Implement Pi_t experiment and document on README.md

This change implements the Pi_t experiment and updates the README.md file with detailed documentation of the experiment, including its objectives, steps, and expected results. The README.md file describes the projects goal to explore the performance of Pi_t, a differentially anonymous mixnet architecture, under various conditions. It outlines the experiment design, including setting up nodes on AWS, implementing a replicated bulletin board, and calculating the minimum number of rounds required for specific values of epsilon and delta.

README.md

@@ -1,26 +1,65 @@
-Pi\_t Experiment
+Implementing Pi\_t
 ================
 
-Overview
---------
+## Introduction
 
-This repository serves as a distributed system project that simulates onion routing with nodes registering to a bulletin board, sending and processing messages securely. Each node maintains a queue of incoming messages, reports its queue length to the bulletin board, and processes messages upon receiving a start signal from the bulletin board.
+This project focuses on implementing Pi_t, a differentially anonymous mixnet architecture, to explore its performance under 
+various conditions. We will conduct experiments to determine the minimum number of rounds required for a given server load 
+and desired parameters ϵ and δ. The experiment will be deployed on AWS with potentially hundreds of nodes, each acting as 
+a relay, and will use a bulletin board to manage node communication.
 
-Features
---------
+## Background
+
+An anonymous communication channel allows parties to communicate over the Internet while concealing their identities. 
+Onion routing is a widely used technique where messages are encapsulated in layers of encryption and sent through a series 
+of intermediary nodes (relays). This project implements Pi_t, an advanced mixnet architecture that enhances the standard 
+onion routing by ensuring differential privacy.
+
+Differential privacy in this context means that the observations of an adversary cannot significantly distinguish between 
+any two communication patterns, thereby protecting the anonymity of the communicating parties.
+
+## Objectives
+
+1. **Deploy Pi_t on AWS**: Set up a network of nodes acting as relays.
+2. Implement a replicated bulletin board to list all participating nodes and their public keys.
+3. **Determine optimal parameters**: Run experiments to find the minimum number of rounds required for specific values of \( \epsilon \) and \( \delta \), while considering server load and churn rates.
+
+## Experiment Design
+The experiment will involve the following steps:
+
+1. **Setup Nodes on AWS**:
+  - Deploy hundreds of nodes on AWS, each configured to act as a relay.
+  - Ensure nodes can communicate with the bulletin board to register their status.
+
+2. **Bulletin Board**:
+  - Implement a fault-tolerant, replicated bulletin board that maintains a list of active nodes and their public keys.
+  - The bulletin board will also broadcast start times and coordinate the rounds of message passing.
+
+3. **Message Passing and Rounds**:
+  - Nodes will send messages in rounds, encapsulating each message in multiple layers of encryption (onions).
+  - Each node will peel off one layer of encryption and forward the message to the next node.
+  - The process will repeat for a specified number of rounds.
+
+4. **Parameter Selection**:
+  - Choose appropriate values for \( \epsilon \) and \( \delta \) to ensure differential privacy.
+  - Calculate the minimum number of rounds required for these values given the server load and churn rates.
+
+## Choosing Parameters
+To determine the optimal parameters for the experiment, we consider the following:
+
+- **Onion Size and Layers**: The size of each onion depends on the number of layers, which corresponds to the number of rounds.
+- **Server Load**: Given a server load \( x \) and desired \( \epsilon \) and \( \delta \) values, determine the minimum number of rounds required.
+- **Churn Rate**: The rate at which nodes go offline (churn rate) affects the maximum number of rounds for maintaining the desired message delivery rate.
 
-*   **Node Registration**: Nodes register with the bulletin board and receive an acknowledgment.
-*   **Queue Management**: Nodes handle client requests, queue messages, and periodically report queue lengths.
-*   **Message Processing**: Nodes build and process onions (messages) and start processing upon receiving a signal from the bulletin board.
-*   **Bulletin Board**: Manages active nodes and coordinates message processing.
 
 Installation
 ------------
 
 1.  Clone the repository:
 
 ```bash
-git clone https://github.com/HannahMarsh/pi_t-experiment.git cd pi_t-experiment
+git clone https://github.com/HannahMarsh/pi_t-experiment.git;
+cd pi_t-experiment
 ```
 
 2.  Install dependencies: