Cristian’s Algorithm is a clock synchronization algorithm is used to synchronize time with a time server by client processes. This algorithm works well with low-latency networks where Round Trip Time is short as compared to accuracy while redundancy-prone distributed systems/applications do not go hand in hand with this algorithm. Here Round Trip Time refers to the time duration between the start of a Request and the end of the corresponding Response.
Below is an illustration imitating the working of Cristian’s algorithm:
Algorithm:
1) The process on the client machine sends the request for fetching clock time(time at the server) to the Clock Server at time 
.
2) The Clock Server listens to the request made by the client process and returns the response in form of clock server time.
3) The client process fetches the response from the Clock Server at time 
and calculates the synchronized client clock time using the formula given below.
![\[ T_{CLIENT} = T_{SERVER} + (T_1 - T_0)/2 \]](https://geeksforgeeks.org/wp-content/uploads/2023/10/quicklatex.com-787d0e5f924d43a3aea97d3c61c8163b_l3.png "Rendered by QuickLaTeX.com")
where 
refers to the synchronized clock time, 
refers to the clock time returned by the server, refers to the time at which request was sent by the client process, refers to the time at which response was received by the client process
Working/Reliability of the above formula:
refers to the combined time taken by the network and the server to transfer the request to the server, process the request, and return the response back to the client process, assuming that the network latency and are approximately equal.
The time at the client-side differs from actual time by at most 
seconds. Using the above statement we can draw a conclusion that the error in synchronization can be at most seconds.
Hence,
![\[ error\, \epsilon\, [-(T_1 - T_0)/2, \, (T_1 - T_0)/2] \]](https://geeksforgeeks.org/wp-content/uploads/2023/10/quicklatex.com-7c4b56d1834f2915c99c00e9801f3ed9_l3.png "Rendered by QuickLaTeX.com")
Python Codes below illustrate the working of Cristian’s algorithm:
Code below is used to initiate a prototype of a clock server on local machine:
C++
// C++ equivalent#include <iostream>#include <string>#include <chrono>#include <ctime>#include <sys/socket.h>// Function used to initiate the Clock Servervoid initiateClockServer() { // Create socket int socketfd = socket(AF_INET, SOCK_STREAM, 0); std::cout << "Socket successfully created" << std::endl; // Set port int port = 8000; // Bind socket to port struct sockaddr_in server_addr; server_addr.sin_family = AF_INET; server_addr.sin_addr.s_addr = INADDR_ANY; server_addr.sin_port = htons(port); bind(socketfd, (struct sockaddr*)&server_addr, sizeof(server_addr)); std::cout << "Socket is listening..." << std::endl; // Start listening to requests listen(socketfd, 5); // Clock Server Running forever while (true) { // Establish connection with client struct sockaddr_in client_addr; int client_len = sizeof(client_addr); int connfd = accept(socketfd, (struct sockaddr*) &client_addr, (socklen_t*)&client_len); std::cout << "Server connected to " << client_addr.sin_addr.s_addr << std::endl; // Respond the client with server clock time std::chrono::time_point<std::chrono::system_clock> now = std::chrono::system_clock::now(); std::time_t time = std::chrono::system_clock::to_time_t(now); std::string time_str = std::ctime(&time); send(connfd, time_str.c_str(), time_str.size(), 0); // Close the connection with the client process close(connfd); }}// Driver functionint main() { // Trigger the Clock Server initiateClockServer(); return 0;} |
Java
import java.net.*;import java.io.*;import java.util.Date;public class ClockServer { // Function used to initiate the Clock Server public static void initiateClockServer() throws IOException { // Create socket ServerSocket serverSocket = new ServerSocket(8000); System.out.println("Socket successfully created"); // Clock Server Running forever while (true) { // Start listening to requests System.out.println("Socket is listening..."); Socket clientSocket = serverSocket.accept(); System.out.println("Server connected to " + clientSocket.getInetAddress()); // Respond the client with server clock time Date now = new Date(); String timeStr = now.toString(); OutputStream os = clientSocket.getOutputStream(); OutputStreamWriter osw = new OutputStreamWriter(os); BufferedWriter bw = new BufferedWriter(osw); bw.write(timeStr + "\n"); bw.flush(); // Close the connection with the client process clientSocket.close(); } } // Driver function public static void main(String[] args) throws IOException { // Trigger the Clock Server initiateClockServer(); }} |
Python3
# Python3 program imitating a clock serverimport socketimport datetime # function used to initiate the Clock Serverdef initiateClockServer(): s = socket.socket() print("Socket successfully created") # Server port port = 8000 s.bind(('', port)) # Start listening to requests s.listen(5) print("Socket is listening...") # Clock Server Running forever while True: # Establish connection with client connection, address = s.accept() print('Server connected to', address) # Respond the client with server clock time connection.send(str( datetime.datetime.now()).encode()) # Close the connection with the client process connection.close()# Driver functionif __name__ == '__main__': # Trigger the Clock Server initiateClockServer() |
C#
using System;using System.Net;using System.Net.Sockets;using System.Text;using System.Threading;class Program{ static void Main(string[] args) { // Trigger the Clock Server initiateClockServer(); } static void initiateClockServer() { // Create socket Socket socketfd = new Socket(AddressFamily.InterNetwork, SocketType.Stream, ProtocolType.Tcp); Console.WriteLine("Socket successfully created"); // Set port int port = 8000; // Bind socket to port IPEndPoint serverAddr = new IPEndPoint(IPAddress.Any, port); socketfd.Bind(serverAddr); Console.WriteLine("Socket is listening..."); // Start listening to requests socketfd.Listen(5); // Clock Server Running forever while (true) { // Establish connection with client Socket clientSock = socketfd.Accept(); Console.WriteLine("Server connected to " + clientSock.RemoteEndPoint.ToString()); // Respond the client with server clock time DateTime now = DateTime.Now; string time_str = now.ToString(); byte[] time_bytes = Encoding.ASCII.GetBytes(time_str); clientSock.Send(time_bytes); // Close the connection with the client process clientSock.Shutdown(SocketShutdown.Both); clientSock.Close(); } }} |
Javascript
const net = require('net');const port = 8000;// function used to initiate the Clock Serverfunction initiateClockServer() { const server = net.createServer(function(connection) { console.log('Server connected to', connection.remoteAddress); // Respond the client with server clock time connection.write(new Date().toString()); // Close the connection with the client process connection.end(); }); server.listen(port, function() { console.log("Socket is listening..."); });}// Driver functionif (require.main === module) { // Trigger the Clock Server initiateClockServer();}// This code is contributed by rishab |
Output:
Socket successfully created Socket is listening...
