Benchmarking script

templates/index.html

@@ -181,5 +181,44 @@
         <button id="ready-button">Not ready</button>
         <button id="end-turn" class="hidden">End Turn</button>
     </div>
+
+    <!-- Benchmarking script -->
+    <script>
+        function RSABench() {
+            console.log("Warming up")
+
+            for (let i = 0n; i < 100n; i++) {
+                window.rsa.pubKey.encrypt(i);
+            }
+
+            console.log("Benching")
+
+            performance.mark("rsa-start")
+            for (let i = 0n; i < 250n; i++) {
+                window.rsa.pubKey.encrypt(i);
+            }
+            performance.mark("rsa-end")
+
+            console.log(`Bench done. Duration: ${performance.measure("rsa-duration", "rsa-start", "rsa-end").duration}`)
+        }
+
+        function PaillierBench() {
+            console.log("Warming up")
+
+            for (let i = 0n; i < 100n; i++) {
+                window.paillier.pubKey.encrypt(i);
+            }
+
+            console.log("Benching")
+
+            performance.mark("paillier-start")
+            for (let i = 0n; i < 250n; i++) {
+                window.paillier.pubKey.encrypt(i);
+            }
+            performance.mark("paillier-end")
+
+            console.log(`Bench done. Duration: ${performance.measure("paillier-duration", "paillier-start", "paillier-end").duration}`)
+        }
+    </script>
 </body>
 </html>

whitepaper/Dissertation.tex

@@ -1,3 +1,5 @@
+% !TeX document-id = {551c9545-e493-4534-9812-732e4f9d41b0}
+% !TeX TXS-program:compile = txs:///pdflatex/[--shell-escape]
 \documentclass[12pt,a4paper]{report}
 
 \usepackage{Bath-CS-Dissertation}
@@ -5,6 +7,7 @@
 \usepackage{amssymb}
 \usepackage{amsthm}
 \usepackage{tikz}
+\usepackage{minted}
 
 \DeclareMathOperator{\lcm}{lcm}
 \DeclareMathOperator{\id}{id}
@@ -546,7 +549,33 @@ The size of the proof of zero communication is, in total, $3290 + 1744 + 2243$ c
 
 \subsubsection{Time complexity}
 
-It is generally remarked that Paillier performs considerably slower than RSA on all key sizes. %todo cite
+It is remarked that Paillier encryption performs considerably slower than RSA on all key sizes. \cite{paillier1999public} provides a table of theoretic results, suggesting that Paillier encryption can be over 1,000 times slower than RSA for the same key size.
+
+\cite{paillier1999public} also remarks that the choice of the public parameter $g$ can improve the time complexity. The selection of $g = n + 1$ is optimal in this regard, as binomial theorem allows the modular exponentiation $g^m \mod n^2$ to be reduced to the computation $1 + gm \mod n^2$.
+
+These results are backed experimentally by my implementation. The following benchmarking code was executed.
+
+\begin{minted}{javascript}
+    console.log("Warming up")
+
+    for (let i = 0n; i < 100n; i++) {
+        keyPair.pubKey.encrypt(i);
+    }
+
+    console.log("Benching")
+
+    performance.mark("start")
+    for (let i = 0n; i < 250n; i++) {
+        keyPair.pubKey.encrypt(i);
+    }
+    performance.mark("end")
+
+    console.log(performance.measure("duration", "start", "end").duration)
+\end{minted}
+
+Performing 250 Paillier encrypts required 49,100ms. On the other hand, performing 250 RSA encrypts required 60ms. This is a difference of over 1,000 times.
+
+Decryption is remarked as being optimisable to constant time through application of Chinese Remainder Theorem.
 
 
 \subsection{Quantum resistance}