 3,530ms & 5,310ms \\
$|n| = 2048$ & 44ms & 68ms & 6,390ms & 8,140ms & 1,980ms & 2,400ms & 15,800ms & 19,000ms \\
$|n| = 4096$ & 225ms & 292ms & 41,500ms & 34,400ms & 14,300ms & 11,400ms & & \\
\bottomrule
\end{tabularx}
\parnotes
@ -1074,18 +1077,18 @@ All measurements were taken on Brave 1.50.114 (Chromium 112.0.5615.49) 64-bit, u
\begin{table}
\fontsize{10pt}{10pt}\selectfont
\caption{Byte size\parnote{1 UTF-16 character, as used by ECMAScript \cite[Section~6.1.4]{ecma2024262}, is 2 or more bytes.} of encoded proofs}
\caption{Byte size\parnote{1 UTF-16 character, as used by ECMAScript \cite[Section~6.1.4]{ecma2024262}, is 2 or more bytes.} of encoded non-interactive proofs}
\label{table3}
\begin{tabularx}{\hsize}{c *6{>{\Centering}X}}
\begin{tabularx}{\hsize}{c *8{>{\Centering}X}}
\toprule
\multirow{2}{*}{Modulus size} & \multicolumn{2}{c}{Proof-of-zero non-interactive} & \multicolumn{2}{c}{\hyperref[protocol1]{Protocol~\ref*{protocol1}} with $t = 24$} & \multicolumn{2}{c}{BCDG Range with $t = 24$}
\multirow{2}{*}{Modulus size} & \multicolumn{2}{c}{Proof-of-zero non-interactive} & \multicolumn{2}{c}{\hyperref[protocol1]{Protocol~\ref*{protocol1}} with $t = 24$} & \multicolumn{2}{c}{BCDG Range with $t = 24$} & \multicolumn{2}{c}{\hyperref[protocol1]{Protocol~\ref*{protocol4}} with $t = 24$}
\tabularnewline
\cmidrule(l){2-3}\cmidrule(l){4-5}\cmidrule(l){6-7}
& JSON & with LZ-String & JSON & with LZ-String & JSON & with LZ-String \\
\cmidrule(l){2-3}\cmidrule(l){4-5}\cmidrule(l){6-7}\cmidrule(l){8-9}
& JSON & with LZ-String & JSON & with LZ-String & JSON & with LZ-String & JSON & with LZ-String \\
\midrule
$|n| = 1024$ & 1,617B & 576B & 338,902B & 95,738B & 123,354B & 34,857B \\
$|n| = 2048$ & 3,153B & 1,050B & 662,233B & 187,333B & 252,230B & 70,868B \\
$|n| = 4096$ & 6,226B & 1,999B & 1,315,027B & 368,646B & 484,117B & 135,990B \\
$|n| = 1024$ & 1,617B & 576B & 338,902B & 95,738B & 123,354B & 34,857B & 895,474B & 248,420B \\
$|n| = 2048$ & 3,153B & 1,050B & 662,233B & 187,333B & 252,230B & 70,868B & 1,746,017B & 485,787B \\
$|n| = 4096$ & 6,226B & 1,999B & 1,315,027B & 368,646B & 484,117B & 135,990B & & \\
\bottomrule
\end{tabularx}
\parnotes