Code below is used to initiate a prototype of a client process on the local machine:
Python3
# Python3 program imitating a client processimport socketimport datetimefrom dateutil import parserfrom timeit import default_timer as timer# function used to Synchronize client process timedef synchronizeTime(): s = socket.socket() # Server port port = 8000 # connect to the clock server on local computer s.connect(('127.0.0.1', port)) request_time = timer() # receive data from the server server_time = parser.parse(s.recv(1024).decode()) response_time = timer() actual_time = datetime.datetime.now() print("Time returned by server: " + str(server_time)) process_delay_latency = response_time - request_time print("Process Delay latency: " \ + str(process_delay_latency) \ + " seconds") print("Actual clock time at client side: " \ + str(actual_time)) # synchronize process client clock time client_time = server_time \ + datetime.timedelta(seconds = \ (process_delay_latency) / 2) print("Synchronized process client time: " \ + str(client_time)) # calculate synchronization error error = actual_time - client_time print("Synchronization error : " + str(error.total_seconds()) + " seconds") s.close() # Driver functionif __name__ == '__main__': # synchronize time using clock server synchronizeTime() |
Output:
Time returned by server: 2018-11-07 17:56:43.302379 Process Delay latency: 0.0005150819997652434 seconds Actual clock time at client side: 2018-11-07 17:56:43.302756 Synchronized process client time: 2018-11-07 17:56:43.302637 Synchronization error : 0.000119 seconds
Improvision in Clock Synchronization:
Using iterative testing over the network, we can define a minimum transfer time using which we can formulate an improved synchronization clock time(less synchronization error).
Here, by defining a minimum transfer time, with a high confidence, we can say that the server time will
always be generated after 
and the will always be generated before 
, where 
is the minimum transfer time which is the minimum value of 
and 
during several iterative tests. Here synchronization error can be formulated as follows:
![\[ error\, \epsilon\, [-((T_1 - T_0)/2 - T_{min}), \, ((T_1 - T_0)/2 - T_{min})] \]](https://geeksforgeeks.org/wp-content/uploads/2023/10/quicklatex.com-331f0bfa7ea58953a609e24699de0274_l3.png "Rendered by QuickLaTeX.com")
Similarly, if and differ by a considerable amount of time, we may substitute by 
and 
, where is the minimum observed request time and refers to the minimum observed response time over the network.
The synchronized clock time in this case can be calculated as:
![\[ T_{CLIENT} = T_{SERVER} + (T_1 - T_0)/2 + (T_{min2} - T_{min1})/2 \]](https://geeksforgeeks.org/wp-content/uploads/2023/10/quicklatex.com-37298035b6c3c1262827c5b0eb437b4f_l3.png "Rendered by QuickLaTeX.com")
So, by just introducing response and request time as separate time latencies, we can improve the synchronization of clock time and hence decrease the overall synchronization error. A number of iterative tests to be run depends on the overall clock drift observed.
Advantages:
Simple and easy to implement: Cristian’s Algorithm is a relatively simple algorithm and can be implemented easily on most computer systems.
Fast synchronization: The algorithm can synchronize the system clock with the time server quickly and efficiently.
Low network traffic: The algorithm requires only one round trip between the client and the server, which reduces network traffic and improves performance.
Works well for small networks: Cristian’s Algorithm works well for small networks where the network latency is relatively low.
Disadvantages:
Requires a trusted time server: Cristian’s Algorithm requires a trusted time server that provides accurate time information. If the time server is compromised or provides incorrect time information, it can lead to incorrect time synchronization.
Limited scalability: The algorithm is not suitable for large networks where the network latency can be high, as it may not be able to provide accurate time synchronization.
Not resilient to network failures: The algorithm does not handle network failures well, which can result in inaccurate time synchronization.
Vulnerable to malicious attacks: The algorithm is vulnerable to malicious attacks, such as man-in-the-middle attacks, which can lead to incorrect time synchronization.
References:
1) https://en.wikipedia.org/wiki/Cristian%27s_algorithm
2) https://en.wikipedia.org/wiki/Round-trip_delay_time
3) https://www.geeksforgeeks.org/socket-programming-python
4) https://en.wikipedia.org/wiki/Clock_drift
